Ag vibrational levels of cyclobutadiene on a new potential energy surface

GVB /[5s3p1d/3s1p] energies were calculated for 31 geometries of cyclobutadiene in the D_2h point group. These geometries differed in the values of the symmetrized internal coordinates for two CC stretching and one CCH bending modes. The data points were fitted to the expansions of in powers of . Variational calculations provided the following energies of the lowest A_g vibrational levels (with respect to the vibrational ground state): 4.4; 1161.2; 1162.3; 1304.0; 1322.8; 1920.3; and 1991.0 cm^?1.     

Potential energy surface and highly excited vibrational lines of NO2 via algebraic approach

The algebraic Hamiltonian of NO₂ is optimized using U(4) algebra via fitting to 102 observed vibrational lines. The RMS error of the fitting is 2.39 cm^?1. We calculated highly excited vibrational energy levels using this optimized Hamiltonian, and then obtained the potential energy surface for the electronic ground state by using the classical limit of the U(4) algebraic Hamiltonian. We also calculated the dissociation energies, the force constants etc. Our results are in good agreement with the other theoretical results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

An ab initio potential energy surface and vibrational energy levels of ZnH2

A three‐dimensional potential energy surface of the electronic ground state of ZnH₂ (${X}^1\sum _g^ +$ ) molecule is constructed from more than 7500 ab initio points calculated at the internally contracted multireference configuration interaction with the Davidson correction (icMRCI+Q) level employing large basis sets. The calculated relative energies of various dissociation reactions are in good agreement with the previous theoretical/experimental values. Low‐lying vibrational energy levels of ZnH₂, ZnD₂, and HZnD are calculated on the three‐dimensional potential energy surface using the Lanczos algorithm, and found to be in good agreement with the available experimental band origins and the previous theoretical values. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

An ab initio potential energy surface and vibrational states of MgH2(1(1)A')

A three-dimensional global potential energy surface for the ground electronic state of MgH(2) is constructed from more than 3000 ab initio points calculated using the internally contracted multireference configuration interaction method with the Davidson correction at the complete basis set limit. Low-lying vibrational energy levels of MgH(2) and MgD(2) are calculated using the Lanczos algorithm, and found to be in good agreement with known experimental band origins. The majority of the vibrational energy levels up to 8000 cm(-1) are assigned with normal mode quantum numbers. However, our results indicate a gradual transition from a normal mode regime for the stretching vibrations at low energies to a local mode regime near 7400 cm(-1), as evidenced by a decreasing energy gap between the (n(1),0,0) and (n(1)-1,0,1) vibrational states and bifurcation of the corresponding wave functions.     

A realistic double many-body expansion potential energy surface for SO2(X1A') from a multiproperty fit to accurate ab initio energies and vibrational levels

A single-valued double many-body expansion potential energy surface (DMBE I) recently obtained for the ground electronic state of the sulfur dioxide molecule by fitting correlated ab initio energies suitably corrected by scaling the dynamical correlation energy is now refined by fitting simultaneously available spectroscopic levels up to 6886 cm(-1) above the minimum. The topographical features of the novel potential energy surface (DMBE II) are examined in detail, and the method is emphasized as a robust route to fit together state-of-the-art theoretical calculations and spectroscopic measurements using a single fully dimensional potential form.     

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.     

Rotational state-dependent mixings between resonance states of vibrationally highly excited DCO (X2A')

Rotational state-dependent mixings between highly excited resonance states of DCO (X (2)A(')) were investigated by stimulated emission pumping spectroscopy via a series of intermediate rotational levels in the B (2)A(') electronic state of the radical. Two examples for such interactions, between pairs of accidentally nearly degenerate vibrational states at energies of E(v) approximately 6450 and E(v) approximately 10 060 cm(-1), respectively, were analyzed in detail. Deperturbations of the measured spectra provided the zeroth-order vibration-rotation term energies, widths, and rotational constants of the states and the absolute values of the vibrational coupling matrix elements. The coupled states turned out to have very different A rotational constants so that their mixings switch on or off as they are tuned relative to each other as function of the K(a) rotational quantum number. The respective zeroth-order states could be assigned to different interlaced vibrational polyads. Thus, when two states belonging to different polyads are accidentally nearly isoenergetic, even very weak interpolyad interactions may start to play important roles. The derived interpolyad coupling elements are small compared to the typical intrapolyad coupling terms so that their influences on the vibrational term energies are small. However, large effects on the widths (i.e., decay rates) of the states can be observed even from weak coupling terms when a narrow, long-lived state is perturbed by a broad, highly dissociative state. This influence contributes to the previously observed strong state-to-state fluctuations of the unimolecular decay rates of the DCO radical as function of vibrational excitation. Similar mechanisms are likely to promote the transition to "statistical" rates in many larger molecules.     

