A generalised 17-state vibronic-coupling Hamiltonian model for ethylene

In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, "The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation," Chem. Phys. 377, 30-45 (2010); and ibid. 382, 132 (2011) (Erratum)], we investigated the electronic structure of ethylene (ethene, C(2)H(4)) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.     

Effect of the overall rotation on the cis-trans isomerization of HONO induced by an external field

Rovibrational eigenenergies of HONO are computed and compared to experimental energies available in the literature. For their computation, we use a previously developed potential energy surface (PES) and a newly derived exact kinetic energy operator (KEO) including the overall rotation for a tetra-atomic molecule in non-orthogonal coordinates. In addition, we use the Heidelberg Multi-Configuration Time-Dependent Hartree (MCTDH) package. We compare the experimental rovibrational eigenvalues of HONO available in the literature with those obtained with MCTDH and a previously developed potential energy surface (PES) [F. Richter et al., J. Chem. Phys., 2004, 120, 1306.] for the cis geometry. The effect of the overall rotation on the process studied in our previous work on HONO [F. Richter et al., J. Chem. Phys., 2007, 127, 164315.] leading to the cis→trans isomerization of HONO is investigated. This effect on this process is found to be weak.     

Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations

A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.     

Symmetry broken self-consistent field approximation for coupled oscillators

A self-consistent field approximation allowing for a change of coordinates is applied to a model of two coupled oscillators considered by Davis and Heller [J. Chem. Phys. 75 , 246 (1981)]. The model accounts well for the unsymmetrical nonstationary states involved in the quantum dynamical tunneling phenomenon.     

An H/D isotopic substitution study of the H5O2+.Ar vibrational predissociation spectra: exploring the putative role of Fermi resonances in the bridging proton fundamentals

To clarify the nature of the motions contributing to the observed multiplet structures in the low-energy (900-1800 cm-1) vibrational spectrum of the H5O2+ "Zundel" ion, we report the evolution of its vibrational fingerprint with sequential H/D isotopic substitution in a predissociation study of the Ar complexes. Of particular interest is the D4HO2+ complex, which displays a single intense band in the vicinity of the asymmetric OHO stretch of the bridging proton, in contrast to the more complex multiplet observed for both H5O2+ and D5O2+ isotopologues. These intensity patterns are consistent with the recent assignment of the bridging proton band's doublet in the H5O2+.Ne spectrum to a 2 x 2 Fermi resonance interaction between the shared proton stretch and a complex background level primarily derived from the O-O stretch together with two quanta of the wagging vibration involving the pyramidal deformations of the flanking H2O groups (Vendrell, O.; Gatti, F.; Meyer, H.-D. Angew. Chem., Int. Ed. 2007, 46, 6918). In addition, the observed trends rule out assignment of the approximately 1800 cm-1 feature in H5O2+ to a combination band of the bridging proton vibration with the O-O stretch, providing a secure foundation for the previously reported scheme that attributes this band to the out-of-phase intramolecular bending fundamental. The observed feature occurs at an unusually high energy for typical HOH bends, however, and we explore the participation of the bridging proton in these eigenstates by following how the calculated harmonic spectrum evolves when artificially large masses are assigned to the proton. The empirical assignments are supported by anharmonic estimates of the isotope shifts evaluated by the diffusion Monte Carlo method.     

Ab initio quantum dynamical study of photoinduced ring opening in furan

The nonadiabatic photoinduced ring opening occurring in the two lowest excited singlet states of furan is investigated theoretically, using wave-packet propagation techniques. The underlying multidimensional potential energy surfaces (PESs) are obtained from ab initio computations, using the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD), reported in earlier recent work [E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Ko?ppel, J. Chem. Phys. 133, 164309 (2010)]. Up to five nuclear degrees of freedom are considered in the quantum dynamical treatment. Four of them represent in-plane motion for which the electronic states in question (correlating with the valence (1)B(2)(V) and Rydberg (1)A(2)(3s) states at the C(2v) ground-state molecular configuration) have different symmetries, A(') and A('), respectively. The fifth mode, representing out-of-plane bending of the oxygen atom against the carbon-atom plane, leads to an interaction of these states, as is crucial for the photoreaction. The nonadiabatic coupling and conical intersection cause an electronic population transfer on the order of ～10 fs. Its main features, and that of the wave-packet motion, are interpreted in terms of properties of the PES. The lifetime due to the ring-opening process has been estimated to be around 2 ps. The dependence of this estimate on the nuclear degrees of freedom retained in the computations is discussed.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

Potential energy surface and rovibrational calculations for the Mg+-H2 and Mg+-D2 complexes

A three-dimensional potential energy surface is developed to describe the structure and dynamical behavior of the Mg(+)-H(2) and Mg(+)-D(2) complexes. Ab initio points calculated using the RCCSD(T) method and aug-cc-pVQZ basis set (augmented by bond functions) are fitted using a reproducing kernel Hilbert space method [Ho and Rabitz, J. Chem. Phys. 104, 2584 (1996)] to generate an analytical representation of the potential energy surface. The calculations confirm that Mg(+)-H(2) and Mg(+)-D(2) essentially consist of a Mg(+) atomic cation attached, respectively, to a moderately perturbed H(2) or D(2) molecule in a T-shaped configuration with an intermolecular separation of 2.62 A? and a well depth of D(e) = 842 cm(-1). The barrier for internal rotation through the linear configuration is 689 cm(-1). Interaction with the Mg(+) ion is predicted to increase the H(2) molecule's bond-length by 0.008 A?. Variational rovibrational energy level calculations using the new potential energy surface predict a dissociation energy of 614 cm(-1) for Mg(+)-H(2) and 716 cm(-1) for Mg(+)-D(2). The H-H and D-D stretch band centers are predicted to occur at 4059.4 and 2929.2 cm(-1), respectively, overestimating measured values by 3.9 and 2.6 cm(-1). For Mg(+)-H(2) and Mg(+)-D(2), the experimental B and C rotational constants exceed the calculated values by ～1.3%, suggesting that the calculated potential energy surface slightly overestimates the intermolecular separation. An ab initio dipole moment function is used to simulate the infrared spectra of both complexes.     

