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WebMTA: A Web-Interface for Ab Initio Geometry Optimization of Large Molecules Using Molecular Tailoring Approach RITWIK KAVATHEKAR,1 SUBODH KHIRE,1 V. GANESH,1,2 ANUJA P. RAHALKAR,1 SHRIDHAR R. GADRE1,2 1

Department of Chemistry, University of Pune, Pune 411 007, India Interdisciplinary School of Scientific Computing, University of Pune, Pune 411 007, India

2

Received 16 June 2008; Revised 22 August 2008; Accepted 28 August 2008 DOI 10.1002/jcc.21132 Published online 22 October 2008 in Wiley InterScience (www.interscience.wiley.com).

Abstract: A web-interface for geometry optimization of large molecules using a linear scaling method, i.e., cardinality guided molecular tailoring approach (CG-MTA), is presented. CG-MTA is a cut-and-stitch, fragmentation-based method developed in our laboratory, for linear scaling of conventional ab initio techniques. This interface provides limited access to CG-MTA-enabled GAMESS. It can be used to obtain fragmentation schemes for a given spatially extended molecule depending on the maximum allowed fragment size and minimum cut radius values provided by the user. Currently, we support submission of single point or geometry optimization jobs at Hartree-Fock and density functional theory levels of theory for systems containing between 80 to 200 first row atoms and comprising up to 1000 basis functions. The graphical user interface is built using HTML and Python at the back end. The back end farms out the jobs on an in-house Linux-based cluster running on Pentium-4 Class or higher machines using an @Home-based parallelization scheme (http://chem.unipune.ernet.in/tcg/mtaweb/). q 2008 Wiley Periodicals, Inc.

J Comput Chem 30: 1167–1173, 2009

Key words: WebMTA; ab initio methods; cardinality guided molecular tailoring approach; geometry optimization; energy; gradients; density matrix; Hartree-Fock method; density functional theory; large molecule

Introduction The use of Internet for scientific searches, data sorting, documentation, communication and a host of other facilities, used by educational and noneducational institutions alike, has created a need for developing super-specialized application tools and utilities to cater to a broad and also niche cliente`le. This includes an increasing user base for computational chemistry softwares to be accessed and availed on demand anywhere and anytime. The boom is supported by pharma companies investing in various domains of scientific computing and allied fields of bioinformatics and cheminformatics. Probably the largest scientific computing users of the Internet are in grid computing1 environments, where virtual supercomputers are set up by networking small computing clusters controlled by complex grid portal management systems. Researchers working in particle physics,2 weather forecasting,3 and molecular modeling4 are perhaps the heaviest users of this infrastructure. Also a class of @Home type of distributed computing resource is getting popular amongst the scientific community5 because of its ability to harness idle processors across the World Wide Web. Browser-based job submission tools such as WebMo6 and Web-

Prop7 allow hassle free access to standard computational chemistry-based software packages. The user need not learn about any complicated procedures or know coding for using the interface while availing the required computing resources. This also permits a large fraternity of scientists to carry out research and enables teachers to conduct courses with minimal IT infrastructure. The surge in number of researchers using ab initio quality codes (such as GAMESS8 and GAUSSIAN9) for molecular modeling (other than trained chemists and physicists) has set a new class of nonprofessional fire-and-forget users. Most of them are handicapped by a resource crunch (financial or computational), lack of time or simply by the inadequacy/theoretical limitations of the package in question. Geometry optimization and property calculation for spatially extended large molecules using ab initio methods are not routinely possible by standard available computational chemistry

Correspondence to: S. R. Gadre; e-mail: [email protected] Contract/grant sponsors: Council of Scientific and Industrial Research (CSIR), New Delhi; Naval Research Board (NRB); Center for Advanced Computing (C-DAC), Pune

q 2008 Wiley Periodicals, Inc.

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packages due to requirement of huge computational power (number of processors, memory, etc.) or package limitations. The scaling of these methods is typically given in terms of power of the number, N, of basis functions involved, i.e., O(Nm), where m is the order of complexity of the method. These methods range from Hartree-Fock (HF) (typical value for large molecules being m ¼ 3), Density functional theory (DFT) (m ¼ 3–4), Møller-Plesset second order perturbation theory (MP2) (m ¼ 5), and Coupled cluster (CC) methods (m ¼ 7). Development of methods for theoretical treatment of large molecules has been a formidable challenge and is being tackled10,11 since 1959. Some earlier as well as recent works by Yang et al.,12–14 Li et al.,15 Kitaura et al.,16 and Zhang et al.17 focus on a linear scaling method termed as divide-and-conquer (DC) approach. DC algorithm involves breaking the main problem into small subproblems, and subsequently patching the results for these subproblems to get the result for the main problem. The authors’ group has independently developed the molecular tailoring approach (MTA)18–21 for geometry optimization and property evaluation along with its parallel implementation in line with the other codes developed earlier22–24 in our laboratory.

Cardinality Guided Molecular Tailoring Approach (CG-MTA) Cardinality guided molecular tailoring approach (CG-MTA; MTA for brief) is a method developed for ab initio calculations on spatially extended large molecules and molecular clusters. It is based on DC-type of algorithm, which is incorporated in locally modified version of public domain ab initio quantum chemistry package GAMESS. The details of the algorithm are given elsewhere.20,21,25,26 MTA cuts a spatially extended large molecule into a set of small, overlapping fragments. While fragmenting, the sensitive structures such as planar rings, multiple bonds are kept intact. Whenever a covalent bond is cut, dummy hydrogen atoms are added at appropriate positions to satisfy the valences. The process of fragmentation is automatic. For a quantitative definition of the quality of fragments, a parameter called R-goodness25,26 is introduced. R-goodness of an atom is defined as the radius of a sphere centered on the atom, which covers maximum of the chemical influence on that atom due to other atoms in the molecule. In other words, R-goodness of atom i in fragment fi is taken as the maximum radius of a sphere centered on i such that all the atoms within this sphere are also included in fi. We illustrate this on the test molecule of avermectin (cf. Fig. 1) with two fragments F3 and F7. Atom number 10 is present in fragments 3 and 7 with R-goodness 3.5 ˚ , respectively. The atom is best represented in fragand 4.7 A ˚ . R-goodness of a ment 7, hence its atomic R-goodness is 4.7 A fragmentation scheme is defined as the minimum of the atomic R-goodness values. Larger the value of R-goodness of a fragmentation scheme, the better is each atom represented and more accurate are the results. Parameters such as maximum allowed size of a fragment and R-goodness control the automatic fragmentation. Various combinations of these produce different fragmentation schemes for the given molecular system.

Figure 1. Details of fragments for the test case of Avermectin. The highlighted portion represents the fragments 7 and 3, respectively. Atom number 10 is present in fragments 7 and 3 and is shown in ˚ and (B) 3.5 A ˚ centered on it. Hence its spheres of radii (A) 4.7 A ˚ .The corresponding overlap between fragments R-goodness is 4.7 A 3 and 7 is also shown (C).

Journal of Computational Chemistry

DOI 10.1002/jcc

A Web-Interface for Ab Initio Geometry Optimization of Large Molecules

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Figure 2. Screenshot of the job submission interface. See text for details. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

MTA also provides analysis for the scheme in terms of average size of fragments, minimum R-goodness achieved in the scheme, scaling factor (the ratio of the total number of atoms in all fragments to the number of atoms in the parent molecule). This analysis is offered as a help to the user for finding the best fragmentation scheme which will require minimal efforts to produce sufficiently accurate results. Earlier benchmarks have showed that a scheme with minimum R-goodness in range 3–4 ˚ , scaling factor less than 5 is good enough for reliable results A for spatially extended molecules with minimal computational efforts.18–20 After fragmentation, cardinality-based expressions for energy and gradients are set up. In general, these equations can be written as: E¼

X

Efi

X

Efi \fj þ þ ð1Þk1

X

Efi \fj \\fk

(1)

X @Efi \fj \\fk X @Efi X @Efi \fj @E ¼ þ þ ð1Þk1 ð2Þ f f \f f \f \\fk i i j @Xl @Xl @Xq @Xli j where E denotes CG-MTA-estimated energy of the parent molecule; fi and fj denote fragments i and j respectively; fi \ fj represents the set of atoms common to these fragments (overlaps). The respective fragment energies and the overlap fragment energies are (Efi) and (Efi\fj) and so on. The fi \ fj overlap fragment is illustrated in Figure 1(C). Terms in eq. (2) are the derivatives of the energy terms used in eq. (1) with respect to the nuclear coordinates, l.

