Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules
TL;DR: In this article, an extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first row atoms carbon to fluorine, where each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively.
Abstract: An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first‐row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single‐determinant molecular‐orbital studies of a group of small polyatomic molecules. Optimization of valence‐shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment.
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TL;DR: In this article, a contract Gaussian basis set (6•311G) was developed by optimizing exponents and coefficients at the Mo/ller-Plesset (MP) second-order level for the ground states of first-row atoms.
Abstract: A contracted Gaussian basis set (6‐311G**) is developed by optimizing exponents and coefficients at the Mo/ller–Plesset (MP) second‐order level for the ground states of first‐row atoms. This has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. The basis is tested by computing structures and energies for some simple molecules at various levels of MP theory and comparing with experiment.
14,120 citations
TL;DR: In this article, two extended basis sets (termed 5-31G and 6 -31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine.
Abstract: Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.
13,036 citations
TL;DR: In this paper, a split-valence extended gaussian basis set was used to obtain the LCAO-MO-SCF energies of closed shell species with two non-hydrogen atoms.
Abstract: Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.
12,669 citations
Book•
10 Mar 1986
TL;DR: In this paper, the use of theoretical models as an alternative to experiment in making accurate predictions of chemical phenomena is discussed, and the formulation of theoretical molecular orbital models starting from quantum mechanics is discussed.
Abstract: Describes and discusses the use of theoretical models as an alternative to experiment in making accurate predictions of chemical phenomena. Addresses the formulation of theoretical molecular orbital models starting from quantum mechanics, and compares them to experimental results. Draws on a series of models that have already received widespread application and are available for new applications. A new and powerful research tool for the practicing experimental chemist.
8,210 citations
TL;DR: In this article, a method is presented which utilizes the calculation of the molecular electrostatic potential or the electric field at a discrete number of preselected points to evaluate the environmental effects of a solvent on the properties of a molecular system.
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TL;DR: The phrase "direct search" is used to describe sequential examination of trial solutions involving comparison of each trial solution with the "best" obtained up to that time together with a strategy for determining (as a function of earlier results) what the next trial solution will be.
Abstract: In dealing with numerical problems for which classical methods of solution are unfeasible, many people have tried various procedures of searching for an answer on a computer. Our efforts in this direction have produced procedures which seem to have had (for us and for others who have used them) more success than has been achieved elsewhere, so that we have been encouraged to publish this report of our studies. We use the phrase \"direct search\" to describe sequential examination of trial solutions involving comparison of each trial solution with the \"best\" obtained up to that time together with a strategy for determining (as a function of earlier results) what the next trial solution will be. The phrase implies our preference, based on experience, for straightforward search strategies which employ no techniques of classical analysis except where there is a demonstrable advantage in doing so. We have found it worthwhile to study direct search methods for the following reasons: (a) They have provided solutions to some problems, of importance to us, which had been unsuccessfully attacked by classical methods. (Examples are given below.) (b) They promise to provide faster solutions for some problems that are solvable by classical methods. (For example, a method for solving systems of linear equations, proposed in Section 5, seems to take an amount of time that is proportional only to the first power of the number of equations.) (c) They are well adapted to use on electronic computers, since they tend to use repeated identical arithmetic operations with a simple logic. Classical methods, developed for human use, often stress minimization of arithmetic by increased sophistication of logic, a goal which may not be desirable when a computer is to be used. (d) They provide an approximate solution, improving all the while, at all stages of the calculation. This feature can be important when a tentative solution is needed before the calculations are completed. (e) They require (or permit) different kinds of assumptions about the functions involved in various problems, and thus suggest new classifications of functions which may repay study. Direct search is described roughly in Section 2, and explained heuristically in Section 3. Section 4 describes a kind of strategy. Sections 5 and 6 describe
4,184 citations
TL;DR: In this article, a least square representation of Slater-type atomic orbitals as a sum of Gaussian-type orbitals is presented, where common Gaussian exponents are shared between Slater−type 2s and 2p functions.
Abstract: Least‐squares representations of Slater‐type atomic orbitals as a sum of Gaussian‐type orbitals are presented. These have the special feature that common Gaussian exponents are shared between Slater‐type 2s and 2p functions. Use of these atomic orbitals in self‐consistent molecular‐orbital calculations is shown to lead to values of atomization energies, atomic populations, and electric dipole moments which converge rapidly (with increasing size of Gaussian expansion) to the values appropriate for pure Slater‐type orbitals. The ζ exponents (or scale factors) for the atomic orbitals which are optimized for a number of molecules are also shown to be nearly independent of the number of Gaussian functions. A standard set of ζ values for use in molecular calculations is suggested on the basis of this study and is shown to be adequate for the calculation of total and atomization energies, but less appropriate for studies of charge distribution.
3,723 citations
1,448 citations
TL;DR: In this paper, it was shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation, and that all necessary integrals can be explicitly evaluated.
Abstract: This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.
1,036 citations