A multi-configurational time-dependent Hartree approach to the eigenstates of multi-well systems

A rigorous and efficient approach for the calculation of eigenstates in polyatomic molecular systems with potentials displaying multiple wells is introduced. The scheme is based on the multi-configurational time-dependent Hartree (MCTDH) approach and uses multiple MCTDH wavefunctions with different single-particle function bases to describe the quantum dynamics in the different potential wells. More specifically, an iterative block Lanczos-type diagonalization scheme utilizing state-averaged MCTDH wavefunctions localized in different wells is employed to obtain the energy eigenvalues and eigenstates. The approach does not impose any formal restriction on the symmetry of the potential or the number of wells. A seven-dimensional model system of tetrahedral symmetry, which is inspired by A·CH(4) type complexes and displays four equivalent potential minima, is used to study the numerical performance of the new approach. It is found that the number of configurations in the MCTDH wavefunctions required to obtain converged results is decreased by roughly one order of magnitude compared to standard MCTDH calculations employing a block-relaxation scheme.     

A multilayer multiconfigurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces

The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by representing the wavepacket in an optimal set of time-dependent basis functions, called single-particle functions. Choosing these single-particle functions to be themselves multidimensional wavefunctions which are represented using a MCTDH representation, a multilayer MCTDH scheme has been constructed and used for quantum dynamics calculations treating up to 1000 degrees of freedom rigorously [Wang and Thoss, J. Chem. Phys. 199, 1289 (2003)]. The present work gives a practical scheme which facilitates the application of the multilayer MCTDH approach, which previously has only been employed to study systems described by model-type Hamiltonians, to molecular systems described by more complicated Hamiltonians and general potential energy surfaces. A multilayer extension of the correlation discrete variable representation (CDVR) scheme employed in MCTDH calculations studying quantum dynamics on general potential energy surfaces is developed and tested in a simple numerical application. The resulting multilayer MCTDH/CDVR approach might offer a perspective to rigorously describe the quantum dynamics of larger polyatomic systems.     

Ab initio large-amplitude quantum-tunneling dynamics in vinyl radical: a vibrationally adiabatic approach

Large-amplitude tunneling in vinyl radical over a C2v planar transition state involves CCH bending excitation coupled to all other internal coordinates, resulting in a significant dependence of barrier height and shape on vibrational degrees of freedom at the zero-point level. An ab initio potential surface for vinyl radical has been calculated at the CCSD(T) level (AVnZ; n=2, 3, 4, 5) for vibrationally adiabatic 1D motion along the planar CCH bending tunneling coordinate, extrapolated to the complete basis set (CBS) limit and corrected for anharmonic zero-point effects. The polyatomic reduced moment of inertia is calculated explicitly as a function of tunneling coordinate, with eigenvalues and tunneling splittings obtained from numerical solution of the resulting 1D Schr?dinger equation. Linear scaling of the CBS potential to match predicted and observed tunneling splittings empirically yields an adiabatic barrier height of DeltaEadiab=1696(20) cm(-1) which, when corrected for zero-point energy contributions, translates into an effective barrier of DeltaEeff=1602(20) cm(-1) consistent with estimates (DeltaE=1580(100) cm(-1)) by Tanaka and coworkers [J. Chem. Phys., 2004, 120, 3604-3618]. These zero-point-corrected potential surfaces are used to predict tunneling dynamics in vibrationally excited states of vinyl radical, providing strong support for previous jet-cooled high-resolution infrared studies [Dong et al., J. Phys. Chem. A, 2006, 110, 3059-3070] in the symmetric CH2 stretch mode.     

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.     

