Standard sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6‐31G and 6‐311G basis sets. Preliminary applications of the modified basis sets to the calculation of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.

Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets

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.

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

Density functional approximations for the exchange‐correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≊EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling‐constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Gorling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence Exc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.

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Rationale for mixing exact exchange with density functional approximations

This article introduces MMFF94, the initial published version of the Merck molecular force field (MMFF). It describes the objectives set for MMFF, the form it takes, and the range of systems to which it applies. This study also outlines the methodology employed in parameterizing MMFF94 and summarizes its performance in reproducing computational and experimental data. Though similar to MM3 in some respects, MMFF94 differs in ways intended to facilitate application to condensed-phase processes in molecular-dynamics simulations. Indeed, MMFF94 seeks to achieve MM3-like accuracy for small molecules in a combined “organic/protein” force field that is equally applicable to proteins and other systems of biological significance. A second distinguishing feature is that the core portion of MMFF94 has primarily been derived from high-quality computational data—ca. 500 molecular structures optimized at the HF/6-31G* level, 475 structures optimized at the MP2/6-31G* level, 380 MP2/6-31G* structures evaluated at a defined approximation to the MP4SDQ/TZP level, and 1450 structures partly derived from MP2/6-31G* geometries and evaluated at the MP2/TZP level. A third distinguishing feature is that MMFF94 has been parameterized for a wide variety of chemical systems of interest to organic and medicial chemists, including many that feature frequently occurring combinations of functional groups for which little, if any, useful experimental data are available. The methodology used in parameterizing MMFF94 represents a fourth distinguishing feature. Rather than using the common “functional group” approach, nearly all MMFF parameters have been determined in a mutually consistent fashion from the full set of available computational data. MMFF94 reproduces the computational data used in its parameterization very well. In addition, MMFF94 reproduces experimental bond lengths (0.014 A root mean square [rms]), bond angles (1.2° rms), vibrational frequencies (61 cm−1 rms), conformational energies (0.38 kcal/mol/rms), and rotational barriers (0.39 kcal/mol rms) very nearly as well as does MM3 for comparable systems. MMFF94 also describes intermolecular interactions in hydrogen-bonded systems in a way that closely parallels that given by the highly regarded OPLS force field. © 1996 John Wiley & Sons, Inc.

Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94

Gaussian-3 theory (G3 theory) for the calculation of molecular energies of compounds containing first (Li–F) and second row (Na–Cl) atoms is presented. This new theoretical procedure, which is based on ab initio molecular-orbital theory, modifies G2 theory [J. Chem. Phys. 94, 7221 (1991)] in several ways including a new sequence of single point energy calculations using different basis sets, a new formulation of the higher level correction, a spin–orbit correction for atoms, and a correction for core correlation. G3 theory is assessed using 299 energies from the G2/97 test set including enthalpies of formation, ionization potentials, electron affinities, and proton affinities. This new procedure corrects many of the deficiencies of G2 theory. There is a large improvement for nonhydrogen systems such as SiF4 and CF4, substituted hydrocarbons, and unsaturated cyclic species. Core-related correlation is found to be a significant factor, especially for species with unsaturated rings. The average absolute devi...

Gaussian-3 (G3) theory for molecules containing first and second-row atoms

Theoretical approach to substituent effects. Structures and stabilities of carbanions XCH2

Ab initio molecular orbital theory has been used to study the six compounds Li/sub 2/H/sub 2/, LiBeH/sub 3/, LiBH/sub 4/, Be/sub 2/H/sub 4/, BeBH/sub 5/, and B/sub 2/H/sub 6/. Geometry optimizations and vibrational analysis at the HF/6-31G* level indicate Li--(H)/sub 2/--Li (D/sub 2h/), Li--(H)/sub 2/--BeH (C/sub 2v/), Li--(H)/sub 3/--BH (C/sub 3v/), HBe--(H)/sub 2/--BeH (D/sub 2h/), HBe--(H)/sub 3/--BH (C/sub 3v/), and H/sub 2/B--(H)/sub 2/--BH/sub 2/ (D/sub 2h/) to the most stable forms. Inclusion of electron correlation corrections at the MP4/6-31G** level does not alter these conclusions. Other isomers were also examined in detail, and it was found that the potential energy surfaces for the species are generally flat. Activation energies for isomer interconversion and hydrogen scrambling reactions are generally less than 10 kcal mol/sup -1/. Examination of the HF/3-21 G potential surfaces indicates that there is no activation energy for the dimerization of LiH or BeH/sub 2/. The same is true for the dimerization of BH/sub 3/ at the correlated MP26-31G* level, although a small barrier is found on the HF/6-31G* surface. Enthalpies of complexation at 298 K from separate LiH, BeH/sub 2/, and BH/sub 3/ fragments, ..delta..H/sup 0//sub 298/, computed by using the HF/6-31G* harmonic frequencies and the MP4/6-31G** electronicmore » energies are as follows: Li/sub 2/H/sub 2/, -45.9; LiBeH/sub 3/, -43.6; LiBH/sub 4/, -60.1; Be/sub 2/H/sub 4/, -30.5; BeBH/sub 5/, -45.7; B/sub 2/H/sub 6/, -36.0 kcal mol/sup -1/.« less

Binary association complexes of lithium monohydride, beryllium dihydride, and borane. Relative isomer stabilities and barrier heights for their interconversion: energy barriers in the dimerization reactions

Molecular orbital theory of the properties of inorganic and organometallic compounds. 2. STO-NG basis sets for fourth-row main-group elements

Theoretical calculations of the aqueous medium effects on the basicities of primary amines

The effect of hyperconjugation of the magnitudes of secondary BETA-deuterium isotope effects has been investigated by ion cyclotron resonance spectroscopy and a b initio molecular orbital theory. Isotope effects measured for ion-molecule equilibria involving formation either of a nonbonded pair of electrons or of a vacant orbital adjacent to a methyl probe have been compared to theoretical calculations which have been restricted to consideration of changes in CH stretching force constants alone. Although this simple theoretical model successfully mirrors the observed BETA effects in the former systems in which the methyl group acts to accept excess electron density, it fails to properly account for the observed effects in those systems where the methyl probe is adjacent to an electron-deficient center. (2 tables)

Douglas J. DeFrees

Papers

Theoretical approach to substituent effects. Structures and stabilities of carbanions XCH2

Binary association complexes of lithium monohydride, beryllium dihydride, and borane. Relative isomer stabilities and barrier heights for their interconversion: energy barriers in the dimerization reactions

Molecular orbital theory of the properties of inorganic and organometallic compounds. 2. STO-NG basis sets for fourth-row main-group elements

Theoretical calculations of the aqueous medium effects on the basicities of primary amines

Role of hyperconjugation if secondary BETA-deuterium isotope effects