Zlatko Bačić

Accurate localized and delocalized vibrational states of HCN/HNC

Results of the first accurate quantum calculation of the delocalized, large amplitude motion vibrational (J=0) levels of HCN/HNC, lying above the isomerization barrier, are presented. The recently developed DVR‐DGB quantum method [Z. Bacic and J. C. Light, J. Chem. Phys. 85, 4594 (1986)] is employed in this work. A model, empirical surface by Murrell et al. is used. All modes are included; the energy level calculation does not involve any approximations. Over a hundred vibrational levels are calculated accurately for this model surface. A number of them lie above the isomerization barrier; some are extensively delocalized over both HCN and HNC minima. Analysis shows that for HCN/HNC the threshold for significant delocalization is determined by the height of the vibrationally adiabatic bending barrier. In addition, the nearest neighbor level spacing distribution is obtained and compared to that of LiCN/LiNC. Various computational aspects of the DVR‐DGB approach, which is applicable to any triatomic molecul...

Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules

An adiabatic approximation for the calculation of excited vibrational (J=0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR‐ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off‐diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second‐order perturbation theory. One uni...

Exact full‐dimensional bound state calculations for (HF)2, (DF)2, and HFDF

Detailed results of the converged full‐dimensional 6D quantum calculations of the vibrational levels of (HF)2, (DF)2, and HFDF, for total angular momentum J=0, are presented. The ab initio 6D potential energy surface by Quack and Suhm was employed. This study provides a comprehensive description of the bound state properties of the HF dimer and its isotopomers, including their dissociation energies, frequencies of the intermolecular vibrations, tunneling splittings, and extent of wave function delocalization. Quantum number assignment of the calculated eigenstates by plotting different cuts through the wave functions worked rather well for (HF)2, but proved to be much harder for (DF)2 and HFDF, indicating stronger vibrational mode mixing in these species. The ground‐state tunneling splitting for the HF dimer from our exact 6D calculations, 0.44 cm−1, is very close to that from a previous 4D rigid‐rotor calculation, 0.48 cm−1 [J. Chem. Phys. 99, 6624 (1993)]. This is in disagreement with the result of a re...

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. IV : Discrete variable representation (DVR) basis functions and the analysis of accurate results for F+H2

Accurate 3D coupled channel calculations for total angular momentum J=0 for the reaction F+H2→HF+H using a realistic potential energy surface are analyzed. The reactive scattering is formulated using the hyperspherical (APH) coordinates of Pack and Parker. The adiabatic basis functions are generated quite efficiently using the discrete variable representation method. Reaction probabilities for relative collision energies of up to 17.4 kcal/mol are presented. To aid in the interpretation of the resonances and quantum structure observed in the calculated reaction probabilities, we analyze the phases of the S matrix transition elements, Argand diagrams, time delays and eigenlifetimes of the collision lifetime matrix. Collinear (1D) and reduced dimensional 3D bending corrected rotating linear model (BCRLM) calculations are presented and compared with the accurate 3D calculations.

Localized representations for large amplitude molecular vibrations

Abstract Two novel, closely related variational quantum approaches for efficient and accurate calculation of highly excited vibrational levels of triatomic molecules are presented. The two approaches employ, in slightly different ways, the discrete variable representation (DVR) and the distributed Gaussian basis (DGB) for representation of the internal degrees of freedom. The scope of their applicability is broad; they are particularly suitable for molecules having one or more large amplitude vibrations, on potential surfaces with several local minima. Although formulated in Jacobi and hyperspherical coordinates, respectively, both approaches can be implemented in any coordinate system for which suitable DVRs can be defined. The DVR allows us to define sequentially problems of lower dimensionality, whose truncated sets of eigenvectors serve as very compact, contracted basis sets for the higher dimensional problem. Other important advantages of the DVR-DGB approaches, as well as applications to molecules like LiCN/LiNC, HCN/HNC and H2O, are discussed.

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

All rovibrational levels of HCN/HNC up to ∼16 000 cm−1, relative to the HCN minimum, for J=0, 1, 2, have been calculated accurately. All internal degrees of freedom are included in these calculations, performed on the realistic, empirical potential surface by Murrel et al. [J. Mol. Spectrosc. 93, 307 (1982)]. Body‐fixed mass‐scaled Jacobi coordinates are employed, together with the discrete variable representation of the large amplitude motion (LAM) angular coordinate, and a 2‐D distributed Gaussian basis for the radial degrees of freedom. The successive diagonalization–truncation procedure results in a compact matrix representation of the full rovibrational Hamiltonian, allowing accurate and efficient determination of a large number (>350 for J=2, p=0 case) of highly excited LAM rovibrational states of HCN/HNC. This approach is suitable for a broad class of floppy, isomerizing triatomic molecules and van der Waals complexes. In addition to energy levels and wave functions, expectation values of Jacobi co...