Vibrational stimulation of the coherent tunneling transition in the cyclopentanone molecule

The tunneling interconversion of the cyclopentanone molecule, which leads to the appearance of tunneling doublets in the microwave spectrum of the system, is studied. The dynamics of interconversion is described by two generalized coordinates, one of which corresponds to bending (non-tunneling promoting mode), while the other of which corresponds to twisting of the molecular plane (tunneling coordinate). The coupling between two coordinates is symmetric. A method for quasi-classical calculation of the wave functions in the tunneling region and of the tunneling splittings of the vibrationally excited states in a two-dimensional potential with symmetric coupling is proposed. The tunneling spectrum of cyclopentanone is calculated. It agrees well with the experimental one, and the tunneling splitting increases by 140 times when the transverse quantum number goes from 0 to 6. The dynamic effect of the vibrationally assisted tunneling is shown to be due to the increase in the width of the tunneling channel with the quantum number of bending mode, as well as to the simultaneous shortening of the tunneling distance. The transition state geometry is found using the wave function at the dividing line of the potential.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2098–2105, December, 1994.This work was supported by the Russian Foundation for Basic Research (Project 94-03-08863). The authors express their gratitude to W. Miller for helpful discussions and to H. Nakamura for a preprint of their work.     

Simulation of inversion motion and N-H stretching overtone spectra of aniline

A curvilinear internal coordinate Hamiltonian is used to simulate the N-H stretching overtone spectra and the associated inversion splittings in aniline. A simple local mode type model is applied to the N-H stretching and H-N-H bending modes. Geometric algebra is employed to derive the kinetic energy operator for the large amplitude inversion motion. Electronic structure calculations at the Moller-Plesset second order perturbation theory and correlation consistent aug-cc-pVTZ basis set level are used to obtain model parameters, some of which have been optimized with the least-squares method using experimental vibrational term values as data. The observed N-H stretching overtone vibrational levels and the inversional tunneling splittings are well reproduced with our approach.     

Theoretical aspects of tunneling-current-induced bond excitation and breaking at surfaces

We have performed a density functional study of the electronic structure, images and vibrationally inelastic tunneling in the scanning tunneling microscope and vibrational damping by excitation of electron-hole pairs of CO chemisorbed on the (111) and (100) faces of Cu. We find that the 2 pi* molecular orbital of CO turns into a broad resonance with parameters that differ significantly from those suggested by inverse and two-photon photoemission measurements. The calculated vibrational damping rate for the internal stretch mode and relative changes in tunneling conductance across vibrational thresholds are in agreement with experiment. The non-adiabatic electron-vibration coupling is well described by the Newn-Anderson model for the 2 pi*-derived resonance whereas this model is not able to describe the non-adiabatic coupling between the tunneling electrons and the vibration. We believe that this model misses an important mechanism for vibrational excitation in tunneling that involves the change of tunneling amplitude by deformation of the tails of the one-electron wavefunctions with vibrational coordinate.     

Ground and asymmetric CO-stretch excited state tunneling splittings in the formic acid dimer

There has been some controversy concerning the assignment of measured tunneling splittings for the formic acid dimer in the vibrational ground state and the asymmetric CO-stretching excited state. The discussion is intimately related to the question whether the fundamental excitation of the CO-vibration promotes or hinders tunneling. Here we will address this issue on the basis of a five-dimensional reaction space Hamiltonian which includes three large amplitude coordinates as well as two harmonic modes whose linear superposition reproduces the asymmetric CO-vibrational mode. Within density functional theory using the B3LYP functional together with a 6-311++G(3df,3pd) basis set we obtain a ground state tunneling splitting which is about 2.4 larger than the one for the CO-stretching excited state.     

