Accurate calculations of bound rovibrational states for argon trimer

Thermodynamic Properties of van der Waals Dimers and Trimers of Nonpolar Gases and Their Correlation with Lennard-Jones Potential Well Depths

A method of unifying the equilibrium thermodynamic properties ΔH^o and ΔG^o relating to the van der Waals dimers and trimers of 15 nonpolar gases (He-Xe, H₂, D₂, CH₄, CF₄, ethene, ethane, CO₂, SF₆, propane, and neopentane) is described. Values of ΔH^o and ΔG^o, obtained at the reduced temperature T_r = 0.7, show good correlation with the respective Lennard-Jones pair potential well depth, calculated from the monomer critical temperature and the acentric factor. Such relationships present the opportunity to estimate the van der Waals dimer and trimer thermodynamic properties of other nonpolar molecules, and examples of seven such applications are given. It is found that the enthalpies of dimerization and trimerization of the 15 gases are about 21 and 29% of the respective condensation enthalpies, providing information about the thermodynamics of small clusters in relation to liquefaction.

Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States

Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to "hit the trifecta" in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH₃CN), to a numerical convergence of accuracy 10^-2 cm^-1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm^-1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers ¹⁶O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Efficient Quantum Mechanical Calculations of Mode-Specific Tunneling Splittings upon Fundamental Excitation in the Dimer of Formic Acid

The formic acid dimer (FAD) is an important benchmark system for understanding the double hydrogen transfer process. Most recently, Zhang et al. measured a few tunneling splittings upon fundamental excitation of FAD precisely (Zhang, Y. et al. J. Chem. Phys. 2017, 146, 244306); however, relevant theoretical studies are very limited. Here, we present a multidimensional quantum dynamics study on mode-specific tunneling splittings upon fundamental excitation in FAD with an efficient theoretical scheme developed by our group in which the process-oriented basis function customization strategy is combined with the preconditioned inexact spectral transform method. Various mode-specific tunneling splittings upon fundamental excitation are systematically calculated, and interesting mode-specific excitation effects on tunneling rate are identified. In particular, the calculated tunneling splittings for the ν₂₂ and ν₂₁ states are in good agreement with experiment, and the remarkable mode-specific suppression effects upon excitation should result from that the antisymmetric vibrational modes hinder the concerted double H-transfer. The present work is helpful to acquire a better understanding of the mode-specific excitation effects on tunneling processes.

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

Several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the z-axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of ¹⁶O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O isomers combined, with rotational excitations up to J = 5 and both inversion parities (21600 coupled ro-vibrational states in total). Splittings between the states of different parities, so-called K-doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for ¹⁶O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O are in excellent agreement with literature (available for low-vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.

Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme

Double proton transfer plays an important role in biology and chemistry, such as with DNA base pairs, proteins and molecular clusters, and direct information about these processes can be obtained from tunneling splittings. Carboxylic acid dimers are prototypes for multiple proton transfer, of which the formic acid dimer is the simplest one. Here, we present efficient quantum dynamics calculations of ground-state and fundamental excitation tunneling splittings in the formic acid dimer and its deuterium isotopologues. These are achieved with a multidimensional scheme developed by us, in which the saddle-point normal coordinates are chosen, the basis functions are customized for the proton transfer process, and the preconditioned inexact spectral transform method is used to solve the resultant eigenvalue problem. Our computational results are in excellent agreement with the most recent experiments (Zhang et al., 2017; Li et al., 2019).

Exact bound rovibrational spectra of the neon tetramer

Exact quantum dynamics calculations are performed for the bound rovibrational states of the neon tetramer (Ne₄) in its ground electronic state, using pair-wise Lennard-Jones potentials and the ScalIT suite of parallel codes. The vibrational states separate into a low-lying group mostly localized to a single potential well and a higher-energy delocalized group lying above the isomerization threshold-with such a structure serving as a testament to the "intermediate" quantum nature of the Ne₄ system. To accurately and efficiently represent both groups of states, the phase-space optimized discrete variable representation (PSO-DVR) approach was used, as implemented in the ScalIT code. The resultant 1D PSO effective potentials also shed significant light on the quantum dynamics of the system. All vibrational states were computed well up into the isomerization band and labeled up to the classical isomerization threshold-defined as the addition of the classical energy of a single bond, ϵ = 24.7 cm^-1, to the quantum ground state energy. Rovibrational energy levels for all total angular momentum values in the range J = 1-5 were also computed, treating all Coriolis coupling exactly.

Statistical properties of the rovibrational bound levels for Ar2Kr

We calculate the rovibrational bound levels with total angular momentum J = 0, 1 of ⁴⁰Ar₂⁸⁴Kr trimer using the slow variable discretization method combined with the finite-element method-discrete variable representation basis. The statistical distributions of the rovibrational levels for J^Π=0^e, 1^e, and 1^o symmetries are presented and the effects of the Axilrod-Teller potential term are considered. For the 0^e and 1^e symmetries, the Axilrod-Teller term makes the spectra become fully chaotic. However, for the 1^o symmetry, statistical properties depend mainly on the coupling between K = 0 and K = 1 and the Axilrod-Teller term has a small effect.