Andrew C. Scheiner

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

The theory for the analytic evaluation of energy gradients for coupled cluster (CC) wave functions is presented. In particular, explicit expressions for the analytic energy gradient of the CC singles and doubles (CCSD) wave function for a closed‐shell restricted Hartree–Fock reference determinant are presented and shown to scale as N6 where N is the one‐electron number of atomic basis functions for the molecular system. Thus analytic CCSD gradients are found to be of the same magnitude in computational cost as is the evaluation of analytic gradients for the configuration interaction singles and doubles (CISD) wave function. Applications of this method are presented for the water molecule and the formaldehyde molecule using a double‐ζ plus polarization (DZ+P) basis set. The CCSD equilibrium geometries, dipole moments, and, via finite differences of gradients, CCSD harmonic vibrational frequencies and infrared intensities are reported. For H2O these results are compared to analogous CISD, CISDT, CISDTQ, and...

The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results

A single and double excitation coupled cluster (CCSD) method restricted to closed‐shell single configuration reference functions is described in explicit detail. Some significant simplifications resulting from the restriction to closed‐shell systems are exploited to achieve maximum computational efficiency. Comparisons for energetic results and computational requirements are made with the single and double excitation configuration interaction (CISD) method. The specific molecules considered include N2, H2O, H3O+, H5O+2, HSOH, and s‐tetrazine (C2N4H2).

Spin contamination in density functional theory

Abstract Local density functional calculations on a series of small, neutrals radicals demonstrate that the unrestricted Kohn-Sham wave-function is much less contaminated by higher spin states than its unrestricted Hartree—Fock couterpart, even for radicals which exhibit major contamination in their standard UHF wavefunction. A study of the dissociation curves for the OH and CN radicals shows that the UKS wavefunction remains essentially spin pure out to about 1.5 times the equilibrium bond length. Some general observations regarding spin contamination in unrestricted SCF wavefunctions are presented.

The malonaldehyde equilibrium geometry: A major structural shift due to the effects of electron correlation

Complete theoretical optimizations of the equilibrium geometry of malonaldehyde have been carried out within the framework of the self‐consistent‐field (SCF) approximation. Both Huzinaga–Dunning double zeta plus polarization (DZ+P) and Pople 6–31G** basis sets have been used, resulting in very similar results. The predicted O ⋅ ⋅ ⋅ H hydrogen bond distance is 1.88 A, in poor agreement with the value 1.68 A deduced from experiment. It appears that the Hartree–Fock approximation is incapable of describing the equilibrium geometry of malonaldehyde in a qualitatively correct manner. However, second‐order perturbation theory yields a structure (O ⋅ ⋅ ⋅ H distance 1.69 A) in good agreement with experiment. The structures of the keto tautomer and the transition state for symmetric intramolecular hydrogen transfer have also been determined, as have harmonic vibrational frequencies for all stationary points.

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Beckes original three‐parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian‐type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug‐cc‐pVTZ (UCC)]. The geometries and dipole moments of over 100 first‐row and second‐row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double‐ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments.

A systematic theoretical study of harmonic vibrational frequencies: The single and double excitation coupled cluster (CCSD) method

Recently developed analytic CCSD gradient methods have been used to predict the harmonic vibrational frequencies of six molecules: CH4, NH+4, HCN, C2H2, HNC, and CO2. In every case a double zeta plus polarization (DZ+P) basis set of size C,N,O(9s5p1d/4s2p1d), H(4s1p/2s1p) was used. Previous analogous studies of H2O, H2CO, and NH3 are extended to form a statistical base of nine molecules. For these molecules 28 harmonic vibrational frequencies (out of total of 35 fundamentals) are thought to be known from experiment. The average errors with respect to experiment were found to be 9.1% (DZ+P self‐consistent field), 3.7% (DZ+P configuration interaction including single and double excitations), and 2.2% (DZ+PCCSD). These statistics should provide guidance for the use of the CCSD method in situations where experimental vibrational frequencies are not available. Infrared intensities are also compared with available experimental data.

The efficient evaluation of configuration interaction analytic energy second derivatives: Application to hydrogen thioperoxide, HSOH

We present an efficient reformulation of the analytic configuration interaction (CI) energy second derivative. Specifically, the Z‐vector method of Handy and Schaefer is used to avoid solving the second order coupled perturbed Hartree–Fock (CPHF) equations. We have incorporated translational–rotational invariance into the new method. We present a more efficient method for the evaluation of the Y matrix contribution. The procedure which has been implemented can accommodate very large basis sets and CI expansions for any general restricted Hartree–Fock (RHF) reference wave function. As a test case, we apply the new procedure to the HSOH molecule using a double zeta plus polarization basis set. This leads to 50 contracted Gaussian basis functions and 116 403 configurations in the CI expansion. Harmonic vibrational frequencies and infrared intensities are predicted for HSOH and its deuterated isotopomers. The analytic method described herein requires only 56% of the central processor unit time used by a numer...

THE EFFECT OF GRID QUALITY AND WEIGHT DERIVATIVES IN DENSITY FUNCTIONAL CALCULATIONS

Full density functional geometry optimizations on hydrogen peroxide and heptane/dimethyl pentane using six different numerical grids are presented. The grids vary in quality and gradients are calculated (1) assuming a fixed grid and no weight derivatives, and (2) with full allowance for a ‘‘moving’’ atom‐centered grid and inclusion of the weight derivatives. The results clearly demonstrate that accurate energies and geometries can be obtained with around 3500 points per atom for medium‐sized systems (up to say 30 atoms) without the necessity of including the weight derivatives. The latter only begin to influence the results for grids which are of insufficient quality to guarantee reliable values in any case.

Ordering of the O-O stretching vibrational frequencies in ozone

The ordering of ν1 and ν3 for O3 is incorrectly predicted by most theoretical methods, including some very high level methods. The first systematic electron correlation method based on one‐reference configuration to solve this problem is the coupled cluster single and double excitation (CCSD) method. However, a relatively large basis set, triple zeta plus double polarization (TZ+2P), is required. Comparison with other theoretical methods is made.

The electronic spectrum of s‐tetrazine: Structures and vibrational frequencies of the ground and excited electronic states

The ground and excited electronic states of the s‐tetrazine molecule have been studied using the methods of ab initio electronic structure theory. In particular, complete self‐consistent field (SCF) optimizations of the equilibrium structures on the X 1Ag, a 3B3u, and A 1Au(C2h)/1B3u (D2h) surfaces using both double‐ζ (DZ) and DZ+polarization (DZ+P) basis sets have been carried out. Harmonic vibrational frequencies have been analytically evaluated at these stationary points. DZ SCF results for higher excited electronic states are also reported with the optimizations on these surfaces having been restricted to D2h symmetry. Single point configuration interaction energies including single and double excitations relative to the SCF references (CISD) have been used to predict both vertical and adiabatic electronic excitation energies for all states investigated herein. In addition the Davidson correction [CISD(+Q)] and the closed shell coupled cluster singles and doubles (CCSD) method have been used to app...