Highly excited vibration–rotation states of floppy triatomic molecules by a localized representation method: The HCN/HNC molecule

Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method

We revisit the collocation method of Manzhos and Carrington [ J. Chem. Phys., 2016, 145, 224110] in which a distributed localized (e.g., Gaussian) basis is used to set up a generalized eigenvalue problem to compute the eigenenergies and eigenfunctions of a molecular vibrational Hamiltonian. Although the resulting linear algebra problem involves full matrices, the method provides a number of important advantages, namely, (i) it is very simple both conceptually and numerically, (ii) it can be formulated using any set of internal molecular coordinates, (iii) it is flexible with respect to the choice of the basis, (iv) no integrals need to be computed, and (v) it has the potential to significantly reduce the basis size through optimizing the placement and the shapes of the basis functions. In the present paper, we explore the latter aspect of the method using the recently introduced, and here further improved, quasi-regular grids (QRGs). By computing the eigenenergies of the four-atom molecule of formaldehyde, we demonstrate that a QRG-based distributed Gaussian basis is superior to the previously used choices.

Theoretical spectroscopic parameters for isotopic variants of HCO+ and HOC. J Chem Phys 2017;147:114111. [PMID: 28938835 DOI: 10.1063/1.4998467]

Theoretical spectroscopic parameters are derived for all isotopologues of HCO⁺ and HOC⁺ involving H, D, ¹⁶O, ¹⁷O, ¹⁸O, ¹²C, and ¹³C by means of a two-step procedure. Full-dimensional rovibrational calculations are first carried out to obtain numerically exact rovibrational energies for J = 0-15 in both parities. Effective spectroscopic constants for the vibrational ground state, ν₁, ν₂, and ν₃ are determined by fitting the calculated rovibrational energies to appropriate spectroscopic Hamiltonians. Combining our vibration-rotation corrections with the available experimental ground-state rotational constants, we also derive the new estimate for the equilibrium structure of HCO⁺, r_e(CH) = 1.091 98 Å and r_e(CO) = 1.105 62 Å, and for the equilibrium structure of HOC⁺, r_e(HO) = 0.990 48 Å and r_e(CO) = 1.154 47 Å. Regarding the spectroscopic parameters, our estimates are in excellent agreement with available experimental results for the isotopic variants of both HCO⁺ and HOC⁺: the agreement for the rotational constants B_v is within 3 MHz, for the quartic centrifugal distortion constants D_v within 1 kHz, and for the effective ℓ-doubling constants q_v within 2 MHz. We thus expect that our results can provide useful assistance in analyzing expected observations of the rare isotopologues of HCO⁺ and HOC⁺ that are not yet experimentally known.

THEORETICAL STUDIES OF $\tilde{A}{}^1 A^{\prime\prime}\to\tilde{X}{}^1 A^\prime$ RESONANCE EMISSION SPECTRA OF HCN/DCN USING SINGLE LANCZOS PROPAGATION METHOD

Using an efficient single Lanczos propagation method, we report the [Formula: see text] resonance emission spectra of HCN and DCN from a number of low-lying vibrational levels of the Ã-state manifold. Our calculations represent the first such undertaking in which a high-quality ab initio based potential energy surface of the excited (Ã1 A″) state and a [Formula: see text] transition dipole surface were used. The results show a significant improvement over previous theoretical work in reproducing experimental stimulated emission pumping spectra of HCN. The improved theory-experiment agreement is attributed to the accurate Ã-state potential energy surface, while the impact of the transition dipole function was found to be relatively minor.

New method for calculating bound states: the A(1) states of Li(3) on the spin-aligned Li(3)(1 (4)A(')) potential energy surface

In this paper, we present a calculation for the bound states of A(1) symmetry on the spin-aligned Li(3)(1 (4)A(')) potential energy surface. We apply a mixture of discrete variable representation and distributed approximating functional methods to discretize the Hamiltonian. We also introduce a new method that significantly reduces the computational effort needed to determine the lowest eigenvalues and eigenvectors (bound state energies and wave functions of the full Hamiltonian). In our study, we have found the lowest 150 energy bound states converged to less than 0.005% error, and most of the excited energy bound states converged to less than 2.0% error. Furthermore, we have estimated the total number of the A(1) bound states of Li(3) on the spin-aligned Li(3)(1 (4)A(')) potential surface to be 601.

Spectroscopy of highly excited vibrational states of HCN in its ground electronic state

An experimental technique based on a scheme of vibrationally mediated photodissociation has been developed and applied to the spectroscopic study of highly excited vibrational states in HCN, with energies between 29,000 and 30,000 cm(-1). The technique consists of four sequential steps: in the first one, a high power laser is used to vibrationally excite the sample to an intermediate state, typically (0,0,4), the nu3 mode being approximately equivalent to the C-H stretching vibration. Then a second laser is used to search for transitions between this intermediate state and highly vibrationally excited states. When one of these transitions is found, HCN molecules are transferred to a highly excited vibrational state. Third, a ultraviolet laser photodissociates the highly excited molecules to produce H and CN radicals in its A 2Pi electronic state. Finally, a fourth laser (probe) detects the presence of the CN(A) photofragments by means of an A-->B-->X laser induced fluorescence scheme. The spectra obtained with this technique, consisting of several rotationally resolved vibrational bands, have been analyzed. The positions and rotational parameters of the states observed are presented and compared with the results of a state-of-the-art variational calculation.

Discrete variable approaches to tetratomic molecules: part I: DVR(6) and DVR(3) + DGB methods

We present two discrete variable representation (DVR) based methods for the determination of the vibrational energy levels of tetratomic molecules. Both methods are designed for orthogonal internal coordinates in a body-fixed reference frame and make use of the DVR of three angular variables. The angular DVRs allow the construction of a fixed-angle three-mode Hamiltonian for the stretching vibrations. For each of the angular triples, the stretching eigenvalue problems are solved by employing 3D radial DVRs in the DVR(6) approach and real three-dimensional distributed Gaussian functions in the DVR(3) + DGB method. The angular degrees of freedom are taken sequentially into account in conjunction with a contraction scheme resulting from several diagonalization/truncation steps. Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR(3) + DGB.