Dynamic coupling between coordinates in a model for biomolecular isomerization

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C(7eq)-->alpha(R) transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.     

Local response dispersion method. II. Generalized multicenter interactions

Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C(6) coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jure?ka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.     

Elastic electron scattering by C2F4

Recent measurements [R. Panajotovic, M. Jelisavcic, R. Kajita, T. Tanaka, M. Kitajima, H. Cho, H. Tanaka, and S. J. Buckman, J. Chem. Phys. 121, 4559 (2004)] and calculations [C. Trevisan, A. E. Orel, and T. N. Rescigno, Phys. Rev. A 70, 012704 (2004)] of the elastic electron cross section for C(2)F(4) differ materially from our earlier calculations [C. Winstead and V. McKoy, J. Chem. Phys. 116, 1380 (2002)]. Some of the differences are readily attributed to approximations made in our computations, but an overall difference in cross section magnitude above ca. 10 eV was surprising. Here we report a reexamination of the electron-C(2)F(4) elastic cross section. After eliminating or minimizing various possible sources of error, we continue to predict a substantially larger cross section at higher energies.     

Ab initio potential energy surfaces and nonadiabatic interactions in the H+ +NO collision system

Ab initio calculations on the H(+)+NO system have been carried out in Jacobi coordinates at the multireference configuration interaction level employing Dunning's correlation-consistent polarized valence triple zeta basis set to analyze the role of low-lying electronic excited states in influencing the collision dynamics relevant to the experimental collision energy range of 9.5-30 eV. The lowest two adiabatic potential energy surfaces, asymptotically correlating to H(+)+NO(X (2)Pi) and H((2)S)+NO(+)(X (1)Sigma(+)), have been obtained. Using ab initio procedures, the (radial) nonadiabatic couplings and the mixing angle between the lowest two electronic states (1 (2)A' and 2 (2)A') have been obtained to yield the corresponding quasidiabatic potential energy matrix. The strengths of the computed vibrational coupling matrix elements reflect a similar trend, as has been observed experimentally in the magnitudes of the state-to-state transition probability for the inelastic vibrational excitations [J. Krutein and F. Linder, J. Chem. Phys. 71, 559 (1979); F. A. Gianturco et al., J. Phys. B 14, 667 (1981)].     

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.     

Three-body problem in quantum mechanics: hyperspherical elliptic coordinates and harmonic basis sets

Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known "symmetric" and "asymmetric" parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems.     

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).     

Complexes of type C6H7(+)·L (L = N2 and CO2) studied by explicitly correlated coupled cluster theory

Complexes of the benzenium ion (C(6)H(7)(+)) with N(2) or CO(2) have been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level [T. B. Adler et al., J. Chem. Phys. 127, 221106 (2007)] and the double-hybrid density functional B2PLYP-D [T. Schwabe and S. Grimme, Phys. Chem. Chem. Phys. 9, 3397 (2007)]. Improved harmonic vibrational wavenumbers for C(6)H(7)(+) have been obtained by CCSD(T?)-F12a calculations with the VTZ-F12 basis set. Combining them with previous B2PLYP-D anharmonic contributions we arrive at anharmonic wavenumbers which are in excellent agreement with recent experimental data from p-H(2) matrix isolation IR spectroscopy [M. Bahou et al., J. Chem. Phys. 136, 154304 (2012)]. The energetically most favourable conformer of C(6)H(7)(+)·N(2) shows a π-bonded structure similar to C(6)H(7)(+)·Rg (Rg = Ne, Ar) [P. Botschwina and R. Oswald, J. Phys. Chem. A 115, 13664 (2011)] with D(e) ≈ 870 cm(-1). For C(6)H(7)(+)·CO(2), a slightly lower energy is calculated for a conformer with the CO(2) ligand lying in the ring-plane of the C(6)H(7)(+) moiety (D(e) ≈ 1508 cm(-1)). It may be discriminated from other conformers through a strong band predicted at 1218 cm(-1), red-shifted by 21 cm(-1) from the corresponding band of free C(6)H(7)(+).     

Path integral calculation of thermal rate constants within the quantum instanton approximation: application to the H + CH4 --> H2 + CH3 hydrogen abstraction reaction in full Cartesian space

The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H + CH4 --> H2 + CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T = 200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used.     

Vibrationally inelastic collisions in H+ +CO system: comparing quantum calculations with experiments

State-resolved cross beam experiments [H. Udseth et al., J. Chem. Phys. 60, 3051 (1974); J. Krutein and F. Linder, J. Chem. Phys. 71, 599 (1979); G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)], coupled with proton energy loss spectroscopy for the inelastic scattering of H(+) from CO in the collision range of 10-30 eV show very low vibrational excitation of the target molecule. Stimulated by the experimentally observed low vibrational inelasticity in the system the ground and the first two low-lying excited electronic potential-energy surfaces have been computed using the ab initio multireference configuration interaction method. Quantum dynamics has been performed on the ground potential energy surface in the framework of vibrational close-coupling rotational infinite-order sudden approximation. The various computed dynamical attributes such as differential and integral cross sections, and average vibrational energy transfer are analyzed in detail, and compared successfully with the available experimental results.