Equilibrium structures and approximate HF vibrational red shifts for ArnHF (n=1-14) van der Waals clusters

This paper presents a theoretical study of the size evolution of equilibrium structures and approximate HF vibrational red shifts for ArnHF van der Waals clusters, with n=1–14. Pairwise additive ArnHF intermolecular potential energy surfaces were constructed from spectroscopically accurate Ar–Ar and anisotropic Ar–HF potentials. The latter depend on vibrational excitation of the HF monomer. The global and energetically close‐lying local minima of ArnHF, n=1–14, for HF v=0 and v=1, were determined using simulated annealing followed by a direct minimization scheme. For ArnHF clusters with n≤8, the lowest‐energy structure always has HF bound to the surface of the Arn subunit. In contrast, for n≥9, the global minimum of ArnHF corresponds to HF inside a cage. Ar12HF has the minimum‐energy configuration of an HF‐centered icosahedron, which appears to be unusually stable. Size dependence of the HF vibrational red shift in ArnHF (n=1–14) clusters was investigated by means of a simple approximation, where the red ...

van der Waals vibrational states of atom–large molecule complexes by a 3D discrete variable representation method: Naphthalene⋅Ar

We present an accurate and efficient method for calculating highly excited 3D van der Waals (vdW) vibrational states of structurally nonrigid M⋅R complexes between an atom R and a large, arbitrarily shaped molecule M. Our method combines the atom–molecule Hamiltonian of Brocks and van Koeven, in which Cartesian components of the vector connecting R and the center of mass of M are used as internal coordinates, with the 3D discrete variable representation (DVR) of all three intermolecular large amplitude degrees of freedom. Our 3D DVR method is aimed at highly anisotropic M⋅R complexes, in which the size of the molecule is typically larger than the average atom–molecule distance. The symmetry of the complex (if any) is exploited by constructing symmetry adapted 3D DVRs which transform under the irreducible representations of the symmetry group, and bring the Hamiltonian matrix to a block diagonal form. The 3D DVR is particularly well suited for description of excited and strongly coupled, delocalized vdW states, and internal motions on very anharmonic intermolecular potentials with multiple minima. We use this method to calculate vdW vibrational energy levels and wave functions of a floppy complex naphthalene⋅Ar. The lower‐lying vdW states are assigned by inspection of the wave function plots.

A theoretical study of vibrational mode coupling in H5O2

The vibrational mode coupling in the protonated water dimer is investigated by performing two types of quantum calculations of the vibrational levels of H5O2+ and D5O2+, utilizing the OSS3(p) potential energy surface by Ojamae et al. [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)]. One is four-dimensional (4D), treating only the central O⋯H(D)+⋯O moiety. Three of the four modes considered, the asymmetric stretch and the two bends, are largely the vibrations of the central proton, while the fourth mode is essentially the O⋯O stretching vibration. The vibrational levels of O⋯H(D)+⋯O are calculated rigorously, as fully coupled (FC), and also in an adiabatic (3+1)D approximation, where the proton asymmetric stretch is treated as adiabatically separated from the other three degrees of freedom. The second set of calculations, designated VCI, is full-dimensional, 15D; it is performed by the code MULTIMODE, which does configuration interaction (CI) calculations using a basis determined ...

He2Cl2 and He3Cl2 van der Waals clusters: A quantum Monte Carlo study

The results of the first variational and Green’s function Monte Carlo calculations of the vibrational ground states of He2Cl2 and He3Cl2 van der Waals (vdW) clusters are presented in this paper. The quantum dynamics of all internal degrees of freedom are treated exactly. The ground state wave function of He2Cl2 is characterized by means of the probability distribution functions of the intermolecular degrees of freedom, which reveal an exceptionally fluxional vdW complex. A simple model for the ground state of HenCl2 vdW clusters was developed. The zero‐point energies of He2Cl2 and He3Cl2 predicted by this model are in remarkable agreement (to within 0.6%) with the accurate results.