The semiclassical self-consistent-field (SC-SCF) approach to energy levels of coupled vibrational modes. II. The semiclassical state-interaction procedure

A method for obtaining energy levels of coupled vibrational modes is described, that utilizes a state-interaction approach combined with semiclassical approximations. The method starts with a semiclassical self-consistent-field calculation of the coupled problem, and uses the eigenstates of the resulting Hartree-like separable SCF vibrational hamiltonian to define a basis set of Hartree products in which the full vibrational hamiltonian is represented and diagonalized. Matrix elements of any interaction potential between single-mode states are approximated semiclassically as the Fourier component of the interaction at the frequency corresponding to the SCF eigenvalue difference. A Fourier-component expression can also be given for the overlap between non-orthogonal single mode states. Thus no wavefunctions ever need to be defined. Application to a sample two-mode problem shows that the method is highly accurate. Further possible applications, in particular to intramolecular rate calculations are noted.     

Quantum mechanical and quasiclassical trajectory scattering calculations for the C(1D) + H2 reaction on the second excited 1 1A" potential energy surface

Time-independent quantum mechanical (QM) and quasiclassical trajectory (QCT) scattering calculations have been carried out for the C(1D) + H2 --> CH + H reaction at a collision energy of 80 meV on a newly developed ab initio potential energy surface [B. Bussery-Honvault et al., Phys. Chem. Chem. Phys. 7, 1476 (2005)] of 1 1A" symmetry, corresponding to the second singlet state 1 1B1 of CH2. A general good agreement has been found between the QM and QCT rotational distributions and differential cross sections (DCSs). In both cases, DCSs are strongly peaked in the forward direction with a small contribution in the backward direction in contrast with those obtained on the 1 1A' surface, which are nearly symmetric. Rotational distributions obtained on the 1 1A" surface are somewhat colder than those calculated on the 1 1A' surface. The specific dynamics and the contribution of the 1 1A" surface to the overall reactivity of this system are discussed.     

A reliable ab initio potential energy surface and vibrational states for the ground electronic state of HgH2(X1Sigma+g)

A three-dimensional global potential energy surface for the ground (X (1)Sigma(+)(g))electronic state of HgH(2) is constructed from more than 13,00 ab initio points. These points are generated using an internally contracted multireference configuration interaction method with the Davidson correction and a large basis set. Low-lying vibrational energy levels of HgH(2), HHgD, and HgD(2) calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins. The majority of the vibrational energy levels up to 9000 cm(-1) are assigned with normal mode quantum numbers. Our results indicate a gradual transition for the stretching vibrations from the normal mode regime at low energies to the local mode regime near 9000 and 8000 cm(-1) for HgH(2) and HgD(2), respectively, as evidenced by a decreasing energy gap between the (0,0,n(3)) and (1,0,n(3)-1) vibrational states and bifurcation of the corresponding wave functions.     

Theoretical investigation of highly excited vibrational states in DFCO: calculation of the out-of-plane bending states and simulation of the intramolecular vibrational energy redistribution

A previously developed modified Davidson scheme [C. Iung and F. Ribeiro, J. Chem. Phys. 121, 174105 (2005)] is applied to compute and analyze highly excited (nu2,nu6) eigenstates in DFCO. The present paper is also devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) initiated by an excitation of the out-of-plane bending vibration (nnu6, n=2,4,6, . . . ,18, and 20). The multiconfiguration time-dependent Hartree method is exploited to propagate the corresponding six-dimensional wave packets. A comprehensive comparison with experimental data as well as with previous simulations of IVR in HFCO [G. Pasin et al. J. Chem. Phys. 124, 194304 (2006)] is presented.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li_2H

A 285-pomt multi-reference configuration-interaction involving single and double excitations ( MRS DCI) potential energy surface for the electronic ground state of L12H is determined by using 6-311G (2df,2pd)basis set.A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a x2 of 4.64×106 The equn librium geometry occurs at Rc=0.172 nm and,LiHL1=94.10°.The dissociation energy for reaction I2H(2A)→L12(1∑g)+H(2S) is 243.910 kJ/mol,and that for reaction L12H(2A')→HL1(1∑) + L1(2S) is 106.445 kl/mol The inversion barrier height is 50.388 kj/mol.The vibrational energy levels are calculated using the discrete variable representation (DVR) method.     

Ab initio potential energy surface and excited vibrational states for the electronic ground state of Li2H

A 285-point multi-reference configuration-interaction involving single and double excitations (MRS-DCI) potential energy surface for the electronic ground state of Li₂H is determined by using 6-311G (2df, 2pd) basis set. A Simons-Parr-Finlan polynomial expansion is used to fit the discrete surface with a X² of 4.64 × 10^-6. The equilibrium geometry occurs at R_e =0.172 nm and <LiHLi =94.10. The dissociation energy for reaction Li₂H(²A)⇑ Li₂(¹⌆_g)+H(²S) is 243.910 kJ/mol. and that for reaction Li₂H(²A)⇑HLi(¹be)+Li(²S) is 106.445 kJ/mol. The inversion barrier height is 50.388 kJ/mol. The vibrational energy levels are calculated using the discrete variable representation (DVR) method. Project supported by the National Natural Science Foundation of China (grant No. 29673029) and by the Special Doctoral Research Foundation of the State Education Commission of China.     

