Mark S. Gordon

General atomic and molecular electronic structure system

A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines.

Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements

The 6‐31G* and 6‐31G** basis sets previously introduced for first‐row atoms have been extended through the second‐row of the periodic table. Equilibrium geometries for one‐heavy‐atom hydrides calculated for the two‐basis sets and using Hartree–Fock wave functions are in good agreement both with each other and with the experimental data. HF/6‐31G* structures, obtained for two‐heavy‐atom hydrides and for a variety of hypervalent second‐row molecules, are also in excellent accord with experimental equilibrium geometries. No large deviations between calculated and experimental single bond lengths have been noted, in contrast to previous work on analogous first‐row compounds, where limiting Hartree–Fock distances were in error by up to a tenth of an angstrom. Equilibrium geometries calculated at the HF/6‐31G level are consistently in better agreement with the experimental data than are those previously obtained using the simple split‐valance 3‐21G basis set for both normal‐ and hypervalent compounds. Normal‐mode vibrational frequencies derived from 6‐31G* level calculations are consistently larger than the corresponding experimental values, typically by 10%–15%; they are of much more uniform quality than those obtained from the 3‐21G basis set. Hydrogenation energies calculated for normal‐ and hypervalent compounds are in moderate accord with experimental data, although in some instances large errors appear. Calculated energies relating to the stabilities of single and multiple bonds are in much better accord with the experimental energy differences.

The isomers of silacyclopropane

Abstract Geometries, relative energies, and electron density distributions in silacyclopropane and five of its isomers are investigated using ab initio methods. VinyIsilane is found to be the most stable isomer, and methyl substitution is preferred at the silicon end of both silaethylene and methyl silylene.

Molecular orbital theory of the electronic structure of organic compounds. I. Substituent effects and dipole moments.

A recent approximate self-consistent molecular orbital theory (complete neglect of differential overlap or CNDO) is used to calculate charge distributions and electronic dipole moments of a series of simple organic molecules. The nuclear coordinates are chosen to correspond to a standard geometrical model. The calculated dipole moments are in reasonable agreement with experimental values in most cases and reproduce many of the observed trends. The associated charge distributions of dipolar molecules show widespread alternation of polarity in both saturated and unsaturated systems. These results suggest that charge alternation may be an intrinsic property of all inductive and mesomeric electronic displacements. ne of the long-term aims of quantum chemistry 0 is to provide a critical quantitative background for simple theories of electron distribution in large molecules. Most theoretical discussions of the role of electronic structure in organic chemistry are at present based either on qualitative arguments (such as the study of resonance structures) with no clear foundation in quantum mechanics, or on postulated relationships between charge distribution and various physical and chemical properties (reactivities, acidities, nmr chemical shifts, etc.), few of which can be subjected to direct test. If quantum mechanical calculations are to lead to independent methods of studying such phenomena, they ought to satisfy the following general conditions. (1) The methods must be simple enough to permit application to moderately large molecules without excessive computational effort. Quite accurate wave functions now exist for many diatomic and small polyatomic molecules, but it is unlikely that comparable functions will be readily available in the near future for the molecules of everyday interest to the organic chemist. To be accessible, a quantum mechanical theory has to be approximate. (2) Even though approximations have to be introduced, these should not be so severe that they eliminate any of the primary physical forces determining structure. For example, the relative stabilities of electrons in different energy levels, the directional character of the bonding capacity of atomic orbitals, and the electrostatic repulsion between electrons are all gross features with major chemical consequences and they should all be retained in a realistic treatment. (3) In order to be useful as an independent study, the approximate wave functions should be formulated in an unbiased manner, so that no preconceived ideas derived from conventional qualitative discussions are built in implicitly. For example, a critical theoretical study of the localization of a two-electron bond orbital ought to be based on a quantum mechanical theory which makes no reference to electron-pair bonds in its basis. Molecular orbital theories satisfy this type of condition insofar as each electron is treated as being free to move anywhere in the molecular framework. (4) The theory should be developed in such a way that the results can be interpreted in detail and used to support or discount qualitative hypotheses. For example, it is useful if the electronic charge distribution calculated from a wave function can be easily and realistically divided into contributions on individual atoms

MacMolPlt: a graphical user interface for GAMESS.

A description of MacMolPlt, a graphical user interface for the General Atomic and Molecular Electronic Structure System, GAMESS, is presented. Major features include an input builder for GAMESS; and display and animation of molecular structure, normal modes of vibration, reaction paths, orbitals, total electron densities, molecular electrostatic potentials, and density differences. The strategy for direct computation of orbital, total electron density, and molecular electrostatic potential surfaces is discussed.

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

Fragmentation Methods: A Route to Accurate Calculations on Large Systems Mark S. Gordon,* Dmitri G. Fedorov, Spencer R. Pruitt, and Lyudmila V. Slipchenko Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States

An Effective Fragment Method for Modeling Solvent Effects in Quantum Mechanical Calculations

An effective fragment model is developed to treat solvent effects on chemical properties and reactions. The solvent, which might consist of discrete water molecules, protein, or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water‐formamide are in good agreement with fully ab initio calculations.

Advances in electronic structure theory: GAMESS a decade later

Publisher Summary This chapter focuses on the new developments in electronic structure theory during the past decade. These developments include new methods in quantum mechanics, including approaches for extrapolating to the full CI and complete basis set limits, novel methods for CASSCF calculations, new coupled cluster techniques, methods for evaluating non-adiabatic and relativistic interactions, new approaches for distributed parallel computing, and QM/MM methods for describing solvent effects and surface science. It is useful to note in this regard that GAMESS is a general-purpose suite of electronic structure and QM/MM methods (including open-and closed-shell Hartree–Fock which has been essentially ignored here) that can be run on virtually any computer, cluster, massively parallel system, or for that matter a desktop Mac or PC. Indeed, GAMESS is used at many universities as an educational tool, making use of its graphical back end MacMolPlt. GAMESS and MacMolPlt can be downloaded at no cost from www.msg.ameslab.gov, with only a simple license required.

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

A new hierarchical parallelization scheme: Generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method(FMO)

A two‐level hierarchical scheme, generalized distributed data interface (GDDI), implemented into GAMESS is presented. Parallelization is accomplished first at the upper level by assigning computational tasks to groups. Then each group does parallelization at the lower level, by dividing its task into smaller work loads. The types of computations that can be used with this scheme are limited to those for which nearly independent tasks and subtasks can be assigned. Typical examples implemented, tested, and analyzed in this work are numeric derivatives and the fragment molecular orbital method (FMO) that is used to compute large molecules quantum mechanically by dividing them into fragments. Numeric derivatives can be used for algorithms based on them, such as geometry optimizations, saddle‐point searches, frequency analyses, etc. This new hierarchical scheme is found to be a flexible tool easily utilizing network topology and delivering excellent performance even on slow networks. In one of the typical tests, on 16 nodes the scalability of GDDI is 1.7 times better than that of the standard parallelization scheme DDI and on 128 nodes GDDI is 93 times faster than DDI (on a multihub Fast Ethernet network). FMO delivered scalability of 80–90% on 128 nodes, depending on the molecular system (water clusters and a protein). A numerical gradient calculation for a water cluster achieved a scalability of 70% on 128 nodes. It is expected that GDDI will become a preferred tool on massively parallel computers for appropriate computational tasks.