Efficient configuration selection scheme for vibrational second-order perturbation theory

Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals

Vibrational heat-bath configuration interaction (VHCI)-a selected configuration interaction technique for vibrational structure theory-has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm-1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.

Performance of Vibrational Self-Consistent Field Theory for Accurate Potential Energy Surfaces: Fundamentals, Excited States, and Intensities

The performance of vibrational structure calculations beyond harmonic approximation in the framework of the vibrational self-consistent field method with second-order perturbation corrections (VSCF-PT2) is investigated in conjunction with very accurate potential energy surfaces (PESs) given by various coupled-cluster electronic structure theories. The quality of anharmonic calculations depends on the accuracy of the underlying multidimensional PES obtained from its functional form, which is given by the level of electronic structure theory. Two such highest levels of typical coupled-cluster electronic structure methods, CCSD and the ″gold standard″ CCSD(T), along with their variants such as CCD, CR-CCL (completely renormalized CR-CC(2,3) approach), and CCSD(TQ) are tested for the construction of accurate anharmonic potentials without any fitting or ad hoc scaling and using cc-pVTZ basis sets. The accuracy of VSCF-PT2 theory in comparison to experimental values is tested for a series of 16 molecules with 135 fundamental bands, 64 overtones, and combination bands and also for 39 intensities. It is found that CCD and CCSD bind the potential tighter than CCSD(T) and the computed VSCF-PT2 transitions are more blue-shifted showing higher deviation from the experiment. In general, VSCF-PT2 results computed at the CCSD(T) potential offer a good cost/accuracy ratio, with the mean absolute deviation and the mean absolute percentage error with the experiment being ∼16 cm^-1 and 1.38, respectively, for fundamentals. Additionally, while the CR-CCL and CCSD(TQ) methods offer similar levels of accuracies as compared to CCSD(T), the former offers a better accuracy/cost ratio than the latter and is a suitable alternative to CCSD(T).

Stochastic simulation of anharmonic dissipation. II. Harmonic bath potentials with quadratic couplings

The workhorse simulating the dissipative dynamics is mainly based on the harmonic bath potentials together with linear system-bath couplings, but a realistic bath always assumes anharmonicity. In this work, we extend the linear dissipation model to include quadratic couplings and suggest a stochastic simulation scheme for the anharmonic dissipation. We show that the non-Gaussian noises induced by the anharmonic bath can be rigorously constructed, and the resulting stochastic Liouville equation has the same form as that for the linear dissipation model. As a preliminary application, we use this stochastic method to investigate the vibration-induced symmetry breaking in two-level electronic systems and find that the characteristic function of the non-Gaussian noises determines the absorption and fluorescence spectra.

Stochastic simulation of anharmonic dissipation. I. Linear response regime

Over decades, the theoretical study of the quantum dissipative dynamics was mainly based on the linear dissipation model. The study of the nonlinear dissipative dynamics in condensed phases, where there exist an infinite number of bath modes, is extremely difficult even if not impossible. This work put forward a stochastic scheme for the simulation of the nonlinear dissipative dynamics. In the linear response regime, the second-order cumulant expansion becomes exact to reproduce the effect of the bath on the evolution of the reduced system. Consequently, a Hermitian stochastic Liouville equation is derived without explicit treatment of the bath. Stochastic simulations for an anharmonic model illustrate that the dynamics dissipated by anharmonic bath exhibits substantial difference on temperature dependence compared to that with the Caldeira-Leggett model.

A weight averaged approach for predicting amide vibrational bands of a sphingomyelin bilayer

Infrared (IR) and Raman spectra of a sphingomyelin (SM) bilayer have been calculated for the amide I, II and A modes and the double-bonded CC stretching mode by a weight averaged approach, based on an all-atom molecular dynamics (MD) simulation and a vibrational structure calculation. Representative structures and statistical weights of SM clusters connected by hydrogen bonds (HBs) are observed in MD trajectories. After constructing smaller fragments from the SM clusters, the vibrational spectra of the target modes were calculated by normal mode analysis with a correction for anharmonicity, using density functional theory. The final IR and Raman spectra of a SM bilayer were obtained as the weight averages over all SM clusters. The calculated Raman spectrum is in excellent agreement with a recent measurement, providing a clear assignment of the peak in question observed at 1643 cm(-1) to the amide I modes of a SM bilayer. The analysis of the IR spectrum has also revealed that the amide bands are sensitive to the water content inside the membrane, since their band positions are strongly modulated by the HB between SM and water molecules. The present study suggests that the amide I band serves as a marker to identify the formation of SM clusters, and opens a new way to detect lipid rafts in the biological membrane.

Second-order many-body perturbation expansions of vibrational Dyson self-energies

Second-order many-body perturbation theories for anharmonic vibrational frequencies and zero-point energies of molecules are formulated, implemented, and tested. They solve the vibrational Dyson equation self-consistently by taking into account the frequency dependence of the Dyson self-energy in the diagonal approximation, which is expanded in a diagrammatic perturbation series up to second order. Three reference wave functions, all of which are diagrammatically size consistent, are considered: the harmonic approximation and diagrammatic vibrational self-consistent field (XVSCF) methods with and without the first-order Dyson geometry correction, i.e., XVSCF[n] and XVSCF(n), where n refers to the truncation rank of the Taylor-series potential energy surface. The corresponding second-order perturbation theories, XVH2(n), XVMP2[n], and XVMP2(n), are shown to be rigorously diagrammatically size consistent for both total energies and transition frequencies, yield accurate results (typically within a few cm(-1) at n = 4 for water and formaldehyde) for both quantities even in the presence of Fermi resonance, and have access to fundamentals, overtones, and combinations as well as their relative intensities as residues of the vibrational Green's functions. They are implemented into simple algorithms that require only force constants and frequencies of the reference methods (with no basis sets, quadrature, or matrix diagonalization at any stage of the calculation). The rules for enumerating and algebraically interpreting energy and self-energy diagrams are elucidated in detail.

First-principles calculations on anharmonic vibrational frequencies of polyethylene and polyacetylene in the Gamma approximation

The frequencies of the infrared- and/or Raman-active (k=0) vibrations of polyethylene and polyacetylene are computed by taking account of the anharmonicity in the potential energy surfaces (PESs) and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the Hartree-Fock and second-order Møller-Plesset (MP2) perturbation levels, providing one-, two-, and/or three-dimensional slices of the PES (namely, using the so-called n-mode coupling approximation with n=3), which are in turn expanded in the fourth-order Taylor series with respect to the normal coordinates. The vibrational part uses the vibrational self-consistent field, vibrational MP2, and vibrational truncated configuration-interaction (VCI) methods within the Gamma approximation, which amounts to including only k=0 phonons. It is shown that accounting for both electron correlation and anharmonicity is essential in achieving good agreement (the mean and maximum absolute deviations less than 50 and 90 cm(-1), respectively, for polyethylene and polyacetylene) between computed and observed frequencies. The corresponding values for the calculations including only one of such effects are in excess of 120 and 300 cm(-1), respectively. The VCI calculations also reproduce semiquantitatively the frequency separation and intensity ratio of the Fermi doublet involving the nu(2)(0) fundamental and nu(8)(pi) first overtone in polyethylene.