A first-principles potential energy surface and vibrational states for hydrogen on Cu(100)

Density-functional theory calculations based on plane-wave expansion and pseudopotential treatment were carried out for atomic hydrogen on a rigid Cu(100) surface. A global potential energy surface was then obtained by using a three-dimensional spline interpolation. It is found that the minimum of the potential is located at the fourfold hollow site with a diffusion barrier of 88 meV at the bridge site. The vibrational states of atomic hydrogen and deuterium on the Cu(100) surface were calculated on the potential surface. Our calculations show that the vibrational states A(1) (0), A(1) (1), E(1), and B(2) (1) of H/Cu(100) exhibit strong localized character and very narrow band widths, whereas other excited vibrational states have considerable delocalized character and broad band widths. The vibrational frequency of 71.2 (51.5) meV for H(D) in the perpendicular direction obtained in this study is in good agreement with the experimentally observed value of 70 (52) meV.     

A reliable new three-dimensional potential energy surface for H(2)-Kr

An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.     

Highly excited vibrational levels of triatomic molecule N2O: U(4) algebraic model

In the U(4) algebraic framework, the triatomic molecules are of U₁(4) ? U₂(4) dynamical symmetry. A molecular Hamiltonian is constructed including the third‐order conbination of the invariant operators. Within this framework, the highly vibrational energy levels of the linear triatomic nitrous oxide molecule, including both bending and stretching vibrations, are studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A new ab initio potential energy surface for studying vibrational relaxation in NO(v) + NO collisions

A new ab initio potential energy surface for the ground state of the NO-NO system has been calculated within a reduced dimensionality model. We find an unusually large vibrational dependence of the interaction potential which explains previous spectroscopic observations. The potential can be used to model vibrational energy transfer, and here we perform quantum scattering calculations of the vibrational relaxation of NO(v). We show that the vibrational relaxation for v = 1 is 4 orders of magnitude larger than that for the related O(2)(v) + O(2) system without having to invoke nonadiabatic mechanisms as had been suggested in the past. For highly vibrationally excited states, we predict a strong dependence of the rates on the vibrational quantum number as has been observed experimentally, although there remain important quantitative differences. The importance of a chemically bound isomer on the relaxation mechanism is analyzed, and we conclude it does not play a role for the values of v considered in the experiment. Finally, the intriguing negative temperature dependence of the vibrational relaxation rate constants observed in experiments was studied using an statistical model to include the presence of many asymptotically degenerate spin-orbit states.     

Study of the C(3P) + OH(X2Pi) --> CO(X1Sigma(g)+) + H(2S) reaction: a fully global ab initio potential energy surface of the X2A' state

The C((3)P) + OH(X (2)Pi) --> CO(X (1)Sigma(g)(+)) + H((2)S) reaction has been investigated by ab initio electronic structure calculations of the X(2)A' state based on the multireference (MR) internally contracted single and double configuration interaction (SDCI) method plus Davidson correction (+Q) using Dunning aug-cc-pVQZ basis sets. In particular, the multireference space is taken to be a complete active space (CAS). Improvement over previously proposed potential energy surfaces for HCO/COH is obtained in the sense that present surface describes also the potential part where the CO interatomic distance is large. A large number of geometries (around 2000) have been calculated and analytically fitted using the reproducing kernel Hilbert space (RKHS) method of Ho and Rabitz both for the two-body and three-body terms following the many-body decomposition of the total electronic energies. Results show that the global reaction is highly exothermic ( approximately 6.4 eV) and barrierless (relative to the reactant channel), while five potential barriers are located on this surface. The three minima and five saddle points observed are characterized and found to be in good agreement with previous work. The three minima correspond to the formation of HCO and COH complexes and to the CO + H products, with the COH complex being a metastable minimum relative to the product channel. The five saddle points correspond to potential barriers for both the dissociation/formation of HCO and COH into/from CO + H, to barriers for the isomerization of HCO into COH and to barriers for the inversion of HCO and COH through their respective linear configuration.     

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne)

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.     

Three rotor potential energy scans, conformational equilibrium constants and vibrational analysis of 3-fluoro-1-propanol CH(2)FCH(2)CH(2)OH

The conformational stability and the three rotor internal rotations in 3-fluoro-1-propanol were investigated by the DFT-B3LYP/6-311+G** and the ab initio MP2/6-311+G** levels of theory. The calculated potential energy curves of the molecule at both levels of theory were consistent with complex conformational equilibria of about 12 minima, all of which were predicted to have real frequencies at both the B3LYP and the MP2 levels. The lowest energy minimum in the potential curves of 3-fluoro-1-propanol was predicted to correspond to the Gauche-gauche-trans (Ggt) conformer in excellent agreement with microwave and electron diffraction results. The equilibrium constants for the conformational interconversion of the molecule were calculated and found to correspond to an equilibrium mixture of about 33% Ggt, 14% Ggg1 and 13% Gg1g and about 43% Ggt, 12% Ggg1 and 10% Gg1g distribution by the B3LYP/6-311+G** and the MP2/6-311+G** calculations, respectively, at 298.15K. The vibrational frequencies of each molecule in its three stable forms were computed at B3LYP level and complete vibrational assignments were made based on normal coordinate calculations and comparison with experimental data of the molecule.