Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets
01 Apr 1984-Journal of Chemical Physics (American Institute of Physics)-Vol. 80, Iss: 7, pp 3265-3269
TL;DR: In this paper, a modified basis set of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions were defined for use with the 6.31G and 6.311G basis sets.
Abstract: 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.
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TL;DR: The M06-2X meta-exchange correlation function is proposed in this paper, which is parametrized including both transition metals and nonmetals, and is a high-non-locality functional with double the amount of nonlocal exchange.
Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.
22,326 citations
TL;DR: In this paper, an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so-called PBE generalized gradient functional with a predefined amount of exact exchange is presented.
Abstract: We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.
13,411 citations
TL;DR: The new local density functional, called M06-L, is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit.
Abstract: We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993
4,154 citations
TL;DR: The M05-2X functional has the best performance for thermochemical kinetics, noncovalent interactions (especially weak interaction, hydrogen bonding, π···π stacking, and interactions energies of nucleobases), and alkyl bond dissociation energies and the best composite results for energetics, excluding metals.
Abstract: We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values: the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal−metal and metal−ligand bond energies, a dipole moment databas...
3,246 citations
TL;DR: In this paper, a new theoretical procedure based on ab initio molecular-orbital theory for the calculation of molecular energies of compounds containing first (Li-F) and second row (Na-Cl) atoms is presented.
Abstract: 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...
2,620 citations
References
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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
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.
8,551 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