Discrete Variable Representation Calculations Research Articles

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules.

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Quantum Calculations on a New CCSD(T) Machine-Learned Potential Energy Surface Reveal the Leaky Nature of Gas-Phase Trans and Gauche Ethanol Conformers.

Ethanol is a molecule of fundamental interest in combustion, astrochemistry, and condensed phase as a solvent. It is characterized by two methyl rotors and trans (anti) and gauche conformers, which are known to be very close in energy. Here we show that based on rigorous quantum calculations of the vibrational zero-point state, using a new ab initio potential energy surface (PES), the ground state resembles the trans conformer, but substantial delocalization to the gauche conformer is present. This explains experimental issues about identification and isolation of the two conformers. This “leak” effect is partially quenched when deuterating the OH group, which further demonstrates the need for a quantum mechanical approach. Diffusion Monte Carlo and full-dimensional semiclassical dynamics calculations are employed. The new PES is obtained by means of a Δ-machine learning approach starting from a pre-existing low level density functional theory surface. This surface is brought to the CCSD(T) level of theory using a relatively small number of ab initio CCSD(T) energies. Agreement between the corrected PES and direct ab initio results for standard tests is excellent. One- and two-dimensional discrete variable representation calculations focusing on the trans–gauche torsional motion are also reported, in reasonable agreement with experiment.

Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

Three low-lying vibrational states of molecular systems are responsible for the signals of linear and third-order nonlinear vibrational spectroscopies. Theoretical studies based on mixed quantum/classical calculations provide a powerful way to analyze those experiments. A statistically meaningful result can be obtained from the calculations by solving the vibrational Schrödinger equation over many numbers of molecular configurations. The discrete variable representation (DVR) method is a useful technique to calculate vibrational eigenstates subject to an arbitrary anharmonic potential surface. Considering the large number of molecular configurations over which the DVR calculations are repeated, the calculations are desired to be optimized in balance between the cost and accuracy. We determine a dimension of the DVR method which appears to be optimum for the calculations of the three states of molecular vibrations with anharmonic strengths often found in realistic molecular systems. We apply the numerical technique to calculate the local OH stretching frequencies of liquid water, which are well known to be widely distributed due to the inhomogeneity in molecular configuration, and found that the frequencies of the 0-1 and 1-2 transitions are highly correlated. An empirical relation between the two frequencies is suggested and compared with the experimental data of nonlinear IR spectroscopies.

Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method

In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant.

The molecular structure of and interconversion tunneling in the argon-cis-1,2-difluoroethylene complex

Guided by ab initio predictions, the structure of the gas-phase complex formed between cis-1,2-difluoroethylene and an argon atom in a pulsed molecular jet is determined using microwave spectroscopy in the 5.7-21.5 GHz region of the spectrum. This is a non-planar, symmetric species, with the argon atom located in the FCCF cavity of the difluoroethylene. The transitions in the microwave spectrum are observed to be split by an interconversion tunneling motion between the two equivalent configurations for the complex with the argon atom located either above or below the difluoroethylene molecular plane. Both one- and two-dimensional discrete variable representation calculations of the tunneling splitting using the ab initio interaction potential for the complex suggest that the barrier to interconversion is overestimated by theory.

The hierarchical expansion of the kinetic energy operator in curvilinear coordinates extended to the vibrational configuration interaction method

The hierarchical expansion of the kinetic energy operator in curvilinear coordinates presented earlier for the vibrational self-consistent field technique is extended to the vibrational configuration interaction (VCI) method. The high accuracy of the modified VCI method is demonstrated by computing first excitation energies of the H(2)O(2) molecule using an analytic potential (PCPSDE) and showing convergence to accurate results from full dimensional discrete variable representation calculations.

Tunneling splittings in water trimer by projector Monte Carlo

We demonstrate the Monte Carlo calculation of multidimensional tunnel splittings in the water trimer without the use of explicit nodal approximations. The calculations are made for the three-dimensional torsional model of the nonbonded hydrogen atom motions. We employ the projection operator imaginary time spectral evolution (POITSE) method, which requires specification of a set of projector operators. The permutation symmetry leading to exchange tunneling is incorporated into these projectors directly. We analyze the optimal choice of the real space vibrational coordinates with a comparative study of local vs nonlocal symmetry-adapted nuclear coordinates. Extraction of the lowest four sets of tunneling states yields good agreement with available discrete variable representation calculations.

A new method for calculating the rovibrational states of polyatomics with application to water dimer

A new method is developed for calculating the lowest few rovibrational states of polyatomic molecules, using the discrete variable representation (DVR). The method is an extension to the diagonalization-truncation procedure which has been used in most DVR calculations to date. It starts with a set of functions which approximately describe the wave function at a set of DVR points, and adds corrections to them by using variation-perturbation theory. This is done iteratively, after the manner of the recently developed iterative secular equation (ISE) method of Slee and LeRoy. This new ‘‘DVR-ISE’’ method can be successfully applied to molecules whose dynamics involve strong coupling between all degrees of freedom. To demonstrate this it is applied to (H2O)2 in calculations of the lowest few energy levels for intermolecular angular motion. Better convergence is obtained than was found possible in conventional finite basis calculations on the same system.

Nonlinear normal modes and local bending vibrations of H+3 and D+3

The structure of bending overtones of the H3+ and D3+ molecular ions at the energies below the barrier to linearity is analyzed using energies and wave functions from full three-dimensional discrete variable representation calculations. The lowest-in-energy states of the vibrational polyads ν2=4,5,6 are shown to follow the localization pattern of local bending modes, three equivalent-by-symmetry principal periodic trajectories of the corresponding classical two-mode system near the equilibrium.

All the bound vibrational states of H3+: A reappraisal

The 3D discrete variable representation (DVR) calculations of Henderson and Tennyson [Chem. Phys. Lett. 173, 133 (1990)] are reanalyzed to find the source of the nonvariational behavior highlighted by Carter and Meyer [J. Chem. Phys. 96, 2424 (1992)]. The discrepancy is found to be caused not by the use of incorrect boundary conditions, but by a failure of the quadrature approximation commonly used in DVR calculations. Corrected DVR calculations show variational but slow convergence. Calculations using the same intermediate vectors as the nonvariational calculations and a corrected final Hamiltonian show greatly enhanced convergence. The vibrational band origins computed with this method are converged to within 2 cm−1 up to 35 000 cm−1. A complete list of these is presented and comparisons made with previous predictions.

Gateway states and bath states in the vibrational spectrum of H +3

Vibrational band intensities are obtained from discrete variable representation calculations of eigenstates for H + 3. Transitions linking highly excited states to the ground state show large variations in intensities, with gateway states corresponding to highly excited bending motion (“horseshoes”) which leak intensity into the nearby bath states. It is suggested that these gateway states may be observable. Implications of these results for the interpretation of the infrared predissociation spectra of H + 3 are discussed.