WebMTA Capabilities and Architecture WebMTA is a web-based interface that provides access to the MTA-enabled GAMESS developed in our laboratory especially for ab initio calculations on extended, large molecules. This interface allows users to submit a complete geometry optimization job for his/her large molecular system on a dedicated cluster in our laboratory. An input for MTA enabled GAMESS is just a standard GAMESS input file with special keywords controlling various parameters for fragmentation schemes. These include (Rgoodness, maximum size, generate overlaps or not, etc.), convergence criteria (gradient, energy, integral and density accuracy), density matrix options (save DM, patch DM, use picked DM, read external DM), system requirements (number of cores/nodes, memory allocation, job time limit), kind of parallelism (queuing system, shared architecture, distributed mode, network file system (NFS) availability), etc. WebMTA assigns default values to all of the above parameters depending on the total number of atoms, number of basis functions and available processors, except maximum allowed fragment size and minimum R-goodness. Values for these two parameters are accepted from the user. The user need not worry about any hardware issues or need not understand the complexity of the fragmentation process or the optimization algorithm. This introduces simplicity in the process of job submission, yet providing the user with control over fragmentation procedure. The login process for WebMTA is similar to that employed in WebProp6 wherein a user enters his/her e-mail ID, and then acknowledges the e-mail verification, followed by entering a security key (generated by a random number generator). After successful verification of the security key, the job submission


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Figure 3. Fragmentation summary page displaying the submitted molecule and using Jmol26 for visualization along with fragment information. See text for details. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

interface is displayed (Fig. 2). The security key also works as the job identifier and the results are mailed to the user on the given email ID with reference to this identifier. This security check ensures (to some extent) that a valid user (human) is accessing the web page. The user is requested to fill in a suitable title, basis set, maximum allowed fragment size (MAXSZ), cut radius ˚ unit (Fig. 2) on the job (RADCUT) and input coordinates in A submission page. It should be noted here that the parameters MAXSZ and RADCUT are preliminary criteria for guiding the automatic fragmentation process, but are not always strictly fol-

lowed due to structural diversity in the molecular systems. Thus, if user is not satisfied with the automatic fragmentation scheme, there is an option to provide the fragments externally by clicking on ‘‘Upload Fragment’’ check box. Fragments are to be provided in a certain format which is exemplified on clicking the ‘‘Input File Format’’ button. Within this option, only the main fragments are to be provided by the user. This input file for these fragments can be generated from MeTA Studio.27 While using this option, the user should ensure that every atom is present in at least one of the main fragments. The automatic fragmentation procedure will


DOI 10.1002/jcc


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Table 1. A Few Test Cases of CG-MTA-Based Geometry Optimization

Using WebMTA. System

Level/Basis

Monesin Avermectin

b-carotene

HF/6-31G(d) HF/6-31G(d) HF/6-31G(d,p) B3LYP/6-31G(d) B3LYP/6-31G(d)

NA (NB) 106 134 134 134 96

(810) (1074) (1290) (1074) (712)

LA (LF)

GP, GN

55 56 56 56 39

3.8, 3.7, 3.7, 3.7, 4.5,

(383) (476) (560) (476) (299)

3.9 3.9 4.2 4.1 4.8

NA, NB, LA, LF, GP, and GN are the total number of atoms, number of basis functions for the parent system, number of atoms in the largest fragment, number of basis functions in the largest fragment, the pendant and nonpendant R-goodness values of the fragmentation scheme, respectively. See text for other details.

required. Further, WebMTA can be accessed over different kinds of network and in principle over the Internet. The WebMTA client and server are both written in Python and are executed as back-end scripts. Entire network communication including CGMTA @Home setup is built on Python sockets. After the job is completed a summary including gradients, energy, and geometry at each optimization cycle is mailed to previously specified email address with total time taken. Online graphics visualization is provided using the packages MeTA Studio27 and Jmol.28 The requirements for each job varies depending on level of theory and basis set, available memory, total number of atoms, number of fragments, and number of basis functions per fragment. Hence, it is difficult to allocate requisite resources a priori but @Home clients can be dynamically added and/or subtracted manually for load balancing. The test results presented below were run on standard Pentium-4 Class machines or higher running desktop GNU/Linux operating system. Figure 4. Structures of molecules taken as test cases. (A) Monesin. (B) Avermectin (C) b-carotene. See text for details.

