Thermal rate constants for Mu + CH4, Mu + C2H6 and Mu + C3H8 and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C3H8 at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH4 using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

We discuss the design and implementation of StarRate, a modern-Fortran program for the calculation of chemical kinetics coupled to anharmonic vibrational perturbative treatments. The program is written in the F language, a carefully crafted subset of Fortran 95, and is conceived in an object-based programming paradigm, i.e. the set of object-oriented programming features supported by Fortran 90/95. StarRate is made up of three main modules handling the involved molecular species, the elementary reaction steps, and the whole reaction scheme. Input data are accessed through an XML interface based on a cross-code hierarchical data format granting interoperability with popular electronic-structure packages and with the graphical interface of the Virtual Multifrequency Spectrometer developed in our group. Data parsing is performed through versatile Python scripts. Test calculations on the isomerization reaction of C-cyanomethanimine using anharmonic densities of states obtained with a development version of Gaussian are reported together with an account of ongoing developments.

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

We present a method for calculating partition functions taking into account anharmonic contributions for systems involving both small-amplitude vibrations and hindered rotations. The Wang-Landau scheme is used in the first case, while two alternative schemes are used for hindered rotation based on imaginary time propagation and fitting of the exact energy levels as a function of quantum number. These two schemes are shown to be complementary in their ranges of applicability (in terms of the torsional rotational constant and the relevant potential). Partition functions for four different molecules are calculated and compared to simpler ones obtained using a harmonic model.

We describe an integrated computational strategy aimed at providing reliable thermochemical and kinetic information on the formation processes of astrochemical complex organic molecules. The approach involves state-of-the-art quantum-mechanical computations, second-order vibrational perturbation theory, and kinetic models based on capture and transition state theory together with the master equation approach. Notably, tunneling, quantum reflection, and leading anharmonic contributions are accounted for in our model. Formamide has been selected as a case study in view of its interest as a precursor in the abiotic amino acid synthesis. After validation of the level of theory chosen for describing the potential energy surface, we have investigated several pathways of the OH + CH2NH and NH2 + H2CO reaction channels. Our results show that both reaction channels are essentially barrierless (in the sense that all relevant transition states lie below or only marginally above the reactants) and once tunneling is taken into the proper account indicate that the reaction can occur under the low temperature conditions of interstellar environments.

We present a calculation of the torsional potential of the three metallocenes of the iron group, that is, ferrocene, ruthenocene, and osmocene, calculated with the GAUSSIAN program suite. Both a variational method (through computation of the exact energy levels) and our Chebyshev imaginary time propagation method are used to calculate the hindered rotation partition function, demonstrating the efficiency of the Chebyshev scheme. The transition from a semirigid through a hindered rotor to the free rotor regime is demonstrated, and the effect of the hindered rotation (as opposed to a harmonic) treatment on the thermodynamics of metallocenes is demonstrated.

Herein we report a full thermodynamic and vibrational investigation of C-cyanomethanimine isomers rooted into the Density Functional Theory (DFT) and the second-order vibrational perturbation theory (VPT2). We show that an anharmonic treatment affects dramatically the vibrational behavior of the molecules, especially thanks to the inclusion of interaction terms between the various modes. Furthermore, the equilibrium constant between the isomers, as well as the rate constant, have been obtained at both harmonic and anharmonic levels showing, as expected, slight but non-negligible differences. To support our investigation, dispersion effects have been employed.

Sturmian basis sets are increasingly finding applications to the description of atomic and molecular structure, because of their mathematical properties and their flexibility regarding the ability to describe features of specific physical problems. However, their nature and properties have not been fully exploited in quantum chemistry. In this work we present a classification of Kepler-Coulomb Sturmian sets, where notations, symmetry properties, useful formulae, and relationships are described in detail, so to provide support for their applications to physical problems. The mathematical solution of Schrodinger equation is given for these sets both in configuration and momentum space, where Sturmian eigenfunctions coincide with hyperspherical harmonics and connections between different sets manifestly appear as elements of angular momentum algebra. Applications of the considered sets and some of their generalizations are also briefly accounted for.

An effort is accounted for in the present paper to exhibit the recently actively investigated connection between the search and use of ”orbitals” as basis sets in applied quantum mechanics and current advances in the mathematics of special functions and orthogonal polynomials, which are in turn motivated by the developments of the quantum theory of angular momentum. The latter theory in modern applications forms the basis for the class of ”spin-network” algorithms. These ”orbitals” enjoy important properties regarding orthogonality and completeness. In configuration space, they are often designated as Kepler-Coulomb Sturmian orbitals, in momentum space they are intimately connected with hyperspherical harmonics. The paper contains a brief presentation including also computational results and a discussion oriented towards the numerical use of these orbitals.

The simple connection between the Slater orbitals, venerable in quantum chemistry, and the Coulomb Sturmian orbitals, more recently employed in atomic and molecular physics, is pointed out explicitly in view of the renewed interest in both as basis sets in applied quantum mechanics. Research in Slater orbitals mainly concerns multicentre, many-body integrals, whereas that on Sturmians exploits their orthonormality and completeness with no need of continuum states. An account of recent progress is outlined, also with reference to relationships between the two basis sets, and with the momentum space and hyperspherical harmonics representations.