Efficient quantum calculations of vibrational states of vinylidene in full dimensionality: a scheme with combination of methods

Full-dimensional quantum calculations of vibrational states of C(2)H(2) and C(2)D(2) are performed in the high-energy region (above 20,400 cm(-1) relative to the acetylene minimum). The theoretical scheme is a combination of several methods. To exploit the full parity and permutation symmetry, the CC-HH diatom-diatom Jacobi coordinates are chosen; phase space optimization in combination with physical considerations is used to obtain an efficient radial discrete variable representation, whereas a basis contraction scheme is applied for angular coordinates. The preconditioned inexact spectral transform method combined with an efficient preconditioner is employed to compute eigenstates within a desired spectral window. The computation is efficient. More definite assignments on vinylidene states than previous studies are acquired using the normal mode projection; in particular, a consistent analysis of the nu(1) (symmetric CH stretch) state is provided. The computed vinylidene vibrational energy levels are in general good agreement with experiment, and several vinylidene states are reported for the first time.     

Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term Lanczos eigensolver

We use a contracted basis+Lanczos eigensolver approach to compute vinylidene-like vibrational states of the acetylene-vinylidene system. To overcome problems caused by loss of orthogonality of the Lanczos vectors we reorthogonalize Lanczos vector and use a coupled two-term approach. The calculations are done in CC-HH diatom-diatom Jacobi coordinates which make it easy to compute states one irreducible representation at a time. The most costly parts of the calculation are parallelized and scale well. We estimate that the vinylidene energies we compute are converged to approximately 1 cm(-1).     

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.     

Long live vinylidene! A new view of the H(2)C=C: --> HC triple bond CH rearrangement from ab initio molecular dynamics.

We present complete active space self-consistent field (CASSCF) ab initio molecular dynamics (AIMD) simulations of the preparation of the metastable species vinylidene, and its subsequent, highly exothermic isomerization to acetylene, via electron removal from vinylidene anion (D(2)C=C(-) --> D(2)C=C: --> DC triple bond CD). After equilibrating vinylidene anion-d(2) at either 600 +/- 300 K (slightly below the isomerization barrier) or 1440 K +/- 720 K (just above the isomerization barrier), we remove an electron to form a vibrationally excited singlet vinylidene-d(2) and follow its dynamical evolution for 1.0 ps. Remarkably, we find that none of the vinylidenes equilibrated at 600 K and only 20% of the vinylidenes equilibrated at 1440 K isomerized, suggesting average lifetimes >1 ps for vibrationally excited vinylidene-d(2). Since the anion and neutral vinylidene are structurally similar, and yet extremely different geometrically from the isomerization transition state (TS), neutral vinylidene is not formed near the TS so that it must live until it has sufficient instantaneous kinetic energy in the correct vibrational mode(s). The origin of the delay is explained via both orbital rearrangement and intramolecular vibrational energy redistribution (IVR) effects. Unique signatures of the isomerization dynamics are revealed in the anharmonic vibrational frequencies extracted from the AIMD, which should be observable by ultrafast vibrational spectroscopy and in fact are consistent with currently available experimental spectra. Most interestingly, of those trajectories that did isomerize, every one of them violated conventional transition-state theory by recrossing back to vinylidene multiple times, against conventional notions that expect highly exothermic reactions to be irreversible. The dynamical motion responsible for the multiple barrier recrossings involves strong mode-coupling between the vinylidene CD(2) rock and a local acetylene DCC bend mode that has been recently observed experimentally. The multiple barrier recrossings can be used, via a generalized definition of lifetime, to reconcile extremely disparate experimental estimates of vinylidene's lifetime (differing by at least 6 orders of magnitude). Last, a caveat: These results are constrained by the approximations inherent in the simulation (classical nuclear motion, neglect of rotation-vibration coupling, and restriction to C(s) symmetry); refinement of these predictions may be necessary when more exact simulations someday become feasible.     

Vibrational calculations in formaldehyde: the CH stretch system

An alternative procedure for the calculation of highly excited vibrational levels in S0 formaldehyde was developed to apply to larger molecules. It is based on a new set of symmetrized vibrational valence coordinates. The fully symmetrized vibrational kinetic energy operator is derived in these coordinates using the Handy expression [Molec. Phys. 61, 207 (1987)]. The potential energy surface is expressed as a fully symmetrized quartic expansion in the coordinates. We have performed ab initio electronic computations using GAMESS to obtain all force constants of the S0 formaldehyde quartic force field. Our large scale vibrational calculations are based on a fully symmetrized vibrational basis set, in product form. The vibrational levels are calculated one by one using an artificial intelligence search/selection procedure and subsequent Lanczos iteration, providing access to extremely high vibrational energies. In this work special attention has been given to the CH stretch system by calculating the energies up to the fifth CH stretch overtone at ∼16000 cm⁻¹, but the method has also been tested on two highly excited combination levels including other lower frequency modes.      

Accurate MRCI and CC study of the most relevant stationary points and other topographical attributes for the ground-state C(2)H(2) potential energy surface

Extensive ab initio calculations have been performed to determine the energy, geometry, vibrational frequencies, and relative energetics of all stationary points of the C(2)H(2) ground-state potential-energy surface. The geometries of acetylene and vinylidene minima as well as all transition states are reported at the CASSCF, MRCI, and CCSD(T) levels with aug-cc-pVXZ basis sets. Other more advanced levels of CC theory have also been utilized where judged adequate, mostly for check purposes. Also reported are theoretical limiting values of the energetics of the reaction, deduced from series of computations using the USTE extrapolation method. The data here reported should be valuable for modeling a single-sheeted global potential energy surface for the title system.     

Semiclassical theory for diatom-diatom collisions

A semiclassical approach to diatom-diatom collisions is presented. The method involves a classical treatment of the translational and rotational motion of both molecules. The vibrational degrees of freedom are quantized using a Morse oscillator approximation. The method is used to evaluate the accuracy of previous calculations based upon the energy-corrected harmonic-oscillator approach.     

Complete experimental rovibrational eigenenergies of HCN up to 6880 cm(-1) above the ground state

The [H,C,N] molecular system is a very important model system to many fields of chemical physics and the experimental characterization of highly excited vibrational states of this molecular system is of special interest. This paper reports the experimental characterization of all 3822 eigenenergies up to 6880 cm(-1) relative to the ground state in the HCN part of the potential surface using high temperature hot gas emission spectroscopy. The spectroscopic constants for the first 71 vibrational states including highly excited bending vibrations up to v(2) = 10 are reported. The perturbed eigenenergies for all 20 rotational perturbations in the reported eigenenergy range have been determined. The 11,070 eigenenergies up to J = 90 for the first 123 vibrational substates are included as supplement to this paper. We show that a complete ab initio rovibrational analysis for a polyatomic molecule is possible. Using such an analysis we can understand the molecular physics behind the Schro?dinger equation for problems for which perturbation theoretical calculations are no more valid. We show that the vibrational structure of the linear HCN molecule persists approximately up to the isomerization barrier and only above the barrier the accommodation of the vibrational states to the double well structure of the potential takes place.     

Structural and spectroscopic studies on 2-pyranones

Experimental methods of infrared, Raman and electronic absorption spectroscopy and DFT calculations using B3LYP functionals and 6-31G** and 6-311++G** basis sets have been used to understand the structural and spectral characteristics of 2-pyranones, 6-phenyl-4-methylsulfanyl-2-oxo-2H-pyran and 6-phenyl-4-methylsulfanyl-2-oxo-2H-pyran-3-carbonitrile in the electronic ground (S₀) and first excited (S₁) states. Information about the size, shape, charge density distribution and site of chemical reactivity of the molecules has been obtained by mapping electron density isosurface with electrostatic potential surfaces (ESP). Based on TD-DFT calculations using 6-31+G**5D basis set, an assignment of absorption peaks in the UV–VIS region has been suggested. The S₁ state is found to be a ¹(π,π*) state. A complete vibrational analysis has been attempted on the basis of experimental infrared and Raman spectra and calculated frequency and intensity of the vibrational bands and potential energy distribution over the internal coordinates. Characteristic vibrational bands of the 2-pyranone ring and methylsulfanyl and carbonyl groups have been identified.     

Rovibrational bound states of neon trimer: quantum dynamical calculation of all eigenstate energy levels and wavefunctions

Exact quantum dynamics calculations of the eigenstate energy levels and wavefunctions for all bound rovibrational states of the Ne(3) trimer (J = 0-18) have been performed using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The Ne(3) energy levels and wavefunctions were computed using a pair-wise Lennard-Jones potential. Jacobi coordinates were used for the calculations, but to identify just those states belonging to the totally symmetric irreducible representation of the G(12) complete nuclear permutation-inversion group, wavefunctions were plotted in hyperspherical coordinates. "Horseshoe" states were observed above the isomerization barrier, but the horseshoe localization effect is weaker than in Ar(3). The rigid rotor model is found to be applicable for only the ground and first excited vibrational states at low J; fitted rotational constant values are presented.     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.     

HO^3^5Cl,HO^3^7Cl,DO^3^5Cl和DO^3^7Cl的振动激发态光谱研究

本文用自洽场组态相互作用方法(SCF-CI)精确计算了次氯酸分子HOCl的振动激发态的能级以及次氯酸分子中的H和Cl分别被D和^3^7Cl取代后的HO^3^7Cl,DO^3^5Cl和DO^3^7Cl的同位素效应, 这些理论计算值与已有的实验结果吻合较好, 还预测了一些尚未观测到的谱线频率及同位素效应。     

Chemical effects of low-energy electron impact on hydrocarbons in the gas phase. IV. Methane

The present work deals with the simulated radiolysis of methane with low energy electrons (3.5 to 17.5 eV). The setup used in this study has been previously described. The influence of electron energy on the yields of the various products (hydrogen, ethylene, ethane, acetylene and propane) formed under electron impact was investigated. Striking features appear on the product appearance curves from which correlations between the observed products and the excited and ionized states of methane were deduced. The chemical reactions of reactive species formed under electron impact were analyzed. The dissociation mechanism of methane molecules excited in singlet states (9.6–10.4 eV and 11.7 eV) and in superexcited states lying just above the first ionization potential were discussed.     

Frequency dispersed transient absorption spectra of dissolved perylene: A case study using the density matrix version of the MCTDH method

A theoretical scheme is presented to calculate non-linear optical spectra of molecules in solution. Starting with electronic structure calculations of the ground and excited state, a subset of vibrational coordinates exhibiting the largest Huang–Rhys factors is assigned. It is used to set up a model Hamiltonian for density matrix multi configurational time-dependent Hartree (MCTDH) calculations. The expression derived for the dissipative part of the equation of motion goes beyond the earlier used Lindblad-form. In order to calculate the non-linear response the electric field strength is introduced into the density matrix equations used to directly determine the polarization. The whole scheme is applied to perylene as a reference case.     

Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation

An effective and general algorithm is suggested for variational vibrational calculations of N-atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the Eckart-Watson Hamiltonians of nonlinear or linear reference configuration. Second, with the help of an exact expression of curvilinear internal coordinates (e.g., valence coordinates) in terms of orthogonal, rectilinear internal coordinates (e.g., normal coordinates), any high-accuracy potential or force field expressed in curvilinear internal coordinates can be used in the calculations. Third, the matrix representation of the appropriate Eckart-Watson Hamiltonian is constructed in a discrete variable representation, in which the matrix of the potential energy operator is always diagonal, whatever complicated form the potential function assumes, and the matrix of the kinetic energy operator is a sparse matrix of special structure. Details of the suggested algorithm as well as results obtained for linear and nonlinear test cases including H(2)O, H(3) (+), CO(2), HCNHNC, and CH(4) are presented.     

Internal coordinate density of state from molecular dynamics simulation

The vibrational density of states (DoS), calculated from the Fourier transform of the velocity autocorrelation function, provides profound information regarding the structure and dynamic behavior of a system. However, it is often difficult to identify the exact vibrational mode associated with a specific frequency if the DoS is determined based on velocities in Cartesian coordinates. Here, the DoS is determined based on velocities in internal coordinates, calculated from Cartesian atomic velocities using a generalized Wilson's B ‐matrix. The DoS in internal coordinates allows for the correct detection of free dihedral rotations that may be mistaken as hindered rotation in Cartesian DoS. Furthermore, the pronounced enhancement of low frequency modes in Cartesian DoS for macromolecules should be attributed to the coupling of dihedral and angle motions. The internal DoS, thus deconvolutes the internal motions and provides fruitful insights to the dynamic behaviors of a system. © 2015 Wiley Periodicals, Inc.