Towards black-box calculations of tunneling splittings obtained from vibrational structure methods based on normal coordinates

A convenient set of vibrational coordinates for 2D calculation of the tunneling splittings of the ground state and some excited vibrational states for the inversion motion in H3O+, H3O-, and H3O

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling of the oxygen atom in the H₃O⁺, H₃O^- ions and in the H₃O radical are analyzed by numerically solving the vibrational Schrödinger equation of restricted (2D) dimensionality. As two vibrational coordinates, we used 1) the distance of the oxygen atom from the plane of a regular triangle formed by three hydrogen atoms and 2) a symmetry coordinate composed of three distances between chemically non-bonded hydrogen atoms. The kinetic energy operator in this case takes the simplest form. The 2D potential energy surface (PES) in the given coordinates was calculated for H₃O⁺ at the CCSD(T)/aug-cc-pVTZ and CCSD(T)-F12/cc-pVTZ-F12 levels of theory. The same 2D PES for the H₃O^- anion and H₃O radical were calculated at the CCSD(T)/aug-cc-pVQZ, CCSD(T)/d-aug-cc-pVQZ and UCCSD(T)/aug-cc-pVQZ, UCCSD(T)/d-aug-cc-pVQZ levels of theory, respectively. The tunneling splittings were calculated for the cations H₃¹⁶O⁺, D₃¹⁶O⁺, T₃¹⁶O⁺, H₃¹⁸O⁺, D₃¹⁸O⁺, T₃¹⁸O⁺. The tunneling splittings for the H₃O^-, D₃O^-, T₃O^- anions and H₃O, D₃O, T₃O radicals were calculated for the first time. The results of calculations demonstrate good agreement with experimental values of the tunneling splittings in the ground state and in some excited vibrational states of the H₃¹⁶O⁺ and D₃¹⁶O⁺ cations.

Instanton calculations of tunneling splittings in chiral molecules

We report the ground state tunneling splittings (ΔE_± ) of a number of axially chiral molecules using the ring-polymer instanton (RPI) method (J. Chem. Phys., 2011, 134, 054109). The list includes isotopomers of hydrogen dichalcogenides H₂ X₂ (X = O, S, Se, Te, and Po), hydrogen thioperoxide HSOH and dichlorodisulfane S₂ Cl₂ . Ab initio electronic-structure calculations have been performed on the level of second-order Møller-Plesset perturbation (MP2) theory either with split-valance basis sets or augmented correlation-consistent basis sets on H, O, S, and Cl atoms. Energy-consistent pseudopotential and corresponding triple zeta basis sets of the Stuttgart group are used on Se, Te, and Po atoms. The results are further improved using single point calculations performed at the coupled cluster level with iterative singles and doubles and perturbative triples amplitudes. When available for comparison, our computed values of ΔE_± are found to lie within the same order of magnitude as values reported in the literature, although RPI also provides predictions for H₂ Po₂ and S₂ Cl₂ , which have not previously been directly calculated. Since RPI is a single-shot method which does not require detailed prior knowledge of the optimal tunneling path, it offers an effective way for estimating the tunneling dynamics of more complex chiral molecules, and especially those with small tunneling splittings.

Tunneling splittings of vibrationally excited states using general instanton paths

A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [J. Chem. Phys. 122, 124311 (2005)] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improves the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.

On the separability of large-amplitude motions in anharmonic frequency calculations

Nuclear vibrational theories based upon the Watson Hamiltonian are ubiquitous in quantum chemistry, but are generally unable to model systems in which the wavefunction can delocalise over multiple energy minima, i.e. molecules that have low-energy torsion and inversion barriers. In a 2019 Chemical Reviews article, Puzzarini et al. note that a common workaround is to simply decouple these problematic modes from all other vibrations in the system during anharmonic frequency calculations. They also point out that this approximation can be "ill-suited", but do not quantify the errors introduced. In this work, we present the first systematic investigation into how separating out or constraining torsion and inversion vibrations within potential energy surface (PES) expansions affects the accuracy of computed fundamental wavenumbers for the remaining vibrational modes, using a test set of 19 tetratomic molecules for which high quality analytic potential energy surfaces and fully-coupled anharmonic reference fundamental frequencies are available. We find that the most effective and efficient strategy is to remove the mode in question from the PES expansion entirely. This introduces errors of up to +10 cm-1 in stretching fundamentals that would otherwise couple to the dropped mode, and ±5 cm-1 in all other fundamentals. These errors are approximately commensurate with, but not necessarily additional to, errors due to the choice of electronic structure model used in constructing spectroscopically accurate PES.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Locating Instantons in Calculations of Tunneling Splittings: The Test Case of Malonaldehyde

The recently developed ring-polymer instanton (RPI) method [J. Chem. Phys. 2011, 134, 054109] is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. The key step is locating the instanton tunneling-path at zero temperature. Here, we show that techniques previously designed for locating instantons in finite-temperature rate calculations can be adapted to the RPI method, where they become extremely efficient, reducing the number of potential energy calls by 2 orders of magnitude. We investigate one technique that employs variable time steps to minimize the action integral, and two that employ equally spaced position steps to minimize the abbreviated (i.e., Jacobi) action integral, using respectively the nudged elastic band (NEB) and string methods. We recommend use of the latter because it is parameter-free, but all three methods give comparable efficiency savings. Having located the instanton pathway, we then interpolate the instanton path onto a fine grid of imaginary time points, allowing us to compute the fluctuation prefactor. The crucial modification needed to the original finite-temperature algorithms is to allow the end points of the zero-temperature instanton path to describe overall rotations, which is done using a standard quaternion algorithm. These approaches will allow the RPI method to be combined effectively with expensive potential energy surfaces or on-the-fly electronic structure methods.

Prediction of Intramolecular Polarization of Aromatic Amino Acids Using Kriging Machine Learning

Present computing power enables novel ways of modeling polarization. Here we show that the machine learning method kriging accurately captures the way the electron density of a topological atom responds to a change in the positions of the surrounding atoms. The success of this method is demonstrated on the four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine. A new technique of varying training set sizes to vastly reduce training times while maintaining accuracy is described and applied to each amino acid. Each amino acid has its geometry distorted via normal modes of vibration over all local energy minima in the Ramachandran map. These geometries are then used to train the kriging models. Total electrostatic energies predicted by the kriging models for previously unseen geometries are compared to the true energies, yielding mean absolute errors of 2.9, 5.1, 4.2, and 2.8 kJ mol(-1) for histidine, phenylalanine, tryptophan, and tyrosine, respectively.