Krishnan Raghavachari

A fifth-order perturbation comparison of electron correlation theories

Abstract Electron correlation theories such as configuration interaction (CI), coupled-cluster theory (CC), and quadratic configuration interaction (QCI) are assessed by means of a Moller-Plesset perturbation expansion of the correlation energy up to fifth order. The computational efficiencies and relative merits of the different techniques are outlined. A new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupled-cluster models.

Quadratic configuration interaction. A general technique for determining electron correlation energies

A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.

Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds

The Gaussian‐2 theoretical procedure (G2 theory), based on ab initio molecular orbital theory, for calculation of molecular energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compounds containing first‐ (Li–F) and second‐row atoms (Na–Cl) is presented. This new theoretical procedure adds three features to G1 theory [J. Chem. Phys. 90, 5622 (1989)] including a correction for nonadditivity of diffuse‐sp and 2df basis set extensions, a basis set extension containing a third d function on nonhydrogen and a second p function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G1 theory because it eliminates a number of deficiencies present in G1 theory. Of particular importance is the improvement in atomization energies of ionic molecules such as LiF and hydrides such as C2H6, NH3, N2H4, H2O2, and CH3SH. The average absolute deviation from experiment of atomization energies of 39 first‐row compounds...

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

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...

Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation

A set of 148 molecules having well-established enthalpies of formation at 298 K is presented. This set, referred to as the G2 neutral test set, includes the 55 molecules whose atomization energies were used to test Gaussian-2 ~G2! theory @J. Chem. Phys. 94, 7221 ~1991!# and 93 new molecules. The G2 test set includes 29 radicals, 35 nonhydrogen systems, 22 hydrocarbons, 47 substituted hydrocarbons, and 15 inorganic hydrides. It is hoped that this new test set will provide a means for assessing and improving new theoretical models. From an assessment of G2 and density functional theories ~DFT! on this test set it is found that G2 theory is the most reliable method both in terms of average absolute deviation ~1.58 kcal/mol! and maximum deviation ~8.2 kcal/mol!. The largest deviations between experiment and G2 theory occur for molecules having multiple halogens. Inclusion of spin‐orbit effects reduces the average absolute deviation to 1.47 kcal/mol and significantly improves the results for the chlorine substituted molecules, but little overall improvement is seen for the fluorine substituted molecules. Of the two modified versions of G2 theory examined in this study, G2~MP2,SVP! theory ~average absolute deviation51.93 kcal/mol! performs better than G2~MP2! theory ~2.04 kcal/mol!. The G2~MP2,SVP! theory is found to perform very well for hydrocarbons, radicals, and inorganic hydrides. Of the seven DFT methods investigated, the B3LYP method has the smallest average absolute deviation ~3.11 kcal/mol!. It also has a significantly larger distribution of error than the G2 methods with a maximum deviation of 20.1 kcal/mol.

Gaussian-3 theory using density functional geometries and zero-point energies

A variation of Gaussian-3 (G3) theory is presented in which the geometries and zero-point energies are obtained from B3LYP density functional theory [B3LYP/6-31G(d)] instead of geometries from second-order perturbation theory [MP2(FU)/6-31G(d)] and zero-point energies from Hartree–Fock theory [HF/6-31G(d)]. This variation, referred to as G3//B3LYP, is assessed on 299 energies (enthalpies of formation, ionization potentials, electron affinities, proton affinities) from the G2/97 test set [J. Chem. Phys. 109, 42 (1998)]. The G3//B3LYP average absolute deviation from experiment for the 299 energies is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. Generally, the results from the two methods are similar, with some exceptions. G3//B3LYP theory gives significantly improved results for several cases for which MP2 theory is deficient for optimized geometries, such as CN and O2+. However, G3//B3LYP does poorly for ionization potentials that involve a Jahn–Teller distortion in the cation (CH4+, BF3+, BCl3+)...

Ideal hydrogen termination of the Si (111) surface

Aqueous HF etching of silicon surfaces results in the removal of the surface oxide and leaves behind silicon surfaces terminated by atomic hydrogen. The effect of varying the solution pH on the surface structure is studied by measuring the SiH stretch vibrations with infrared absorption spectroscopy. Basic solutions ( pH=9–10) produce ideally terminated Si(111) surfaces with silicon monohydride ( 3/4 SiH) oriented normal to the surface. The surface is found to be very homogeneous with low defect density (<0.5%) and narrow vibrational linewidth (0.95 cm−1 ).

Gaussian‐1 theory: A general procedure for prediction of molecular energies

A general procedure is developed for the computation of the total energies of molecules at their equilibrium geometries. Ab initio molecular orbital theory is used to calculate electronic energies by a composite method, utilizing large basis sets (including diffuse‐sp, double‐d and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. The theory is also used to compute zero‐point vibrational energy corrections. Total atomization energies for a set of 31 molecules are found to agree with experimental thermochemical data to an accuracy greater than 2 kcal mol−1 in most cases. Similar agreement is achieved for ionization energies, electron and proton affinities. Residual errors are assessed for the total energies of neutral atoms.

Gaussian-4 theory

The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is assessed on the 454 experimental energies in the G305 test set [L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005)], and the average absolute deviation from experiment shows significant improvement from 1.13 kcal/mol (G3 theory) to 0.83 kcal/mol (G4 theory). The largest improvement is found for 79 nonhydrogen systems (2.10 kcal/mol for G3 versus 1.13 kcal/mol for G4). The contributions of the new features to this improvement are analyzed and the performance on different types of energies is discussed.

Gaussian‐2 theory using reduced Mo/ller–Plesset orders

Two variations of Gaussian‐2 (G2) theory are presented. In the first, referred to as G2 (MP2) theory, the basis‐set‐extension energy corrections are obtained at the 2nd order Mo/ller–Plesset (MP2) level and in the second, referred to as G2(MP3) theory, they are obtained at the MP3 level. The methods are tested out on the set of 125 systems used for validation of G2 theory [J. Chem Phys. 94, 7221 (1991)]. The average absolute deviation of the G2(MP2) and G2(MP3) theories from experiment are 1.58 and 1.52 kcal/mol, respectively, compared to 1.21 kcal/mol for G2 theory. The new methods provide significant savings in computational time and disk storage.