Tests and Benchmarks

take care of generating overlapping fragments and setting up the cardinality expression. Clicking on the ‘‘Submit’’ button brings the user to the fragment summary page (Fig. 3). Information displayed on this page includes number of main fragments, average size of fragments, minimum R-goodness, minimum nonpendant R-goodness, scaling factor, and a list of atomic R-goodness values.16,17 The user can scan the data-set and decide whether the fragmentation scheme is suitable for his/her job. If it is not up to the mark, he/she can hit a ‘‘BACK’’ button and refragment the system. Currently, the interface supports optimization at HF and DFT levels of theory. The job is submitted in a First-In-First-Out queuing system on the server. This is handled by a WebMTA backend running on the server, while the WebMTA clients, of which multiple instances can be booted, pull the jobs. Thus load is distributed across such many WebMTA clients. Once the job is accepted by WebMTA client CG-MTA jobs are farmed out across the distributed network using @Home parallelism. It is unique in the sense that no special configuration like password-less rsh/ssh is

We present here a few test cases run on the WebMTA interface. These cases are chosen to present the flexibility of the fragmentation scheme with regard to the spatial distribution of the molecule. These structures are depicted in Figure 4. The details of level of theory, basis sets, and fragmentation schemes are summarized in Table 1. Initial geometries for all the WebMTA test cases are first optimized using STO-3G or 6-31G basis set at respective level of theory. The first test case of Monesin consists of 106 atoms. Monesin is extracted from the bark of Chrysophyllum glycyphloeum and is used as an astringent. An arbitrary geometry is optimized at HF/STO-3G level and employed as the initial geometry for CG-MTA based optimization at HF/6-31G(d) level of theory ˚ . The largest fragment with R-goodness values of 3.5 and 3.7 A in this scheme consists of 55 atoms and 383 basis functions, while the total number of basis functions involved in the actual calculation is 810 (cf. Table 1). Actual single-point energy and gradient calculation of monesin at HF/6-31G(d) level of theory took 13 min on a cluster of four Core 2 Quad @ 2.4 GHz machines with 4 GB RAM and 250 GB of hard disk each. The corresponding CG-MTA based calculation took 4.5 min per opti-


DOI 10.1002/jcc


Gmax and Grms denote maximum gradient norm and RMS gradient, respectively. Energy and gradients are in a.u. See text for details. a For all the cases, 20 optimization cycles are carried out with larger fragments than those reported in Table 1. This ensures reliable estimation of energies and gradients.

(0.00037, (0.00057, (0.00050, (0.00064, (0.00054, 22183.79090 22907.52863 22907.65711 22923.69425 21556.81592 (0.00023, (0.00027, (0.00019, (0.00032, (0.00009, 22183.79071 22907.52844 22907.65704 22923.69436 21556.81572 (0.05175, (0.04131, (0.01457, (0.04382, (0.01263, 22183.74427 22907.50798 22907.65654 22923.67091 21556.80142 (0.05101, (0.04123, (0.01451, (0.04392, (0.01260, 22183.74494 22907.50817 22907.65669 22923.67109 21556.80018 Monesin HF/6-31G(d) Avermectin HF/6-31G(d) Avermectin HF/6-31G(d,p) Avermectin B3LYP/6-31G(d) b-carotene B3LYP/6-31G(d)

System level/Basis

CG-MTA

0.01117) 0.00690) 0.00187) 0.00749) 0.00050)

Initial geometry

Table 2. Comparison of Actual and CG-MTA-Based Energy and Gradients.

a

Actual

0.00024) 0.00680) 0.00187) 0.00748) 0.00433)

Energy (Gmax, Grms) in a.u.

