Rabeh Morrar

Faïz Gallouj

The Growth of the Service Sector in Palestine: The productivity challenge

Keywords: Services, productivity, economic performance, Palestine

This paper is one of the first to discuss service sector productivity in Palestine. We have empirically addressed the main factors that are responsible for growth in productivity in the Palestinian service sector, and discussed the impact of intra-sectoral heterogeneity on the growth of productivity using a panel data provided by the Palestinian Central Bureau of Statistics. The results show that FDI has a positive and significant influence on the growth of labor productivity. Capitalintensive service sectors have a high influence on the growth of labor productivity compared to other sectors, while public services and traditional services such as retail trade, the sale and repair of motor vehicles and land transport are the main areas responsible for weak growth in service productivity. The political instability also negatively affects the growth of productivity in the service sector. In order to increase productivity in traditional services, new policies should be adopted, based on the use of ICTs. Government should adopt an efficient plan aimed at absorbing the thousands of unskilled workers who lost their jobs inside Israel, and this should be based not on expansion of the public sector but on the rehabilitation of these workers, employing them in the various economic sectors.

Introduction

The Palestinian economy faces many challenges. Firstly, it is highly dependent on the Israeli economy -more than 73% of Palestinian imports of goods and services originated in Israel in 2010 (PCBS, 2012). Secondly, the restrictions imposed upon it by Israel impede the development of a viable Palestinian economy. These restrictions take several forms: control over raw materials, control over the borders of Palestinian areas and prevention of the construction of industrial zones. They result in political instability, and they distort the investment climate. Thirdly, the productive sector suffers from a lack of competences and financial resources in both public and private sectors. The Palestinian Authority mainly depends on foreign aid to support its budget. The final challenge results from the technological revolution and strong growth in ICTs seen over the past two decades; this has accelerated economic openness and trade liberalization, creating a high competitive pressure on the Palestinian fragile economy.

In the course of the past twenty years, Palestine has experienced a high increase in the significance of the service sector, in comparison with other productive sectors (manufacturing and agriculture). The service sector's share of GDP grew steadily from 50% in 1995 to 60% in 2009, while manufacturing sector's share fell from 21.3% in 1994 to 13.8% in 2009. Value added grew by 14.3% between 1995 and 2010, production by 13.3%, and labour by 7.3%. This confirms the fact that the Palestinian economy is a service economy, and that service sectors will be playing a leading role in the Palestinian economy in the coming years, strengthening its competitive power at both local and national levels.

Unlike other productive sectors, service activities in Palestine are characterized by their ability to emerge and develop in unstable and complex environments. In contrast to the manufacturing sector, which is heavily dependent on the import of raw materials from or through Israeli distribution channels, incurring high transaction costs and taking a very long time, development of the service sector is less dependent on availability of raw materials. The service sector in Palestine mainly depends on human resources -classified as skilled (education, knowledge-intensive services, etc.) and unskilled labour (retail and wholesale trade, hotels and restaurants, personal services, etc). Lastly, unlike the manufacturing sector which mainly depends on complex technologies and machines (costly and difficult to source), the service sector is able to exploit the progressing ICT sector.

Service sector productivity growth in Palestine was around 6.5% between 1995 and 2009, which is higher than the one experienced in other developing countries. For example, the growth of productivity in Middle East and North Africa (MENA) was only about 1.5% between 2000and 2008(UN national accounts, 2009)). This higher growth of productivity is explained by the fact that the service sector in Palestine was very impotent before 1995 because of the Israeli occupation of the Palestinian lands, which impeded the development of service sectors. It should be noted that before that date some sectors like ICTs, financial services, R&D didn't even exist. It is only after the signing of the Oslo agreements between Israel and Palestine in 1993, that Palestine experienced a high development of its service sector, which led to a higher growth of the service sector productivity than that of other similar economies in the region or other developing countries.

However, the increase of the growth rate of the service sector productivity hides a high heterogeneity between service subsectors themselves. The data published by the Palestinian Central Bureau of Statistics (PCBS) in the last two decades show that between 1995 and 2009, traditional and public services experienced low growth in productivity (e.g. 6.77% for retail trade, 6.28% for transportation and 5.77% for hotel and restaurants) in comparison with some other sectors mainly new born ones (e.g. R&D grew by 200.7%, ICT by 30% and real state by 124.6%). This might negatively impact the overall productivity growth in the service sectors because the traditional and public services account for more than 90% of service firms and organisations in Palestine and employ more than 85% of employees, while the high productivity growth sectors are still very small sectors that employ low number of employees. In this context, in comparison with the manufacturing sector, the service sector productivity growth is slow. Between 1995 and 2009, productivity in the manufacturing sector grew by 9.1% -as against 6.5% in the service sector. Given that the Palestinian economy is a service economy, this negatively influences the overall productivity.

To the best of our knowledge, this paper is the first to discuss service sector productivity in Palestine. Its main objective is to empirically determine the main factors that are responsible for the productivity growth, and the factors that explain the productivity growth gap between service and manufacturing sectors. A further objective of this paper is to discuss the intra-sectoral heterogeneity of the Palestinian service sector and its impact on the growth of productivity, and how the political instability in Palestine leads to such a heterogeneity. This article is organized as follows: first, it provides a general overview of the service sector in Palestine, and then discusses the productivity challenge in services and the relationship between service development and productivity growth. Finally, it investigates the determinants of productivity growth in the Palestinian service sector using data provided by PCBS.

1. The Service sector in Palestine: a general overview Since 1970s, the service sector in Palestine has faced many restrictions and distortions which have hampered its growth and development. Until the mid-1990s, certain service sectors (such as the R&D, financial and telecommunications sectors) either didn't exist in Palestine, or were very small. Other sectors (such as air and sea transport) still do not exist in Palestine. In the past 20 years, following the Oslo Accords of 1993, much effort has been put in by both the private and public sectors in a bid to reform and restructure the service sector. This has resulted in an increased contribution by the service sector, in terms of GDP and employment, as well as fast growth in some service sectors such as the public sector, postal services and telecommunications, and the real estate sector.

Service sector dynamics in Palestine: two distinct periods

The dynamics of the service sector in Palestine can be split into two distinct periods. The first of these is that of the Israeli occupation of the Palestinian territories. The second began in the mid-1990s after the Oslo Accords was signed between Israel and the Palestinian Authorities.

During the first period, Palestinian service sectors were focused on activities which facilitated Israeli domination of the Palestinian economy. This was true of retail and wholesale trade, which facilitated the flow of Israeli products into the Palestinian market, as well as of the land transport developed in order to freight Israeli products and transport the Palestinian labour force from Palestinian areas to Israel [START_REF] Jafari | Service sector in Palestine and its role in development process[END_REF][START_REF] Naser | Reinforcement of endogenous capacity of Palestinian economy[END_REF]. Other service sectors (such as the financial sector, tourism and telecommunications) grew very slowly due to occupation restrictions. Moreover, the strict restrictions imposed on international trade between Palestine and the rest of the world led to weakness in the support services for international trade, including international transport, marketing, insurance, refrigeration and storage [START_REF] Jafari | Service sector in Palestine and its role in development process[END_REF][START_REF] Naser | Reinforcement of endogenous capacity of Palestinian economy[END_REF]. Some of these distortions in the service sector continued even during the second period, following the Oslo Accords and the establishment of the Palestinian Authority. If we exclude public services, then retail trade and repair of motor vehicles and motorcycles are still the most prominent services in Palestine, comprising around 72% of the firms and employ more than 60% of the private sector labour force.

A large proportion of workers who were deprived of their jobs in Israel because of the political situation after the second Intifada1 in 2000 were employed either in public services (mainly security forces) or in the retail trade, where most jobs are unskilled. For example, based on PCBS data, the number of employees in retail trade grew by around 7% in 2001 and 5% in 2002, i.e. the number of employees increased from 62,000 in 2001 to 70,000 employees in 2002.

In some services (such as knowledge-intensive services), the employment rate decreased because of the second intifada. For example, in the first year of intifada (2001), employment in real estate activities decreased by around 21%, R&D by 31% and ICT by 6%.

The second period saw changes in the structure of the service sector, such as the rising of new service activities like financial services, research and development, ICT services and tourism. The period of peace which followed the end of the first intifada, and the signature of the Oslo Accords in 1993, prompted the flow of Foreign Direct Investment -mainly in the financial and telecommunications sectors. Furthermore, local investors invested in sectors such as hotels, restaurants, and business services.

Nevertheless, the share of these activities in the value added, the production, the employment, and the productivity of the whole service sector remains very weak. Furthermore, these activities face tough competitive pressure from Israel and other countries in the region. For example, in 2009, only 3.1% of the labour force worked in postal services and telecommunications, 0.66% in computer and related activities and 0.26% in the R&D sector. The ratio of value-added to overall value in the service sector is less than 1% in computer and relative activities, R&D and real estate activities. There are many reasons for this: (I) the lack of corresponding competences under occupation, ii) Israel's persistent control over the movements of goods and people across the frontiers of the Palestinian territories, even after the Oslo Accords, iii) uncertainty in the sustainability of the peace period, which discourages foreign investors, iv) manufacturing sector weakness. These structural weaknesses in the Palestinian service sector are not corrected by relevant public policy. This policy gap, which was evident during the occupation period, remains after the Oslo Accords. In contrast with other developing or emerging countries such as India, Malaysia or the Gulf countries, the Palestinian Authority does not establish any public policy to support the development of the service sectors in general or strategic capital and knowledge services where ICTs can play a prominent role in prompting growth in productivity. Most of the workshops, conferences and round tables held in the Palestine over the past two decades have focused on which policies should be adopted in order to develop the manufacturing sector -considered the only one likely to furnish growth and competitiveness.

The transportation sector is limited to land transport. Neither air nor water transport exists. Israel still does not allow Palestine to build an airport in the West Bank, and it destroyed the only airport in Gaza at the beginning of the second intifada. It still bans the construction of a seaport in Gaza -the only Palestinian channel to the Mediterranean Sea. Of course all these limitations have a strong negative influence on international trade, tourism, education, and hotels and restaurants.