A microwave and quantum chemical study of cyclopropanethiol

The microwave spectra of cyclopropanethiol, C(3)H(5)SH, and one deuterated species C(3)H(5)SD, have been investigated in the 20 - 80 GHz frequency range. The spectra of the ground vibrational state and of three vibrationally excited states of the parent species of a conformer which has a synclinal ("gauche") arrangement for the H-C-S-H chain of atoms, was assigned. The H-C-S-H dihedral angle is 76(5)° from synperiplanar (0°). The b-type transitions of the ground and of the vibrationally excited states of the parent species were split into two components, which is assumed to arise from tunneling of the proton of the thiol group between two equivalent synclinal potential wells. No splitting was resolved in the spectrum of C(3)H(5)SD. The tunneling frequency of the ground vibrational state of C(3)H(5)SH is 1.664(22) MHz. The tunneling frequency of the first excited-state of the C-S torsion is 52.330(44) MHz, whereas this frequency is 26.43(13) and 3.286(61) MHz, respectively, for the first excited states of the two lowest bending vibrations. The dipole moment of the ground vibrational state of the parent species is μ(a) = 4.09(5), μ(b) = 2.83(11), μ(c) = 0.89(32), and μ(tot) = 5.06(16) × 10(-30) C m. The microwave study has been augmented by high-level density functional and ab initio quantum chemical calculations.     

Theoretical investigation of intramolecular vibrational energy redistribution in highly excited HFCO

The present paper is devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) in HFCO initiated by an excitation of the out-of-plane bending vibration [nnu(6)=2,4,6,...,18,20]. Using a full six-dimensional ab initio potential energy, the multiconfiguration time-dependent Hartree (MCTDH) method was exploited to propagate the corresponding six-dimensional wave packets. This study emphasizes the stability of highly excited states of the out-of-plane bending mode which exist even above the dissociation threshold. More strikingly, the structure of the IVR during the first step of the dynamics is very stable for initial excitations ranging from 2nu(6) to 20nu(6). This latter result is consistent with the analysis of the eigenstates obtained, up to 10nu(6), with the aid of the Davidson algorithm in a foregoing paper [Iung and Ribeiro, J. Chem. Phys. 121, 174105 (2005)]. The present study can be considered as complementary to this previous investigation. This paper also shows how MCTDH can be used to predict the dynamical behavior of a strongly excited system and to determine the energies of the corresponding highly excited states.     

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.     

Stereomutation tunneling switching dynamics and parity violation in chlorineperoxide Cl-O-O-Cl

In a search for efficient spectroscopic avenues toward experiments on molecular parity violation, we investigate the stereomutation tunneling processes in the axially chiral chlorine isotopomers of Cl2O2 by the quasi-adiabatic channel reaction path Hamiltonian (RPH) approach and the corresponding parity violating potentials by means of quantum chemical calculations including our recently developed Multiconfiguration linear response (MC-LR) approach to electroweak quantum chemistry. The calculated ground-state torsional tunneling splittings for all isotopomers of Cl2O2 are much smaller than the parity violating energy differences Delta(pv)E between the enantiomers of these molecules and therefore parity violation is predicted to dominate the quantum dynamics of stereomutation at low energies. We also compare these with torsional ground-state tunneling splittings and parity violating energy differences of the whole series of axially chiral HXYH(+) isotopomers (with X, Y= Cl(+), O, S, Se, Te). A comparison with our previous results for the homologous molecule Cl2S2 shows that for Cl2O2 a spectroscopic high-resolution analysis should be easier and the energy region of large tunneling splittings should be more easily accessible by IR excitation. We thus propose a scheme using "tunneling switching" with vibrational excitation in order to carry out the measurement of time-dependent parity violation in superposition states of initially well-defined parity. We discuss the advantages and drawbacks of such an experiment that can be carried out entirely in the IR spectral range (for Cl2O2 or related molecules).     

Unraveling the spectroscopy of coupled intramolecular tunneling modes: a study of double proton transfer in the formic-acetic acid complex

The rotational spectrum of the hetero dimer comprising doubly hydrogen-bonded formic acid and acetic acid has been recorded between 4 and 18 GHz using a pulsed-nozzle Fourier transform microwave spectrometer. Each rigid-molecule rotational transition is split into four as a result of two concurrently ongoing tunneling motions, one being proton transfer between the two acid molecules, and the other the torsion/rotation of the methyl group within the acetyl part. We present a full assignment of the spectrum J = 1 to J = 6 for the ground vibronic states. The transitions are fitted to within a few kilohertz of the observed frequencies using a molecule-fixed effective rotational Hamiltonian for the separate A and E vibrational species of the G(12) permutation-inversion symmetry group. Interpretation of the motion problem uses an internal-vibration and overall-rotation angular momentum coupling scheme and full sets of rotational and centrifugal distortion constants are determined. The tunneling frequencies of the proton-transfer motion are measured for the ground A and E methyl rotation states as 250.4442(12) and -136.1673(30) MHz, respectively. The slight deviation of the latter tunneling frequency from being one half of the former, as simple theory otherwise predicts, is due to different degrees of mixing in wavefunctions between the ground and excited states.     

Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.     

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.     

Jet cooled spectroscopy of H2DO+: Barrier heights and isotope-dependent tunneling dynamics from H3O+ to D3O+

The first high resolution spectroscopic data for jet cooled H2DO+ are reported, specifically via infrared laser direct absorption in the OH stretching region with a slit supersonic jet discharge source. Transitions sampling upper (0-) and lower (0+) tunneling states for both symmetric (nu1+ <-- 0+, nu1- <-- 0-, and nu1- <-- 0+) and antisymmetric (nu3+ <-- 0+ and nu3- <-- 0-) OH stretching bands are observed, where +/- refers to wave function reflection symmetry with respect to the planar umbrella mode transition state. The spectra can be well fitted to a Watson asymmetric top Hamiltonian, revealing band origins and rotational constants for benchmark comparison with high-level ab initio theory. Of particular importance are detection and assignment of the relatively weak band (nu1- <-- 0+) that crosses the inversion tunneling gap, which is optically forbidden in H3O+ or D3O+, but weakly allowed in H2DO+ by lowering of the tunneling transition state symmetry from D(3h) to C(2v). In conjunction with other H2DO+ bands, this permits determination of the tunneling splittings to within spectroscopic precision for each of the ground [40.518(10) cm(-1)], nu1 = 1 [32.666(6) cm(-1)], and nu3 = 1 [25.399(11) cm(-1)] states. A one-dimensional zero-point energy corrected potential along the tunneling coordinate is constructed from high-level ab initio CCSD(T) calculations (AVnZ, n = 3,4,5) and extrapolated to the complete basis set limit to extract tunneling splittings via a vibrationally adiabatic treatment. Perturbative scaling of the potential to match splittings for all four isotopomers permits an experimental estimate of DeltaV0 = 652.9(6) cm(-1) for the tunneling barrier, in good agreement with full six-dimensional ab initio results of Rajamaki, Miani, and Halonen (RMH) [J. Chem. Phys. 118, 10929 (2003)]. (DeltaV0 (RMH) = 650 cm(-1)). The 30%-50% decrease in tunneling splitting observed upon nu1 and nu3 vibrational excitations arises from an increase in OH stretch frequencies at the planar transition state, highlighting the transition between sp2 and sp3 hybridizations of the OHD bonds as a function of inversion bending angle.     

Microwave spectrum, conformation and intramolecular hydrogen bonding of 2,2,2-trifluoroethanethiol (CF3CH2SH)

The microwave spectrum of 2,2,2-trifluoroethanethiol, CF3CH2SH, and of one deuterated species, CF3CH2SD, has been investigated in the 7-80 GHz spectral interval. The microwave spectra of the ground and three vibrationally excited states belonging to three different normal modes of one conformer were assigned for the parent species, and the vibrational frequencies of these fundamentals were determined by relative intensity measurements. Only the ground vibrational state was assigned for the deuterated species. The identified form has a synclinal arrangement for the H-S-C-C chain of atoms and the corresponding dihedral angle is 68(5) degrees from synperiplanar (0 degrees). A weak intramolecular hydrogen bond formed between the thiol (SH) group and one of the fluorine atoms is stabilizing this conformer. There is no evidence in the microwave spectrum for the H-S-C-C antiperiplanar form. The hydrogen atom of the thiol group should have the ability to tunnel between two equivalent synclinal potential wells, but no splittings of spectral lines due to tunneling were observed. The microwave work was augmented by quantum chemical calculations at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory.