Anharmonic vibrational frequencies and vibrationally averaged structures and nuclear magnetic resonance parameters of FHF−

Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory

Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear-electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein, we develop the analytic Hessian for cNEO-DFT energy with respect to the change in nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicomponent cNEO coupled-perturbed Kohn-Sham (cNEO-CPKS) equations, which describe the response of electronic and nuclear orbitals to the displacement of nuclear (expectation) positions. With the analytic Hessian, the vibrational frequencies of a series of small molecules are calculated and compared to those from conventional DFT Hessian calculations as well as those from the vibrational second-order perturbation theory (VPT2). It is found that even with a harmonic treatment, cNEO-DFT significantly outperforms DFT and is comparable to DFT-VPT2 in the description of vibrational frequencies in regular polyatomic molecules. Furthermore, cNEO-DFT can reasonably describe the proton transfer modes in systems with a shared proton, whereas DFT-VPT2 often faces great challenges. Our results suggest the importance of nuclear quantum effects in molecular vibrations, and cNEO-DFT is an accurate and inexpensive method to describe molecular vibrations.

Molecular Vibrational Frequencies within the Nuclear-Electronic Orbital Framework

A significant challenge for multicomponent quantum chemistry methods is the calculation of vibrational frequencies for comparison to experiment. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically key protons, quantum mechanically. The Born-Oppenheimer separation between the quantum and classical nuclei prevents the direct calculation of vibrational frequencies corresponding to modes composed of both types of nuclei. Herein an effective strategy for calculating the vibrational frequencies of the entire molecule within the NEO framework is devised and implemented. This strategy requires diagonalization of an extended NEO Hessian that depends on the expectation values of the quantum nuclei as well as the coordinates of the classical nuclei and is constructed with input from multicomponent time-dependent density functional theory (NEO-TDDFT). Application of this NEO-DFT(V) approach to molecular systems illustrates that it accurately incorporates the most significant anharmonic effects. This general theoretical formulation opens up a broad spectrum of new directions for multicomponent quantum chemistry.

Symmetry and dynamics of FHF− anion in vacuum, in CD2Cl2 and in CCl4. Ab initio MD study of fluctuating solvent–solute hydrogen and halogen bonds

Asymmetric solvation of FHF⁻ by halogen- and hydrogen-bonding solvents breaks the symmetry of the anion.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

Second-order many-body perturbation study of solid hydrogen fluoride under pressure

A linear-scaling, embedded-fragment, second-order many-body perturbation (MP2) method with basis sets up to aug-cc-pVTZ is applied to the antiparallel structure of solid hydrogen fluoride and deuterium fluoride under 0-20 GPa of ambient pressure. The optimized structures, including the lattice parameters and molar volume, and phonon dispersion as well as phonon density of states (DOS), are determined as a function of pressure. The basis-set superposition errors are removed by the counterpoise correction. The structural parameters at 0 GPa calculated by MP2 agree accurately with the observed, making the predicted values at higher pressures a useful pilot for future experiments. The corresponding values obtained by the Hartree-Fock method have large, systematic errors. The MP2/aug-cc-pVDZ frequencies of the infrared- and Raman-active vibrations of the three-dimensional solids are in good agreement with the observed and also justify previous vibrational analyses based on one-dimensional chain models; the non-coincidence of the infrared and Raman mode pairs can be explained as factor-group (Davydov) splitting. The exceptions are one pair of modes in the librational region, for which band assignments based on a one-dimensional chain model need to be revised, as well as the five pseudo-translational modes that exist only in a three-dimensional treatment. The observed pressure dependence of Raman bands in the stretching region, which red-shift with pressure, is accounted for by theory only qualitatively, while that in the pseudo-translational region is reproduced with quantitative accuracy. The present calculation proves to be limited in explaining the complex pressure dependence of the librational modes. The hydrogen-amplitude-weighted phonon DOS at 0 GPa is much less structured than the DOS obtained from one-dimensional models and may be more realistic in view of the also broad, structureless observed inelastic neutron scattering spectra. All major observed peaks can be straightforwardly assigned to the calculated peaks in the DOS. With increasing pressure, MP2 predicts further broadening of bands and breach of the demarcation between the pseudo-translational and librational bands.