The public sector in Palestine grew sharply after the institution of the Palestinian Authority, which employed thousands of employees in the ministries and public departments and in the security forces, in order to perform the functions transferred to it by the occupation authority. Therefore, between 1995 and 2000, the absorptive capacity of employment for the service sector (mainly in the public sector) grew by 5% annually, reaching 61% of the total labour force in 2000. This evolution mainly led to the rise of disguised unemployment, mainly in public services, and put huge pressure on the fiscal budget.

By the beginning of the second intifada in 2000, public sector employment increased at a fast pace becauseas we mentioned earliermany of the employees who lost their jobs in Israel because of the second intifada in 2000 were employed in public services. For example, the proportion of workers in the public sector in the West Bank increased from 19% in 2000Bank increased from 19% in to 23% in 2002Bank increased from 19% in , and from 31.5% in 2000Bank increased from 19% in to 41.4% in 2002, in , in the Gaza strip. It should also be noted that the employment rate of Palestinians in Israel decreased from 18.8% in 2000 to 9.3% in 2002.

There was no economic justification for increased public sector employment; this was just an unstudied strategy implemented by the Palestinian government in order to solve the severe unemployment caused by the second intifada. Obviously, the productivity of labour in the public sector heavily declined, given that the increase in labour was not offset by equivalent increases in value-added or production.

While the wages of employees in the public sector were increasing, average weekly hours worked -and therefore production -was declining. For example, the average weekly hours worked in the public sector fell from 41.86 in 1999, 39.1 in 2001 to 24.41 in 2010. In contrast, the hourly wage increased from 7. 69 NIS in 1999, 7.89 NIS in 2001to 11.93 NIS in 2010(Daoud and Shanti, 2012).

The economic performance of the service sector in Palestine

In this section we describe the economic performance of services for the period 1995-2010, using indicators such as international trade, number of employees, number of firms, value added, etc. We begin with a general comparison of the service and manufacturing sectors, before addressing the service sector by its various subsectors, and finally we consider foreign trade in services.

Service Sector vs. Industrial Sector

As illustrated by several indicators in Figure 3, with the exception of productivity, service sector performance was better than industrial sector performance over the past two decades. The service sector employment growth rate was 3 times higher than that of the industrial sector. This is mainly due to the occurrence of the second intifada in 2001, which led to the closing of many industrial firms because of Israeli restrictions on the import of raw materials and the long siege against Palestinian cities (especially Nablus, the main industrial city). Furthermore, as mentioned above, many of the employees who lost their jobs in Israel were absorbed by the service sector -mainly into public defense and the retail trade. According to PCBS data, for example, in 2001 the employment rate increased by 6.6% in the service sector -whereas in the industrial sector, it decreased by 15%.

The increase in number of firms, value added and intermediate consumption was also higher in services than in manufacturing. In 2010, 66.9% of employees in Palestine were employed in the service sector, and the service sector contributed to around 66% of value added (see Table 1). This confirms our previous statement that Palestinian economy is a service economy

Service Sector Structure in Palestine

Table 2 shows that there is a high level of heterogeneity between service sub-sectors in terms of major economic indicators such as employment rate, number of firms, output and value added, etc. This heterogeneity is however not specific to the Palestinian economy, since it holds true for all service economies. Other personal services such as the sale and repair of motor vehicles accounted for around 9% of employees and 9% of firms in the service sector. This result confirms that the distortions introduced by more than 30 years of occupation are still alive and kicking after the Oslo Accords.

Knowledge-intensive and capital-intensive services such as postal services and telecommunications, R&D, computer and related activities and business activities still accounted for just a small share of employees and firms in the service sector. For example, the computer and related services and R&D sectors respectively account for around 0.4% and 0.1% of employment in the service sector. This result illustrates the weak interest in knowledge and R&D services in Palestine, which will negatively affect the ability of the economy to innovate and develop.

Except for postal services and telecommunications, the value added and output of these sectors represent only a small share of the value added and the output of the whole service sector. For example, the value added for computer and R&D activities accounts for less than 1% of the total, indicating weak performance of these sectors in Palestine.

The relatively high proportion of value added and output of the postal services and telecommunications sector (around 20% for output and 24% for value added) in Palestine illustrates the prominent role that this sector is playing, and appeals for more investment in it, as well as its inclusion in the core interest of public policy.

The public sector contribution to value added and output is relatively low. For example, value added was around 6% in both education and the health sector, 2% in activities of membership organisation and 1% in recreational culture and sporting activity. Taking into account the high level of employment in these sectors, the productivity level will be negatively impacted.

International trade in the service sector

International trade in the service sector has steadily grown over the past two decades (see Figure 2). Based on Palestinian Central Bureau of Statistics (PCBS) data, Figure 2 shows that service exports increased from $44.1 million in 1997 to $266.1 million in 2010. Service imports also increased from $290.2 million in 2007 to $572.2 million in 2010.

The gap between service and industrial sector exports is decreasing. The ratio of service to industrial exports increased from 11.5% in 1997 to 46% in 2010. This is mainly related to the growth of the service sector over the past two decades and to the service sector's aforementioned ability to deal with the political situation in Palestine and bypass barriers impeding goods and peoples movements. The improvement of security and the political situation since the end of the second intifada in 2006 has led to growth in some service sectors -the tourism, hotel and restaurant sectors, for example -through the influx of tourists, mainly to religious sites in Jerusalem and Bethlehem. 2. The productivity issue in the service sector Productivity is the basic economic indicator built to measure production efficiency and economic growth. It is defined as the relationship between output and the inputs necessary to produce it. This definition is built on the hypothesis that the output is tangible and well defined (therefore relatively easy to measure). However insofar as they concern intangible and interactive products, services raise important issues about the definition and measurement of productivity [START_REF] Delaunay | Les enjeux de la sociite' de service[END_REF][START_REF] Hill | On goods and services[END_REF][START_REF] Gadrey | Services: La Productivité en question[END_REF][START_REF] Gadrey | The characterization of goods and services: An alternative approach[END_REF][START_REF] Djellal | Measuring and improving productivity in services: Issues, Strategies and Challenges[END_REF]. We consider some of these prior to discussing the relationship between development of the service sector and growth in productivity.

Measuring productivity in the service sector

The measurement of productivity in manufacturing raises several problems and issues which have been addressed at length in the literature [START_REF] Schreyer | Quality-adjustment of price indices in ICT industries: Simulation of effects on measured real output in 5 OECD countries[END_REF][START_REF] Gullickson | Possible measurement bias in aggregate productivity growth[END_REF][START_REF] Nordhaus | Alternative methods for measuring productivity[END_REF]. In services, the problems are more severe [START_REF] Djellal | Measuring and improving productivity in services: Issues, Strategies and Challenges[END_REF]Maroto and Rubalcalba 2008;Wölfl, 2004;[START_REF] Bosworth | Numbers matter: the US statistical system and a rapidly changing economy[END_REF][START_REF] Griliches | Output measurement in the service sector[END_REF] and given that world economies are now mainly service economies, the mismeasurement and underestimation of service productivity is likely to lead to an incorrect evaluation of overall economic performance. The productivity gap between the manufacturing and service sectors is also related to measurement issues.

The main difficulty in measuring service productivity lies not in the definition and measurement of inputs (labour and capital) but in the identification and definition of output. These difficulties are related to the fluid nature of the service process, the intangibility and invisibility of service production and the co-production or cocreation of many services.

For example, [START_REF] Maclean | Lagging productivity growth in the service sector: Mismeasurement, mismanagement or misinformation[END_REF] states that production in the service sector is underestimated mainly in financial services, real estate, business and personal services, because of their intangible nature and because their quality depends on the inputs provided by users of the services in question.

Recent measurement experiments consider complementarity between productivity and quality [START_REF] Johnston | Service productivity: Towards understanding the relationship between operational and customer productivity[END_REF]Van Ark, 2006). In other words, in order to measure productivity, they use such indicators as utility, quality, availability, etc. This has changed the value of productivity in many countries, to reflect the service sector's actual role in the economy [START_REF] Triplett | The early 21st century US productivity expansion is still in services[END_REF].

The relationship between service sector development and growth in productivity

The relationship between service sector development and growth in productivity is more apparent in developed countries. Growth in productivity comes mainly from productive services (ICT services, R&D, KIBS, telecommunications, transportation, etc.) and the intensive use of ICTs in most service sectors.

Several reasons push developed countries towards introducing drastic changes in their strategies with regard to development of the service sector and stimulation of service productivity. Firstly, most developed countries are now service economies in which the service sector accounts for the largest proportion of both GDP and employment. Secondly, the proportion of service products in international trade is steadily increasing in most of these countries. It is therefore important to adopt new policies, intertwined with globalization and open market operations. Thirdly, many service activities which had been protected by monopoly power have become open to competition and require new policies aimed at encouraging investment and increasing competition.

Productivity is affected by numerous factors: at human level (skills, experience, training, education, etc.), firm level (organisation structure, innovation, technology, etc.), and national level (economic growth, regulation, public policy, globalization, openness, etc.).

In the case of South Korea, [START_REF] Jones | Boosting Productivity in Korea's Service Sector[END_REF] explains the fact that labour productivity growth in the service sector has been weak (relative to manufacturing) by weak competition in services resulting from strict product market regulation, a low level of import penetration and inflows of Foreign Direct Investment (FDI). This demand eliminating domestic entry barriers, reducing barriers to trade and FDI inflows, reforming regulations and laws, and upgrading competition. Another challenge aimed at accelerating growth in service productivity in South Korea is the restructuring of small SMEs (which account for more than 90% of employment in the service sector) focusing on high-growth potential service sectors such as financial services and telecommunications.

Many works consider labour productivity in the service sector to be affected by globalization and trade liberalization (Sjoholom, 1997;Javantha Kumaran, 1999;[START_REF] Chen | Efficiency change and the growth in productivity: The Asian growth experience[END_REF]Mei Hsu & Been-Lon Chen, 2000;[START_REF] Phan | Trade liberalisation and manufacturing performance in Thailand 1990-2000[END_REF]. Sjoholom (1997) found that the openness strategy in Indonesia led to increased service trade as well as improved service productivity. The same result has been established for Thailand (Javantha Kumaran, 1999), Australia [START_REF] Phan | Trade liberalisation and manufacturing performance in Thailand 1990-2000[END_REF] and South Korea [START_REF] Kwak | Changing trade policy and its impact on TFP in the Republic of Korea[END_REF].

Foreign Direct Investment (FDI) is one of the most important outputs of globalization. It leads to the inflow of knowledge and technology (technology spillover), skills and experiences of developed economies. The positive relationship between FDI in the service sector and labour productivity has been experienced in many countries. In Taiwan, Mei Hsu & Been-Lon Chen (2000) found that FDI in the service sector (mainly in SMEs) led to increased service exports and labour productivity. Chin [START_REF] Chen | Efficiency change and the growth in productivity: The Asian growth experience[END_REF] studied the relationship between FDI and service productivity in 10 Asian countries, finding a positive relationship based on the ability of these countries to absorb foreign knowledge and technologies. [START_REF] Koirala | Productivity and technology in Nepal: -An analysis of foreign and domestic firms[END_REF] established that FDI in Nepal led to increased productivity in foreign firms, in comparison with local firms. This was mainly due to greater use of capital-intensive technology. Similar results were reported in the case of South Africa by Robert and Thoburn ( 2004), who found that FDI in the textile sector led to a major increase in labour productivity, due to the intensive use by foreign firms of capital technology.

Lack of experience, skills and knowledge in the service sector limits local economies' ability to take advantage of FDI. Local employees might not be able to deal with modern technology or absorb skills and experiences originating in foreign countries (Ismail et al. 2010).

The literature also addresses the relationship between immigration and the economic performance of home country, leading to ambivalent conclusions. Some studies underline the positive impact of immigration on the economic performance of sending countries. This is mainly due to increasing income from remittances, access to finance for starting new businesses, increasing ability to smooth consumption, and tapping into the knowledge and resources provided by the international community [START_REF] Azam | Migrants' remittances and the household in Africa: A review of evidence[END_REF]. According to [START_REF] Ratha | Outlook for Remittance Flows 2010-11[END_REF] migrants from developing countries sent over $315 billion to their origin countries in 2009.

Other studies underline the negative impact for immigration. For example, [START_REF] Bhagwati | The Brain Drain International Integration of Markets for Professionals and Unemployment: A Theoretical Analysis[END_REF] and [START_REF] Stark | Inducing Human Capital Formation: Migration as a Substitute for Subsidies[END_REF] disagree on whether immigration is good for sending countries. Immigration of high skilled labor or the so-called "brain drain" can cause a loss of public resources invested in their education, reduce the productive capacity, and worsen the business environment mainly in the sectors which need for high skilled labor like knowledge intensive business services, ICT, health and education.

It is difficult to understand the economic performance of Middle East economies (Palestine, Lebanon, Syria, Jordan, etc), only relying on economic factors as explanatory variables. Political variables in countries experiencing (civil, political or armed) conflicts play an important role. The literature provides many references that establish a negative relationship between political instability and economic performance [START_REF] Evia | Socio-political conflict and economic performance in Bolivia, CeSifo working paper[END_REF][START_REF] Polachek | Does conflict disrupt growth? Evidence of the relationship between political instability and national economic performance[END_REF][START_REF] Alesina | Political Instability and Economic Growth[END_REF].

Political instability can distract resources away from production, tends to reduce investment and is therefore likely to reduce economic growth and productivity.

Strategies to enhance service productivity in developing countries

Developing countries have adopted a set of strategies to prompt the growth of the service sector and to enhance the overall economic performance. In particular, during the last two decades, many developing countries have introduced regulation reforms in order to attract local and foreign investments and facilitate trade in services. Therefore service exports in developing countries have been steadily growing over the last two decades, even more than in most of developed countries.

In the Middle East, the service sector experienced significant changes in policies and regulations, with the aim to enhance the contribution of service sector in economic growth and productivity. For example, according to Dubai Chamber of Commerce Statistics, the United Arab Emirates' investments in the service sector increased from 40% in 1985 to 72% of total investments in 2003, which led to increasing the share of the service sector in GDP from 38% in 1985 to 71% in 2003.

In Jordan, which economy is similar to the Palestinian economy in terms of structure and scarcity of natural resources, the government adopted a set of policies to develop the service sector and to prompt its overall productivity. First, in 2000 the government offered tariff and tax reduction for investment projects in many service sectors like hotels and restaurants, hospitals, shipping, railways, tourism, distribution of water. Second, it launched the Jordan Services Modernization Program "JSMP" in cooperation with private sector and NGOs. This program supports SMEs in the service sector in order to increase their competitiveness in local and international market and enhance the share of service products in Jordanian exports.

In Egypt, despite the high contribution of the service sector in GDP (more than 55%), the potentials of this sector are not exploited efficiently, and therefore its productivity is still low (Ghoneim and Helmey, 2007). Many of the service subsectors are not exploited enough either for local or for international demand. The contribution of the service sector in GDP mainly involves tourism and transportation (Suez Canal). Ghoneim and Helmey denote that both public and private policies should be directed towards the adoption of an overall reforming plan where capital and knowledge intensive services should play a prominent role in order to enhance the productivity in the service sector,

Determinants of Productivity in the Palestinian Service Sector

The service sector has grown steadily in Palestine over recent decades. It now accounts for the largest share in terms of value added, number of firms, employment, and GDP. However productivity growth in services is weaker than in the industrial sector

The purpose of this section is to try to establish which factors result in productivity growth in the service sector. This will help determine factors or policies which could help bridge the productivity gap with the industrial sector.

There is high fluctuation in service sector productivity growth. This is mainly related to the complex political situation in Palestine, and the restrictions imposed by Israel. For example, productivity growth fell by nearly 29% between 2000 and 2002, then grew by almost 21% in 2003. The highest productivity growth rate was in 2008, one year after application of the economic reform plan adopted by Prime Minister Salam Fayyad, which entailed building vital infrastructures and institutions for a Palestinian state, attracting FDI mainly in telecommunication and financial sector, and cleaning up corruption.

Methodology and Empirical Approach

The difficulty of accessing data about certain economic indicators in Palestine has hampered the construction of a comprehensive model which includes all variables likely to impact productivity growth. For example, the literature considers laws and regulations, use of technology, and innovation to play a significant role in improving productivity growth in the service sector -yet there is no available data about such variables in Palestine.

Furthermore, the Palestinian Central Bureau of Statistics (PCBS) only provides sectoral-level data (as opposed to firm-level); we are therefore limited, here, to sectoral-level analysis.

In this section, we develop an econometric approach to analyzing the determinants of growth in labour productivity in the service sector, using panel data for the period between 1995 and 2009. A sample size of 234 is used; this was obtained by multiplying the number of service sectors ( 18) by the number of years between 1997 and 2009 (13). The data about both the dependent and independent variables are obtained from the PCBS which provides this kind of data starting from 1995.

We conclude that a fixed effects approach will be preferable in scenarios. Using the Lagrange multiplier test, we found the data structure to be consistent with panel data; pooled OLS regression is therefore not the appropriate method for estimating our relationship. Secondly, using the Hausman test, we found a correlation between the individual characteristics of service subsectors, and other independent variables.

In the fixed effect model, 17 dummy variables are defined for each of the service sectors, while sewage and refuse disposal sector is used as a reference sector for buildding the dummy variable.

Given the methodological issues outlined above, our empirical approach is based on the following equation:

Productivity it =β 0 +β 1 (ci/firm) it +β 2 (nb_firm) it + β 3 FDI it +β 4 (exp/output) it + β 5 K it +B 6 (migrant)+ β 7 D 1 +B 8 D 2 +Ui
Productivity represents the dependent variable which is measured using labour productivity (value added/# of employees). We use the growth in labour productivity between two years because it offers a dynamic measure for economic performance. Ci/firm is the growth ratio of intermediate consumption to number of firms in each sector, which measures the impact on labour productivity of firms' use of intermediate consumption. Nb_firm accounts for the growth rate in number of firms in each service sub-sector. Data shows that the service sub-sectors having a high growth rate in the number of firms are characterized by the highest labour productivity growth rate. FDI represents the share of Foreign Direct Investment in each service sector. FDI has increased sharply in the last two decades. It increased from $595.5 million in 1997 to $1378.3 million in 2010, which confirms the prominent role played by FDI in the Palestinian economy. Exp/output represents the growth of ratio of export to output. This variable measures the degree of service sector globalization and openness, which, in many countries, plays a significant role in pushing productivity growth. Sectors which seek to enhance exports should improve competitiveness and therefore production efficiency. K is growth in capital input employed by the service sector. Firm-level data usually shows a positive relationship between large firms and labour productivity. D1 is a dummy variable for capital intensity sectors (D1=1 if the service sector is capital intensive). If K/L is above average value then the service sector uses capital-intensive technology. Many studies found a significant relationship between intensity of labor and productivity growth. D2 is a dummy variable denoting the political instability, which equals one if the conflict between Palestine and Israel is active, and zero if not. In this view, the period between 1995 to 2009 is divided into three phases. The first from 1995 to 2000 after the signing of Oslo Agreement experienced a state of stability and relative prosperity and growth in investments in most of the economic sectors. The second is the period of 2 nd Intifada between 2000 and 2005. It negatively impacts most of the economic sectors because of the destruction by Israel of the infrastructure, the invasion of Palestinian areas, the closure of Palestinian areas by hundreds of checkpoints which highly impeded the trade between different areas inside Palestine and between Palestine and other countries.

The third period between 2006 and 2009 experienced a high decrease in violence between, although 2008 has experienced an Israeli war against Gaza. The variable "Migrant" represents the number of international migrants from Palestine. This variable measures the effect of immigration on the economic performance of the service sector. It is expected to have low impact on the productivity growth of the service sector. Based on PCBS data, the number of emigrants from Palestine is considered low in comparison with countries that experience political instability. This is attributed to the bad 1948 experience of Palestinian people regarding displacement and emigration. For example, based on PCB data, the number of emigrants in 2009 was only 7,122 persons, and 35% of them are students, meanwhile, the number of returnees to Palestine was 6,426.

Results and Discussion

Table 3 summarizes the main results of the regression equation estimation. Durbin Watson test of autocorrelation shows no existence of autocorrelation, and Wald test denotes no trace of heteroscedasticity. The level of determination of the independent variables gives R 2 around 0.96, which means that they explain around 96% of the change in the growth of productivity. The degree of tolerance for the independent variables gives values less than 10, which means no multicollinearity in the model.

We found that the ratio of intermediate consumption to number of firms has no significant impact on labour productivity. This means that sectors with strong growth in intermediate consumption do not necessarily have strong growth of production. For example, intermediate consumption in the retail trade grew by 12% between 1995 and 2009, whereas productivity grew by only around 7%. A similar result holds for hotels, restaurants, and computer activities. This result contradicts the findings of [START_REF] Rao | Productivity growth in service industries: A Canadian success story[END_REF] who concluded that intermediate input intensity is the most important contributor to labour productivity in the USA service sector. This contribution might be explained by the nature of the intermediate inputs. Indeed ICTs and knowledge account for a high proportion of intermediate consumption in developed countrieswhich is not the case in developing countries.

Strong growth in the number of service firms has a positive impact on labour productivity. This is illustrated by postal services, telecommunications, and R&D. For example, postal services and telecommunications have strong growth in both number of firms (around 370%) and productivity (around 30%) between 1995 and 2009. Public policy should thus be oriented toward prompting investment in knowledgeintensive services such as R&D, real estate services, and capital-intensive services such as postal services and telecommunications.

In our analysis, FDI (which is mostly in postal services and telecommunications and financial services) has limited influence on the growth of service productivity. This result is not consistent with [START_REF] Jones | Boosting Productivity in Korea's Service Sector[END_REF] or Mei Hsu & Been-Lon Chen (2000), who establish that higher FDI inflow leads to higher labour productivity in the service sector. The low impact of FDI on productivity growth (around 0.07) is explained by the fact that FDI is still weak in Palestine because of the political situation and Israel's control over more than 85% of Palestinian lands.

Export growth has no significant impact on growth of labour productivity, which is mainly related to fluctuation in trade in services, due to the political situation and the second intifada. Furthermore, the trade liberalization policies implemented in Palestine were mostly not beneficial to the Palestinian economy. They led to a rise in the trade deficit, especially given the restrictions on the movements of goods and services imposed by Israel. For example, Israel's control of the borders between Palestine and the rest of the world, as well as its checkpoints between cities, restrict the flow of tourists into Palestine. This is limited to holy cities such as Jerusalem and Bethlehem, and causes significant harm to the tourism, hotel and restaurant sectors.

Capital growth has a positive impact on labour productivity, which is consistent with the results provided by the literature. In line with the literature [START_REF] Rao | Productivity growth in service industries: A Canadian success story[END_REF][START_REF] Uppenberg | Innovation in productivity growth in the EU service sector[END_REF], we note that capital-intensive business services have more impact on labour productivity than labour-intensive services. This is also consistent with the fact that capital-intensive services are characterized by a strong productivity growth. For example, PCBS data indicates that postal services and telecommunications productivity grew by 30% between 1995 and 2010.

This result provides an explanation for the weak performance of the Palestinian service sector regarding productivity growth. Indeed most service sectors in Palestine are labour-intensive (trade, sales and repair of motor vehicles, and hotels and restaurants). Furthermore, they mainly employ unskilled workers.

More than 12,000 students graduate from Palestinian universities every year, yet in 2010 around 45% of them remained unemployed (PCBS, 2010). Skilled labour is thus not appropriately exploited in the service sector. Furthermore, even those graduates who are employed lack the relevant skills and trainings needed in their jobs. This results in the creation of a gap between the service sector growth and productivity growth within the service sector.

To increase the labour productivity in the service sector, the government should adopt a national programme for the rehabilitation of the thousands of workers who lost their jobs in Israel after 2001, upgrading their abilities and merging them into the Palestinian economy in a rational way. Universities and private organizations should implement innovative programs in order to enhance the abilities and know-how of graduates. This will enable service activities to employ them appropriately and enhance their productivity. Furthermore, to meet international standards, most service sectors -and especially distribution services -should invest much more heavily in knowledge and ICTs within their supply chain.

The impact of the political instability and the increase of violence between Israel and Palestine will weaken the growth of productivity in the service sector. During the period of second Intifada between 2000 and 2005, Israel layed siege to the Palestinian areas with hundreds of checkpoints between cities and villages, as well as daily invasions of the Palestinian areas, which seriously affected all the economic activities in Palestine. Negative influence on service sectors was apparent mainly in retail trade, wholesale trade, transportation, tourism and real state because of checkpoints and Israeli destructions of infrastructure (mainly roads),.

Result of regression analysis shows no significant impact of migration on the growth of productivity. This result is normal given that the period of study didn't experience a remarkable migration from Palestine, even the period of second Intifada when the socio-economic situation in Palestine was very miserable. Palestinian people had a bad experience with migration in 1948 (when the State of Israel was created); they left their houses for a short period to protect their life and then became refugees in all over the world until present.

With the exception of the education sector, public services have no significant impact on productivity growth in the service sector. This confirms weak productivity among workers in public services. With regard to the education sector, Palestine has the lowest illiteracy rate in the Arabic countries. According to the Palestinian Central Bureau of Statistics, illiteracy was 6% in 2009, and the rate of enrolment in basic education (grades one to ten) has steadily grown over the past two decades. The Ministry of Higher Education has taken into account relevant policies and documents developed nationally and internationally in order to improve the performance of the education sector, including Postal services and telecommunications have the highest impact on the growth of productivity. This sector combines high use of capital-intensive services, a large share of FDI, high employment of skilled labour (engineers, IT experts, accountants, and consultants), and high growth of value added. It is also considered the most innovative sector, thanks to the diversity of services it offers, its processes and marketing approaches.

The real estate sector has also a very positive impact on productivity growth. This is related to high growth in the construction sector following the Oslo Accords and the construction of the Palestinian institutions. Furthermore, the construction sector attracts most investors due to the high demand for housing in Palestine.

ehT R&D sector also has a strong effect on the growth of labour productivity. This is related to the outstanding efficiency of workers in this sector, who are mostly welleducated and highly skilled workers. Demand for R&D services is also rising in other sectors such as telecommunication, financial services, drugs manufacture, etc. In developed countries, R&D is one of the most productive sectors in the economy, leading to spillover effects on all other economic sectors and enhancing overall economic productivity. However, in Palestine, this sector suffers from a lack of interest from both public and private sectors. For example, R&D accounts for less than 0.1% of employment and less than 0.05% of number of firms in the service sector in 2009. Neither the Ministry for Higher Education, nor most Palestinian universities allocate a budget to R&D.

The hotels and restaurants sector is characterized by low impact on productivity growth, despite having seen strong growth following the Oslo Accords. This may be consistent with the restrictions imposed by Israel on the tourism sector. Many foreigners who come to visit the holy sites in Jerusalem and Bethlehem have to travel via Israeli airports, and these visitors are used to book hotels inside Israel. Moreover, Arabs from most Arabic countries are not allowed to enter Palestine. The Palestinian ministry of tourism should also adopt a plan to encourage tourism in the Palestinian area, encouraging the use of ICT (internet, facebook, etc.) in particular. The private sector should also invest more heavily in restaurants and hotels, using ICT to connect them.

Traditional service sectors in Palestine such as retail trade, or the sale and repair of motor vehicles and land transport, have no significant impact on productivity growth in the service sector. This confirms what we have mentioned previously about weak productivity growth within these sectors, the unskilled nature of the labour force, and the limited use of capital-intensive technology and ICTs. Land transportation is hampered by the many impediments introduced by hundreds of Israeli checkpoints throughout the Palestinian areas, and infrastructure weakness -especially the absence of major roads and railway lines between cities.

Conclusion

In this work, we have empirically addressed weak productivity growth in the Palestinian service sector. The results show that those sectors with strong growth in intermediate consumption do not necessarily have strong production growth, whereas sectors with strong growth in number of firms have a positive impact on the growth of labour productivity. Trade liberalization policies implemented in Palestine were inefficient in enhancing the growth of labour productivity in services. Trade in services still suffers from a deficit, mainly due to Israeli restrictions against the Palestinian economy. FDI has a positive and significant influence on the growth of labour productivityproviding a clue as to the role FDI are likely to play in developing countries, given their ability to provide spill-over effects in terms of new knowledge and technologies. FDI should therefore be directed towards capitalintensive services and business services, in order to prompt the growth in these sectors which will go on to enhance growth in labour productivity. Capital-intensive service sectors have a significant influence on the growth of labour productivity. Therefore, in order to increase their contribution to productivity, service sectors should invest far more heavily in new technologies -mainly ICTs. The international migration of Palestinian people has no significant impact on the productivity growth of the service sector, which is related to the low ratio of migration in the last two decades. It appears that the period of active conflict and violence negatively affects the growth of service productivity. This means that the stopping of the Israeli occupation of the Palestinian areas is one of the key factors likely to enhance the productivity of service sector in Palestine.

Public services and traditional services such as retail trade, the sale and repair of motor vehicles and land transport are the main areas responsible for weak growth in service productivity. These sectors employ more than 80% of service sector employees, yet they suffer from weak productivity growth which strongly influences overall growth of service productivity. Capital-intensive and knowledge-intensive services have a high impact on service productivity growth -but up until now, these constitute only small sectors in terms of number of firms and employment rates, and are not able to drive the productivity growth rate in the service sector.

To increase productivity in traditional services, new policies should be adopted, based on the use of ICT by service firms or public institutions. Government should adopt an efficient plan aimed at absorbing the thousands of unskilled workers who lose their jobs inside Israel, and this should be based not on expansion of the public sector but on the rehabilitation of these workers, employing them in the various economic sectors.

Figure 3 :

 3 Figure 3: Growth in value added, productivity, employment, number of firms, and intermediate consumption between 1995 and 2010 in the service and industrial sectors

Figure 2 :

 2 Figure 2: International trade in services between 1997 and 2010

  (a) The Palestinian Reform and Development Plan 2008-2012; (b) The Education for All Plan and its Terms of Reference; and (c) The Millennium Development Goals.

Table 1 :

 1 Distribution of value added, production, employment, number of firms, and intermediate consumption between Palestinian economic sectors in 2010.

		Ratio of	Ratio of	Production	Employment
		value added	intermediate	ratio	ratio
			consumption
	Service sector	66.2%	31.6%	54.3%	66.9%
	Industrial	25.2%	52.1%	34.3%	19.5%
	sector
	Construction	3.4%	7.6%	4.7%	1.67%
	sector

Table 2 :

 2 Percentage of firms, employees, compensation of employees, output, intermediate consumption and value added in service sector in 2009

	Sector	Value	Intermediate	Output	Compensation	# Of	# Of firms or
		added	consumption (%)	(%)	of employees	employee	institutions
		(%)			(%)	s (%)	(%)
	Sale and repair of	9.20	10.38	9.41	6.76	9.20	8.98
	motor vehicles
	Wholesale trade	9.50	5.61	8.72	4.53	3.65	2.36
	Retail trade, repair of	28.8	31.1	29.31	16.05	43.89	59.45
	personal goods
	Hotels and restaurant	4.20	11.16	5.64	4.92	6.39	0.562
	Land transport	1.60	4.08	2.13	2.90	1.57	0.52
	Supporting & auxiliary	1	0.85	0.96	0.66	0.55	0.44
	transport
	Postal services and	23.6	8.72	20.67	11.20	2.22	0.38
	telecommunication
	Real estate activities	0.27	0.39	0.29	0.27	0.17	0.21
	Renting of machinery	0.32	0.29	0.31	0.18	0.40	0.43
	without operator
	Computer and related	0.34	0.51	0.38	0.47	0.48	0.62
	activities
	R&D	0.36	0.19	0.32	0.93	0.19	0.05
	Other business activity	2.59	4.32	2.94	4.31	3.61	3.59
	Education	6.52	5.94	6.40	24.14	8.75	2.57
	Health and social work	6.01	7.88	6.39	10.58	6.62	4.66
	Sewage and refuse	0.01	0.02	0.01	0.02	0.01	00
	disposal
	Membership	2.43	3.56	2.66	8.83	5.54	2.00
	organisation activities
	Recreational culture	1.31	1.63	1.37	1.63	2.50	2.08
	and sporting activities
	Other service activity	1,78	3.37	2.10	1.63	4.25	6.02
	Source: Author calculation based on PCBS data

In 2009, distribution and social services represented the largest service sectors in Palestine, in terms of employment. Retail trade accounted for nearly 44% of employees and 59.5% of firms, and social services accounted for around 28% of employees and 17% of firms in the service sector.

Table 3 :

 3 Results of growth determinants in service productivity estimation

	Variable	Coefficient	T-test
	g_)Ci/firm(	-0.122	0.304
	g_nb_firm	0.481	0.003***
	g_FDI	0.073	0.003***
	g_(export/output)	1.676	0.88
	g_(K(	0.213	0.02**
	D1	0.598	0.001***
	D2	0.195	0.049
	Migrants	0.913	0.77
	Service sector
	Sale and repair of motor	0.167	0.51
	vehicles
	Wholesale trade	0.875	0.001***
	Retail trade, repair of personal	-0.10	0.74
	goods
	Hotels and restaurant	0.489	0.075*
	Land transport	0.640	0.15

Intifada or uprising is a description of the period in which the conflict between Israel and Palestine is active. The first Intifada was between 1987 and 1993.


Christophe Narth

Louis Lagardère

Etienne Polack

Nohad Gresh

Qiantao Wang

David R Bell

Joshua A Rackers

Jay W Ponder

Pengyu Y Ren
email: pren@mail.utexas.edu

Jean-Philip Piquemal

Étienne Polack

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short-range

Introduction

The field of molecular modeling is growing exponentially. The increase of available crystallographic structures [1][2][3] over the years has posed a substantial challenge for molecular force field development. For such systems, classical approaches still encounter successes but also reach their limits when describing non-bonded interactions which can only be reliably computed tum and classical approaches is too wide to be ignored, should one attempt to be predictive.

First-generation force fields ignore polarization effects and employ a simple electrostatic term while a van der Waals interaction term takes the role of a buffer contribution including all quantum-like effects. To compute interaction energies of high accuracy that could be compared directly to quantum chemistry and/or experiments, one should build force fields that embody all anisotropic effects and are able to separately reproduce all quantum contributions. Among all terms, electrostatics remains prominent. [START_REF] Lodish | Molecular cell biology[END_REF][START_REF] Pratt | Fundamentals of biochemistry: life at the molecular level[END_REF] Point charges can appropriately capture some long-range electrostatics but, quantum chemistry clearly shows the need to go beyond such an approximation to handle anisotropic interactions. Usually, distributed multipoles are used to account for polarization, but they are devoid of the short-range electrostatic quantum effects, the so-called charge penetration, which occurs when the molecular densities overlap. Various strategies have been employed to include such effects. They range from damping functions [START_REF] Slipchenko | [END_REF]7 to neural networks 8 and to newly developed point-distributed electron densities such as the gem 9,10 potential. Quantum mechanical force fields 11 also address this topic. Clearly, both short-and long-range electrostatics do matter and one would like to treat them in concert. This was done in the context of gem that uses continuous electrostatics which resort to electron densities. To do so, a generalized Smooth Particle Mesh Ewald approach was introduced which handles Hermite Gaussians thereby including penetration effects. As shown initially by Darden et al, 12,13 the pme and spme strategies provide a scaling improvement enabling to deal with electrostatics in periodic boundary conditions with a N log(N ) complexity as compared to the usual direct space N 2 . In this contribution we propose a simple strategy based on a damping function to include short-range penetration within a distributed multipole spme framework. Its aim is to be applicable to modern polarizable molecular dynamics using force fields such as amoeba 14 and sibfa. 7,[15][16][17][18][19] The paper is organized as follows. We first present our choice of charge penetration correction.

We then briefly recall the spme methodology for distributed multipoles before presenting a newly developed coupled approach. Finally, we present the parametrization procedure, the numerical results and a parallel implementation.

Charge Penetration

The question of the atomic charge description has previously been investigated. 7,9,[20][21][22][23][24][25] In classical force fields, the charge distribution is modeled using point charges calibrated on the Molecular Electrostatic Potential (mep) computed with qm (Quantum Mechanical) methods. 26 Although the anisotropy, is not directly taken into account even in the case of mep fitting, 27,28 this method is still widely used among various communities as it allows the simulation of very large systems due to its low computational cost.

The Distributed Multipole Analysis 29 (dma) has been shown to be a suitable description of the charge distribution to improve electrostatics. Other distributed multipole methods exist. For example, one of the first full-fledged polarizable force fields, sibfa, 7,15-18 (Sum of Interactions Between Fragments Ab-initio computed), originally used the multipole partitioning scheme developed by Vigné-Maeder and Claverie. 30,[START_REF] Claverie | Contribution à l'étude des interactions intermoléculaires[END_REF] Nevertheless, none of these multipole methods properly account for the overlap of molecular densities at short-range.

In physical systems, this overlap gives rise to a mainly attractive energy denoted electrostatic penetration. Hence, distributed multipolescan not be rigorously accurate at all ranges because of their classical approximation of electrostatics: theycan not describe the purely quantum mechanical charge penetration effect.

From quantum intermolecular perturbation theory, one can see that charge penetration exhibits an exponential decay being density overlap-dependent. [START_REF] Hohenstein | [END_REF] Charge penetration has been widely studied in qm. For example, Jeziorska et al studied Helium dimer intermolecular potential to find a classical description of its potential by means of Energy Decomposition Analysis (eda), here Symmetry Adapted Perturbation Theory 33 34 (sapt).

We extended this sapt study to Neon and Argon dimers. Figure 1 exhibits the electrostatic component for these three rare gas dimers as a function of their interatomic distances.

One can notice i) the existence of a non-zero electrostatic energy component at short-range and ii) the confirmation of the exponential decay. This observation and the fact that the rare gas charge is zero, and therefore does not have any classical electrostatic contribution, suggests that short-range effects should also be included. In that context, Piquemal et al Figure 1: Electrostatics contribution of rare gas dimers in kcal/mol have proposed a damping correction 7,18 grounded in Quantum Chemistry (qc) (see equation 1). Indeed, the electrostatic energy between two monomers (A and B) can be expressed as :

E elec = -2 i ν Z ν |ϕ i (1)| 2 r iν dr 1 3 -2 j µ Z µ |ϕ j (2)| 2 r jµ dr 2 3 + 4 i  |ϕ i (1)| 2 |ϕ j (2)| 2 r 12 dr 1 3 dr 2 3 + µ ν Z µ Z ν r µν (1)
where µ (ν) and ϕ i (ϕ j ) are, respectively, the nucleus and the unperturbed molecular orbitals of monomer A (B) and Z is the atomic number. The first two terms define nucleus-electron attraction, the third the electron-electron repulsion and the fourth the nucleus-nucleus repulsion. This strongly suggests that mimicking such a term is a key ingredient to correctly model all the components of electrostatics. The electronic integrals explain the appearance of electrostatic exponential decay. As charge penetration is missing, it seems reasonable to consider the outer-shell electrons (electronic valence) in the construction of an overlap-based short-range correction. Indeed, as shown in Figure 1 the atomic size is important, and is closely linked to the magnitude of the penetration effect. One would like to consider van der Waals-like radii as a component of the parametrization. In that context, 18 Piquemal et al proposed a short-range correction to the multipolar electrostatics that includes all these features and was originally implemented in sibfa. The latter modifies the charge-charge, charge-dipole and charge-quadrupole interactions.

The aim of this paper is to include and to reparametrize this correction in the framework of the Smooth Particle Mesh Ewald. The proposed correction modifies the charge-charge

(2) and charge-dipole (3). The latter involves an damped charge that is also appicable to correct the charge-quadrupole interactions. 18 These three terms are the dominant ones. 7

E * m i -m j = 1 r ij [Z i Z j -Z i (Z j -q j )(1 -exp(-α j r ij )) -Z j (Z i -q i )(1 -exp(-α i r ij )) + (Z i -q i )(Z j -q j )(1 -exp(-β i r ij )(1 -exp(-β j r ij )] (2)
where α i = γ/r i vdw and β i = δ/r i vdw , γ and δ are normalization coefficients and r i vdw the van der Waals radius of atom i. Z i is the electronic valence of the atom i, q i the charge (monopole) of atom i.

E * m i -d j = µ j .r ji r 3 ij (Z i -(Z i -q i )(1 -exp(-η i r ij )) (3)
where η i = χ/r i vdw , with χ a normalization coefficient.

ing to nucleus-nucleus repulsion. The formulation considers two more contributions, nucleuselectron attraction and electron-electron repulsion, where the damping function appears. It describes the depletion of the electronic cloud at short-distance. Following the same idea, the charge-dipole also accounts for this depletion by modulating the charge. 20 It is worth mentioning that at long-range, this term tends to the classical coulombic electrostatic expression. In Molecular Dynamics (md), conformational exploration of space can lead to very short-interatomic distances where multipoles clearly fail to recover the qm values due to the lack of charge penetration effect. Usually such errors are compensated by parametrization of the van der Waals terms. However, there is no guarantee of a systematic compensation during such md simulations, the lack of which could lead to errors. In order to apply this methodology to large systems and perform md, we propose to couple this approach to the Smooth Particle Mesh Ewald 12 (spme).

Smooth Particle Mesh Ewald

spme is based on the Ewald summation 35 which suggests to split the electrostatics into two terms, a short-range E dir and a long-range one E rec and whose complexity is N 2 or even N 3/2 . 36 spme decreases it to N log N by using Fast Fourier Transforms (fft). 35 spme can be applied to condensed phase. In that case, the lower complexity leads to particularly large time savings for large systems in Molecular Dynamics. spme is an efficient and adaptable algorithm, as its formulation for multipoles 37,38 and for the charge penetration correction suggests. In this section, we show how to modify the general spme formulas in order to include the charge penetration correction.

Let U be a neutral unit cell with N particles in position (r i ) i∈{1,••• ,N } and respective multipolar moments ( Li ) i∈{1,••• ,N } , (a 1 , a 2 , a 3 ) its basis and Σ the system made of an infinite number of images of the unit cell.

For any integers n 1 , n 2 , n 3 , m 1 , m 2 and m 3 we will note

n = n 1 a 1 + n 2 a 2 + n 3 a 3 m = m 1 a * 1 + m 2 a * 2 + m 3 a * 3 ,
where (a * 1 , a * 2 , a * 3 ) is the dual basis of (a 1 , a 2 , a 3 ) (i.e. a * i • a j = δ ij ).

The electrostatic energy of the system is

E elec (Σ) = 1 2 n 1≤i,j≤N Li Lj 1 |r j -r i + n| , (4)
where the prime means that the terms i = j are not summed up when n = 0. If we consider multipoles up to quadrupoles, then the operators Li can be written as

Li (m) = q i + µ i • ∇ i + Q i : ∇ i ∇ i , (5)
where ∇ i is the gradient at r i , µ and Q are the dipoles and the quadrupole moments.

For any m ∈ R 3 we define the structure factor

S(m) = j Lj (m) exp(2πm • r j ) ( 6
)
where Lj is the Fourier transform of the operator Lj , i.e.

Lj = q j + 2iπµ j • m -(2π) 2 Q j : mm, (7)
If Σ is supposed to be surrounded by a medium with infinite dielectric constant, then it has been shown that for any β > 0 the sum can be split as 38

E elec (Σ) = E dir + E self + E rec , (8)
where

E dir = n 1≤i,j≤N Li Lj erfc (β|r j -r i + n|) |r j -r i + n| , (9)
E self = - β √ π N j=1 q 2 j + 2β 2 3 µ 2 j -2q j Tr(Q j ) + 4β 4 5 2Q j : Q j + Tr 2 (Q j ) , (10)
and ( 11)

E rec = 1 2πV m =0 exp(-π 2 m 2 /β 2 ) m 2 S(m)S(-m). (12)
The self energy term 39 E self is a bias due to the Ewald summation and does not have any physical meaning. Both the direct and the reciprocal sums converge rapidly. A 9 Å cutoff is common, allowing a O(N ) computational complexity for the direct sum. The B-spline approximation of the structure factor on a grid of dimensions K 1 × K 2 × K 3 enables the reciprocal energy to be approximated by Ẽrec = 1 2

K 1 -1 k 1 =0 K 2 -1 k 2 =0 K 3 -1 k 3 =0 Q(k 1 , k 2 , k 3 ) • (θ rec * Q)(k 1 , k 2 , k 3 ), ( 13
)
where Q is a derivable function obtained after interpolation of the structure factors at the nodes of the grid; and θ rec a pair-potential function independent of particle position. The regularity of Q implies that the force in position i can be approximated by

Fi = -∇ i Ẽr = 1 2 K 1 -1 k 1 =0 K 2 -1 k 2 =0 K 3 -1 k 3 =0 ∇ i Q(k 1 , k 2 , k 3 ) • (θ rec * Q)(k 1 , k 2 , k 3 ). ( 14
)
In principle, the short-range correction is only in the direct space and therefore we will show that no modification of the reciprocal sum is required. We will detail our strategy of implementation aimed at an optimal scalability of the corrected electrostatics. As we discussed, the presented implementation in spme requiries a modification of the direct sum only. To do so, we need to reexpress the damping function by Piquemal et al. in more convenient form as a simple correction to the direct sum.

Coupling Smooth Particle Mesh Ewald and a penetration correction

Let us define E * elec the total modified/damped electrostatic energy of the system Σ.

E * elec (Σ) = 1 2 n 1≤i,j≤N E * m i -m j + E * m i -d j + E * m i -q j + E d i -d j + E d i -q j + E q i -q j ( 15
)
where E d i -d j is the interaction between dipoles of site i and site j ; E m i -q j , E d i -q j and E q i -q j are respectively the interaction between monopole/dipole/quadrupole of site i and quadrupole of site j. Let us define E pen the total charge penetration energy,

E pen = E * elec -E elec = n 1≤i,j≤N E * m i -m j -E m i -m j + E * m i -d j -E m i -d j (16)
Let us define the undamped electrostatic interaction between the monopoles of sites i

and j E m i -m j , let us also define the undamped electrostatic interaction between the dipole of site j and the monopole of site i E m i -d j .

E * m i -m j -E m i -m j = (q i -Z i )(q i -Z j )(exp(-β i r ij ) -1)(exp(-β j r ij ) -1) -(q j -Z i )Z j (exp(-α i r ij ) -1) -(q i -Z j )Z i (exp(-α j r ij ) -1) -q i q j + Z i Z j (17) E * m i -d j -E m i -d j = µ j .r ji r 3 ij (Z i -q i )exp(-ηr ij ) (18)
E * elec = E elec + E pen (19)
The same strategy has been followed to correct the charge-quadrupole interaction. 18 As seen in section 2.1, E pen can not be simply included into the spme framework, as we should take a large cutoff for the direct sum to avoid any persistence of penetration outside the direct sum treatment.

Indeed, the charge penetration energy is prominent at short-range and tends quickly to zero at long-range because of its exp(-x)/x n (with n = 1, 3) form (see figure 4) but not necessarily fast enough to be maintained within the Ewald direct sum cutoff. As such Ewald cutoff is essential for scalability, one would like to separately handle spme and penetration issues. This justifies the choice of an additional cutoff method dedicated to penetration.

Indeed, for a given precision, one can always find a cutoff for penetration that guarantees an error inferior to this threshold. As such an approach generates a discontinuity and nonderivability in the potential function near the cutoff limit. We will couple it with a switching function that ensures derivability of the energy during a md. Many smoothing functions have been proposed 40 and we chose to use the one defined in Ref. 41 and 42 (equation ( 20)).

Hence, for every distance r, the potential energy is equal to V (r) • S(r) where V (r) is the unswitched function. The interactions are not modified for distances less than an inner cutoff distance R in and are smoothed to zero at the outer cutoff R out . Besides, the continuity of the first derivatives prevents jumps in the energy during md or minimization, which could lead to non-physical phenomena such as heating.

Such a technique enables to keep the long-range effects and the computational advantage of spme using ffts with an optimal Ewald cutoff, while just adding a computationally cheap correction term with its own cutoff (see Figure 2). Besides, numerical simulations of common systems (up to tens of thousands of atoms) show that a cutoff between 6 and 8 Å guarantees an error inferior to 10 -3 kcal/mol (see Figure 2). Of course, the smoothing function makes possible to choose a more aggressive cutoff of 4 Å(see Figure 2) which will capture most of the penetration interaction in common systems leading to significant computational speedup. Overall the final cost in term of computational ressources of the penetration correction is inferior to 10 per cent of the total penetration corrected multipolar electrostatics.

S(r) =                1 r ≤ R in (R 2 out -r 2 ) 2 (R 2 out +2r 2 -3R 2 in ) (R 2 out -R 2 in )3 R in < r ≤ R out 0 r > R out (20)

Parametrization

The electrostatic correction includes four empirical parameters: two for charge-charge interactions (core-electron attraction and electron-electron repulsion), one for charge-dipole interactions, and one for charge-quadrupole. Those were initially adjusted on water dimers. [43][44][45][46] As various parametrization strategies are possible, the atomic radii can be used as a pa-rameter in order to reproduce the charge penetration effect. We apply this methodology to various choices of distributed multipoles. We focused on the gdma approach by Stone 29 and on the electrostatic potential (esp) ? ren2011polarizable fitted multipoles used in the amoeba force field. We first follow the initial parametrization strategy developed for sibfa and then we choose a simpler exponential functional form for the parametrization that does not take into account any atom radii. In this form, the parameters are the previously defined exponents 18 : α i , β i and η i .

We focused our parametrization on a well established panel of intermolecular systems extracted from the S66 dataset as well as on selected configurations of water dimers obtained from high level ab-initio computation 44,47,48 . Several qm intermolecular energy decomposition techniques are now available such as reduced variational space 49 (rvs) or sapt. 34 sapt offers the possibility to include all types of intermolecular interactions, as it allows to take into account electronic correlation. Because our upcoming implementation should reproduce all of them in a new anisotropic polarizable force field based on ab-initio calculation, we chose to calibrate the electrostatics on sapt. Note that the idea is to reproduce electrostatic trends at all ranges, with a special focus at short-ranges where charge penetration matters, which could make a perfect match with qm reference values difficult.

The first step of our calibration was to find the best set of parameters for ten different water dimers associated to stationary point on the ab-initio potential energy surface (denoted A on Figure 3). Four of these dimers were chosen (see Figure 4) to refine our results because they represent different chemical situations. Next, a new dimer (denoted B on Figure 3) as well as monomer-water systems (step 2 on Figure 3) can be calibrated. Thus, new parameters can be tested on dimers involving non-calibrated monomers (denoted C on Figure 3). This also allows to validate the previous calibration.

Each system was considered at its lower energy value configuration and at different intermolecular distances. These kind of variation are likely to happen in md and accounting for them will make our model more robust, as it would be able to sample density overlapping

Computational Details

The parallel implementation was first tested on the sgi uv 2000 supercomputer of the ics The following numerical results are all based on computations made on this supercomputer.

(
sapt calculations have been performed using psi4 50 at third order for water dimers and second for the others, using aug-cc-ptz basis sets. All GDMA multipoles were computed from density at the MP2(full)/aug-cc-ptz. would think that having more centers improve electrostatics. Overall, the esp fit strategy seems to improve the agreement with sapt results. The addition of more centers has been already described in the literature by Claverie and Stone 16,29 as a way to capture higher order effects, atoms plus bond midpoints being equivalent to the addition of octupoles within a distributed multipoles analysis. Such an observation might need, however, to be reconsidered.

Numerical Results

Indeed, the derivation of multipoles is usually said to be non-empirical, however, choices exist within the gdma algorithm including the choice of the partition approach, the choices of the hydrogen radius etc. Here we tried various settings and kept the following values for the gdma approach (space partitioning : switching 2, Hydrogen radius 0,325 Å). Choices also exist for the esp fitted multipoles as, within the procedure, the charge is initially derived from gdma and is kept frozen whereas dipole and quadrupole moments are reoptimized to minimize the differences with respect to the ab initio electrostatic potential. Overall, with all possible choices, a continuum of multipoles set can be derived with strong energetical differences. Which one should be chosen and are the esp fitted multipoles really better.

The application of the damping function to distributed multipoles casts a new light on such an issue. Clearly, the atoms plus bond midpoints gdma and esp fitted multipoles corrected results (see table 2 ) are improved by damping but surprisingly the best agreement is found for the damping of atoms only gdma multipoles. A clear-cut explanation can be found by a careful analysis of the multipolar values alone (table 1) compared to sapt.

Both gdma (atoms plus midpoints) and esp multipoles energies are too high. Indeed, even, with the best choice of settings, some gdma configurations energies are almost equal the full quantum sapt energies that embodies penetration and therefore that should be larger. In a sense, the apparently good behavior of the multipolar energies is artificial and is a consequence of a spurious fit that only minimizes the esp potential without providing an adequate physical picture of the distribution of moments on centers. It is of course, exacerbated by the use of damping functions that add another correction to gdma analysis.

In other words, if the multipolar energy of a given configuration is, by chance, spuriously correct, the damping correction will only destroy the fictitious agreement. For large basis sets, the advantage of having a larger number of centers tend to generate lower quality distributed multipoles because of the difficult handling of diffuse function. 29 Damping indeed requires physically meaningful multipoles with a consistent representation of the different angular momenta. For esp fitted multipoles, no charge redistribution is provided for the reoptimization of the dipole and quadrupole moments. It generates a better fit for some configurations but also partially reduces anisotropy. Indeed, moments are related to atomic orbital symmetries. If one component is overfitted, the others are clearly less accurately or spuriously described. Overall, whatever, the strategy to parametrize the damping function, one has to start to analyze the multipolar energy behavior compared to sapt: both sets of energies should be clearly different as multipoles do not embody penetration energy. Any attempt to damp overfitted energies will lead to a loss of accuracy when damping is added, especially if one studies various anisotropic interactions. If well-balanced multipoles are extracted, the damping is then increasingly effective as the order of correction tend towards charge-quadrupole (see appendix). If overfitted multipoles are chosen, one can still strongly reduce the error with SAPT but a charge-charge correction should be prefered as higherorder corrections will be perturbed by the spurious anisotropy of the charge distribution. It may lead to double countings of the penetration effect for configurations where multipoles are already overestimated. Overall, on the 10 dimer configurations, the best choice is based on gdma multipoles up to quadrupole fitted on atoms only and corrected by a damping function going up to the quadrupole level.

Besides the application to a sibfa-like protocol, we also applied this methodology to treat charge penetration within amoeba framework, which use only atom centered esp multipoles on various systems. As we discussed, esp multipoles do take not full advantages of higher order penetration correction as the charge-dipole damping appears already weaker than in the case of well behaved multipoles.

In all these cases, we have significantly improved the amoeba results without modifying the existing sets of multipoles (amoeba09).

For the previously discussed water dimers, the maximum energy variation between the first six configurations, corresponding to the lowest energies, the charge-charge correction reproduced well the behavior of sapt energy variations between configurations (energy difference between the most and the less stable configuration : 2.5 for sapt) whereas other corrections appear strongly less anisotropic (0.9 kcal/mol for Ref. 25). Even for this simplest level of correction, penetration effects are well recovered. Indeed, figure 4 represents the electrostatic energy between two water molecules as a function of their intermolecular distance in Angströms. The first two geometries (fig. 4a and4b) correspond to strong H-bonds while the third (fig. 4c) involves two H-bonds and the fourth (fig. 4d) weak interactions. We also report the root mean square error for intermolecular distance scans (from 1.4 to 2.7 A) of selected water dimers (S66 is an additional water geometry extracted from S66 set)

in Table 3 which confirms the improvement of the amoeba model in different configurations and the robustness of the correction at very short-range. The small improvement between the rmse's regarding water dimer 7 (Figure 4d) could be explained by its being a high lying energy dimer obtained only at the CCSDT level. 43 Indeed, for this kind of system, the charge penetration correction remains subtle because of the importance of electronic correlation and of the difficulty to model interaction involving the use of very diffuse basis function. We continue our investigation on other chemical functions: methanol (MeOH) and methyl amine (MeNH2) (see appendix Tables 5 and6 respectively). Finally, we investigate again benzene (see appendix table 7, 8 and 9). In all these cases, we improved the electrostatics using amoeba multipoles and particularly for benzene dimers. The approximation only breaks at very -unphysical-short-range. We report all our results in Figure 4, a plot of the results obtained with the correction against sapt reference values. This graph includes all the presented molecules and their distance scans from near equilibrium up to short-distances. The electrostatic interactions energies of some of these complexes are for distances far below equilibrium and for these penetration effects can be very significant. As one can see from tables (appendix), the penetration correction always improved the results compared to sapt, even for the cases where esp multipolar energies were really off (see benzene results), with the wrong interaction sign in all cases.

To conclude, we extended our tests to charge system, studying complexes of metal cations with water including K + , N a + , M g 2+ ,Ca 2+ and Zn 2+ . As expected from the sibfa previous work, penetration effects are a key element to model metals. The simple addition of the charge-charge correction allows a very close agreement with reference sapt datas.

Parallel Implementation

The loops involved in the computation of the correction term can be easily parallelized with a shared memory (openmp), distributed memory (mpi) or hybrid (openmp/mpi) paradigm.

The additional routines are included in a parallel version of the spme that we developed in the upcoming Tinker-hp software [51][52][53][54] : the atom sites and the corresponding energy and forces are distributed among processes using a spatial decomposition. ? Furthermore, as the cutoff used in the correction term (between 6 and 8 Å) is usually smaller than the real space cutoff (see Figure 2) used in the spme, no additional cross-processor communication of the atomic positions between each time step is necessary. The parallel scaling of the computation of the correction using MPI is showed on graph 7 for a water box of 60 000 atoms in a cubic unit cell where each edge is 84 Angströms long. Our tests showed that a pure MPI implementation is faster than a hybrid one before reaching a scaling plateau, but once this plateau is reached, the hybrid implementation allows to make use of more cores and to improve the best timing. The best timings obtained to compute both the electrostatic forces using spme, and the correction, using the pure MPI implementation are shown in table 4, as well as the best timings obtained with the hybrid implementation (with 2 OpenMP threads per MPI process). With a cutoff of 8 Å, which is beyond convergence, the total penetration cost is only 25 per cent in both cases. Of course, as we discussed, such a cutoff can be chosen more aggressi vely. A more aggressive cutoff of 4 angströms (see figure 2) captured 99 per cent of penetration interaction and led to strong decrease of the computation cost which became lower than 10 per cent.

Conclusions

We have studied the general coupling of an empirical short-range charge penetration correction to the spme. The corrected spme approach allows a computationally efficient and accurate improvement of electrostatics in polarizable simulations by correcting the shortrange charge-charge, charge-dipole and charge-quadrupole terms. The method has been implemented in the Tinker-hp software and the additional cost of the short-range damping function shown to be small as the global electrostatics implementation exhibits a favorable parallel scaling at the MPI and OPEN-MP/MPI hybrid levels. A separate cutoff for the pen-etration term coupled to a switching function has been implemented in order to maintain the possibility of a performance optimization of SPME thanks to the separate Ewald cutoff. Initial tests have been performed in the context of the amoeba and sibfa force fields (esp and gdma approaches respectively). Substantial improvements were noted in the agreement of standard non-corrected multipolar interaction energies (from Stone multipoles 29 ) compared to sapt ab-initio reference data. As we discussed the effects of spurious fit of distributed multipoles, the need of comparing atom-centered gdma to sapt is highlighted as one wants to avoid overfitted multipolar energies. When distributed moments are physically meaningful, the correction exhibits a systematic improvement when adding charge-charge, then charge-dipole and charge-quadrupole corrections. For some sets of multipoles, like the esp one, that exhibit some fictitious inclusion of penetration the correction should be limited to the charge-charge correction only. For these types of multipoles, specific parametrization procedure has been recently proposed in reference 55 based on esp derivation of the damping parameters.

Finally it is important to point out that, at the end, an error compensation between the damping function and the set of multipoles has to be found. Others damping function exist and will be studied in order to find the best agreement according to the different force field models (Rackers et al, in preparation). This opens two possible strategies as one can focus on the sole optimization of the chargecharge term to obtain a significant improvement of atom centered multipolar electrostatics at a very low computational cost. Strategies in that direction are currently studied in the context of amoeba-like potentials.

A second strategy includes higher order damping corrections (charge dipole and beyond), as presented in the sibfa potential. Such an implementation is therefore the starting point of sibfa portage into Tinker-hp. Prospective applications in biochemistry, pharmacology and nuclear science 22,[56][57][58] should benefit from the inclusion of charge penetration in PBC molecular dynamics with improved representation of short-range contributions exchange-repulsion and charge transfer and long-range polarization and dispersion. To conclude, it is important to point out that future inclusion of such correction in polarizable molecular dynamics will require either to reparametrize the van der Waals contribution for the case of amoeba-like potentials or to use the penetration-corrected electrostatics in conjunction with an explicit exchange-repulsion contribution like in sibfa.

A Appendix

A.1 Forces ∂(E * m i -m j -E m i -m j ) ∂r α i = (r j -r i ) α r α ij (Z i (Z j -q j )exp(-α j r ij )(α j + 1 r ij ) + Z j (Z i -q i )exp(-α i r ij )(α i + 1 r ij ) + (Z i -q i )(Z j -q j )(exp(-(

β i + β j )r ij )(β i + β j + 1 r ij ) -exp(-β i r ij )(β i + 1 r ij ) -exp(-β j r ij )(β j + 1 r ij )) (21)
∂(E * m i -d j -E m i -d j ) ∂r α i = (Z i -q i )exp(-ηr ij ) r 3 ij (µ α j + (r j -r i ) α µ j .r ji r ij (η + 3 r ij )) (22)
A.

Torques

Because the energy correction term contains permanent dipole moments that are usually defined in local frames binded to neighboring atoms, the derivatives of this term with respect to the positions of these atoms have to be taken into account. These are often improperly refered to as 'torques'. Suppose that the k-th atom is used to define the local frame in which the dipole moment µ j is written, then the corresponding derivative is the following :

d(E * m i -d j -E m i -d j ) dr α k = ∂(E * m i -d j -E m i -d j ) ∂r α k + < ∂(E * m i -d j -E m i -d j ) ∂µ j , ∂µ j ∂r α k > (23)
d(E * m i -d j -E m i -d j ) dr α k = ∂(E * m i -d j -E m i -d j ) ∂r α k + < (Z i -q i )exp(-ηr ij ) r ji r 3 ij , ∂µ j ∂r α k > ( 24
)
where the derivatives of µ j involve the derivatives of the derivatives of the rotation matrix used to go from the local to the global frame

Figure 2 :

 2 Figure 2: Convergence cutoff study of penetration energy. Energy in kcal/mol.

Figure 3 :

 3 Figure 3: Flowchart Automated Calibration Procedure (ACP)

Figure 4 :

 4 Figure 4: Water dimers electrostatic profile as function of intermolecular distance in kcal/mol. sapt is the red line. amoeba the green dashed line. cp-amoeba the blue dashed dot line.

Figure 5 :

 5 Figure 5: Correlation between sapt and the penetration correction in kcal/mol within binding range for various dimers (see legend)

Figure 6 :

 6 Figure6: Cation-water complexes : electrostatic variation as function of cation-O distance in kcal/mol. sapt is the red line, amoeba the green dashed line and the penetration correction blue dashed-dot line. a) K + water complex. b) N a + water complex. c) M g 2+ water complex. d) Ca 2+ water complex. e) Zn 2+ water complex.

Table 1 :

 1 Comparison of the pure multipolar electrostatic energy (in kcal/mol) water dimers. gdma i describes the multipolar sites scheme, i = 1 atoms only and i = 2 atoms and bonds.

	index gdma 2 gdma 1 esp sapt
	1	-6.91	-6.73 -6.04 -7.96
	2	-5.22	-5.15 -5.28 -6.72
	3	-4.88	-4.85 -5.22 -6.52
	4	-4.72	-4.82 -4.63 -6.61
	5	-3.55	-3.76 -4.26 -5.71
	6	-3.19	-3.44 -4.20 -5.41
	7	-3.52	-3.58 -3.15 -4.84
	8	-1.28	-1.26 -0.94 -1.49
	9	-3.87	-3.79 -3.15 -4.71
	10	-2.24	-2.21 -2.03 -2.71

Table 2 :

 2 Comparison Columns 2 to 4 of table 1 describe the values of the gdma, atoms and bond midpoints then atoms only and esp fitted multipoles energies. In the first approximation, compared to reference sapt and to atoms only gdma multipoles, one

	25 sapt

of the penetration corrected electrostatics (in kcal/mol) water dimers. gdma i describes the multipolar sites scheme, i = 1 atoms only and i = 2 atoms and bonds. index cp-gdma 2 cp-gdma 1 cp-esp Ref.

including pure multipolar interactions (Table

1

) and damped multipolar ones (Table

2

). Such configurations are clearly difficult as they embody various types of orientations involving very different anisotropic orbital interactions.

Table 3 :

 3 rmse for distance scans of water dimers (see text) in kcal/mol (reference sapt)

	water dimer cp-amoeba amoeba
	1	0.51	2.81
	3	0.25	1.66
	4	1.22	4.86
	7	1.39	1.88
	S66	0.69	2,21

Table 4 :

 4 Absolute best timings (in seconds) and number of cores used (in parentheses) for the computation of the electrostatic forces with SPME and of the correction in our implementation.

		Pure MPI Hybrid OpenMP/MPI
	spme	0.070 (256)	0.040 (512)
	cp-amoeba 0.025 (256)	0.015 (512)

Table 7 :

 7 multipolar electrostatics and penetration correction decomposed sapt gdma 1 E pen E pen charge-charge E pen charge-dipole E pen charge-quadrupoleWe have retained the S66 47 dimer notations. Tables reports electrostatic energy in kcal/mol.

	-8.18	-6.73 -1.44	-1.22		-0.11	0.12
	-6.64	-5.15 -1.48	-1.15		-0.14	0.20
	-6.36	-4.85 -1.51	-1.14		-0.15	0.23
	-6.58	-4.82 -1.76	-1.57		-0.03	0.15
	-5.78	-3.76 -2.02	-1.65		-0.08	0.29
	-5.58	-3.44 -2.14	-1.70		-0.10	0.34
	-4.71	-3.58 -1.13	-1.13		0.03	0.03
	-1.43	-1.26 -0.18	-0.25		0.04	-0.04
	-4.84	-3.79 -1.04	-1.00		-0.03	0.02
	-2.82	-2.21 -0.61	-0.58		-0.02	0.01
			Table 8: CP-amoeba parameters
			fragments	atoms	α	β	η
			water	H O	3.5 2.9 1.7 4.0 4.9 4.7
				H(-H3C) 3.5 2.6 4.7
			methanol	C(-CH3) 5.8 4.9 2.5 O 6.4 4.5 0.7
				H (-O) 4.8 2.9 1.7
				H(-H3C) 3.5 2.7 4.7
			methylamine	C(-CH3) 4.8 5.4 2.5 N 4.8 4.8 2.7
				H (-N) 2.5 2.9 1.7
			benzene	C H	2.8 2.5 2.8 3.5 2.3 2.5

Acknowledgements

We wish to thanks Marie-France Couret for technical support. This work was also supported in part by French state funds managed by calsimlab and the anr within the Investissements d'Avenir program under reference anr-11-idex-0004-02. Qiantao Wang, David R. Bell and Pengyu Ren are grateful for support by the Robert A. Welch Foundation (F-1691) and the National Institutes of Health (gm106137), as well as the high performance computing resources provided by tacc and xsede (tg-mcb100057). Funding from French CNRS through PICS grant between UPMC and UT Austin is acknowldeged. Jean-Philip Piquemal and Étienne Polack acknowledge funding from the Délégation Générale de l'Armement (DGA), Maîtrise NRBC, from the French Ministry of Defense.