Stochastic many-body perturbation theory for anharmonic molecular vibrations

Efficiently Calculating Anharmonic Frequencies of Molecular Vibration by Molecular Dynamics Trajectory Analysis

Two efficient methods, the Eckart frame algorithm and the multiorder derivative algorithm, for vibrational frequency calculation directly based on the raw data of atomic trajectory from the state-of-the-art first-principles molecular dynamics simulation are presented. The Eckart frame approach is robust to retrieve the full set of anharmonic fundamental frequencies of any molecule from the atomic trajectory for a sufficiently long molecular dynamics simulation at a temperature close to 0 K. In addition to the fundamental vibrational frequencies, the multiorder derivative approach is universal for the calculations of vibrational frequencies based on the molecular dynamics result in a wide range of temperatures. The accuracy, efficiency, and applicability of these two methods are demonstrated through several successful examples in calculating the anharmonic fundamental vibrational frequencies of methane, ethylene, water, and cyclobutadiene.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Fundamental frequency from classical molecular dynamics

We give a theoretical validation for calculating fundamental frequencies of a molecule from classical molecular dynamics (MD) when its anharmonicity is small enough to be treated by perturbation theory. We specifically give concrete answers to the following questions: (1) What is the appropriate initial condition of classical MD to calculate the fundamental frequency? (2) From that condition, how accurately can we extract fundamental frequencies of a molecule? (3) What is the benefit of using ab initio MD for frequency calculations? Our analytical approaches to those questions are classical and quantum normal form theories. As numerical examples we perform two types of MD to calculate fundamental frequencies of H2O with MP2/aug-cc-pVTZ: one is based on the quartic force field and the other one is direct ab initio MD, where the potential energies and the gradients are calculated on the fly. From those calculations, we show comparisons of the frequencies from MD with the post vibrational self-consistent field calculations, second- and fourth-order perturbation theories, and experiments. We also apply direct ab initio MD to frequency calculations of C-H vibrational modes of tetracene and naphthalene. We conclude that MD can give the same accuracy in fundamental frequency calculation as second-order perturbation theory but the computational cost is lower for large molecules.