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.

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.

Singlet and triplet electronic excitation energies have been calculated for Ne, CH(2), C(2), N(2), and H(2)O using the Monte Carlo configuration interaction (CI) method. We find that excitation energies can be predicted to within a few tens of meV of full CI (FCI) results using expansions consisting of only a few thousand configuration state functions as compared to the O(10(8)) configurations occurring in the corresponding FCI expansions. The method provides a consistently accurate and balanced description of electronic excitations with accuracy for small molecular systems comparable to the equation-of-motion coupled cluster method with full triples.

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.

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.

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.

Various preconditioners and eigenvector targeting strategies in combination with the Davidson and Olsen methods are presented for solving eigenvalue equations encountered in vibrational configuration interaction, its response generalization, and vibrational coupled cluster response theory. The targeting methods allow significant flexibility and robustness in computing selected vibrational states, which are particularly important in the often occurring but nontrivial cases of near degeneracies. We have investigated the effect of a mode-excitation level-based generally applicable preconditioning scheme aiming to improve the robustness of the more standard diagonal preconditioning method. Although increasing convergence rates may be achieved in general through a hierarchy of these preconditioners, the strategy is not always beneficial in terms of CPU time. Features of the methods are demonstrated in calculations of the overtone vibrational states of formaldehyde and the fundamental states of vinyl fluoride, vinyl chloride, vinyl bromide, and naphthalene.

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.