Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12.

We present an implementation of analytical energy gradients for the explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections [CCSD(T)-F12]. The accuracy of the CCSD(T)-F12 analytical gradient technique is demonstrated by computing equilibrium geometries for a set of closed-shell molecules containing first- and second-row elements. Near basis-set limit equilibrium geometries are obtained with triple-zeta correlation consistent basis sets. Various approximations in the F12 treatment are compared, and the effects of these are found to be small.

Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory.

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

Analytical energy gradients for second-order multireference perturbation theory using density fitting.

We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.

Communication: extended multi-state complete active space second-order perturbation theory: energy and nuclear gradients.

The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.

A Lanczos-chain driven approach for calculating damped vibrational configuration interaction response functions.

We present an approach based on the Lanczos method for calculating the vibrational configuration interaction response functions necessary for evaluating the pure vibrational contributions to the polarizabilities and first hyperpolarizabilities of molecules. The method iteratively builds a tridiagonal representation of the central response matrix, which is subsequently used for solving the response equations. From the same chain, the response functions can be evaluated approximately for any frequency as well as using any complex damping factor. Applications to formaldehyde, cyclopropene, and uracil illustrate the concepts presented.

Vibrational absorption spectra calculated from vibrational configuration interaction response theory using the Lanczos method.

The Lanczos method is used to efficiently obtain the linear vibrational response function for all frequencies in an arbitrary interval. The complex part of the response function gives the absorption spectrum which can subsequently be analyzed. The method provides a way to obtain global information on the absorption spectrum without explicitly converging all vibrational eigenstates of the system. The tridiagonal Lanczos matrix used to obtain the response functions needs only be constructed once for each operator. Example calculations on cyclopropene and uracil are presented.

Use of reversed-phase liquid chromatography for determining the lipophilicity of alpha-aryl-N-cyclopropylnitrones.

The relationship between a reversed-phase high-performance liquid chromatography (RP-HPLC) retention parameter and various calculated log P-values of our previously synthesized alpha-aryl-N-cyclopropyl-nitrone derivatives was investigated. The RP-HPLC experiments were carried out with acetonitrile-water and methanol-water mixtures as mobile phases and with two kinds of stationary phases of different polarity. The retention parameter, log k(w) was obtained by linear extrapolation of the log k retention to pure water as the mobile phase. The calculated log P-values were C log P, ACD/log P, R log P, A log P, LogKow, X log P and M log P. Statistically, highly significant correlations were found between log k(w) and the calculated log P-values with squared correlation coefficients ranging from 0.771 (with A log P) to 0.956 (with C log P). In addition, the comparative molecular similarity indices analysis (CoMSIA) method was also applied to correlate the log k(w) retention parameter of the compounds with their molecular fields. Statistically significant CoMSIA models were obtained between log k(w) and the hydrophobic and steric molecular fields of our compounds. The CoMSIA models describe how the structure of the nitrone derivatives influences (through hydrophobic and steric interactions with the stationary phase) the chromatographic retention of the compounds.

[Fragment-based drug design using stereoisomers. A case study of analogues of the phenol group in the Bioster database]. / Fragmentum-alapú hatóanyagtervezés a bioizosztéria alkalmazásával. Esettanulmány: a fenolcsoport analogonjai a Bioster adatbázisban.

This case study examined various structural features of the 55 bioisosteric fragments of the phenol group registered in version 2002.1 of the Bioster database. The size, calculated lipophilicity and H-bond donor or acceptor character of the fragments were found to vary on a fairly wide scale. In most cases, molecular modelling calculations indicated similarities in the electrostatic potential maps of the fragments.