CG-MTA

0.00003) 0.00006) 0.00003) 0.00009) 0.00003)

Final geometry

Actual

0.00007) 0.00013) 0.00007) 0.00010) 0.00009)

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mization cycle on the same hardware. Few last cycles of optimization are carried out with better quality fragments having R˚ to obtain reliable results. With this goodness of 3.8 and 4.0 A scheme, each cycle of optimization took about 6 min on the above-mentioned hardware. A comparison of actual and CGMTA based energy and gradients for initial and the final geometries at HF/6-31G(d) level of theory is reported in Table 2. Avermectin is an anti-parasitic drug procured by fermenting a strain of Streptomyces. This molecule is optimized at HF/631G(d), HF/6-31G(d,p), and B3LYP/6-31G(d) levels of theory. The scheme at HF/6-31G(d) level consists of an R-goodness ˚ with maximum fragment size of 476 bavalue of 3.7 and 3.9 A sis functions. Total number of basis functions involved in this calculation is 1074. During this optimization, energy is lowered by 0.0202 a.u., the final maximum gradient 2.7 3 1024 a.u. and RMS gradient by 6.0 3 1025 a.u. (cf. Table 2). Final geometry from this run is taken as initial geometry for optimization at HF/ 6-31G(d,p). Although the same fragmentation scheme is used, due to changes in geometry during earlier optimization the non˚ is increased to 4.2 A ˚ (cf. Table 1). pendant R-goodness of 3.9 A At HF/6-31G(d,p) level, the largest fragment contains 560 basis functions while the total number of basis functions is 1290. This final geometry is further subjected to optimization at B3LYP/631G(d) level with the same fragmentation scheme as used in the earlier optimization runs. At B3LYP/6-31G(d) level, the final maximum gradient is 3.2 3 1024 a.u. and RMS gradient is 9.0 3 1025 a.u. with an energy difference of 0.0232 a.u. The last few optimization steps of all these jobs are run with larger sized fragments, for ensuring reliable estimation of energies and gradients. The test case of b-carotene consists of 96 atoms and is optimized at B3LYP/6-31G(d) level of theory. b-carotene is an orange colored photo active pigment found in plants. This calculation involved 712 basis functions. The input values of MAXSZ and RADCUT being 38 and 3.8, respectively, giving 4 main fragments, with the largest fragment containing 39 atoms and 299 basis functions. CG-MTA estimates for energy and gradients corresponding to the initial and final geometries are given in Table 2 along with their actual counterparts. It shows that during optimization, the energy is lowered by about 0.016 a.u. and maximum gradient norm is changed from 1022 to 1025 a.u. The last few optimization steps are run with larger sized fragments to ensure consistency in the results. Each geometry optimization step with WebMTA took about 12 min on a cluster of four Core 2 Quad @ 2.4 GHz machines with 4 GB RAM and 250 GB of hard disk each, running @Home clients. The corresponding time for the actual calculation is about 30 min on identical hardware. Table 2 compares the actual and CG-MTA energies and gradients. The actual energies and gradients given in Table 2 are single point runs at the corresponding CG-MTA optimized geometries and not actual complete geometry optimization runs. Error analysis for CG-MTA has been reported in refs. 18–20. Earlier reported runs have shown that the actual optimized geometries and energies generally match well with the CG-MTA optimized ones. It is observed that energies differ to the order of 1 millihartree and the RMS gradient values are of the order of 1024. This is further confirmed in the present work. Some of these test cases require formidable computational infrastructure


DOI 10.1002/jcc


for actual ab initio computations. By using CG-MTA methodology, such jobs can be easily performed and WebMTA provides a user-friendly interface to the same. We welcome users to run some test jobs using WebMTA. The users of WebMTA are requested to cite the complete GAMESS reference8 and requisite papers concerning WebMTA.19,20,21,25

Concluding Remarks Geometry optimization is a routine protocol followed for every quantum chemical calculation. The nonfeasibility of performing large ab initio calculations can be overcome to a great extent by using CG-MTA approach through WebMTA. Also huge amount of time and computational resources could be saved. We have showcased here a few selected test cases highlighting the performance and capabilities of this interface. We invite the fraternity of researchers and educationists, especially those with minimal resources, to avail this facility. As of this writing, WebMTA performs fragmentation of the closed shell molecule, single point energy and gradient evaluation and geometry optimization at HF and DFT (B3LYP, BHHLYP and BLYP) levels of theory. WebMTA supports these calculations for closed shell systems containing atoms up to atomic number 20. For a spatially large molecule containing many planar rings, users are requested to manually feed the fragments for WebMTA implementation. Currently a limit of 80– 200 atoms and/or maximum of 1000 basis functions is imposed, which will be enhanced in future depending on the availability of additional computational resources.

Acknowledgments SRG is thankful to Department of Science and Technology (DST), New Delhi for the award of J. C. Bose Fellowship.

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DOI 10.1002/jcc