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.     

The impact of approximate VSCF schemes and curvilinear coordinates on the anharmonic vibrational frequencies of formamide and thioformamide

The accuracy of the vibrational self-consistent field (VSCF) method for the computation of anharmonic vibrational frequencies in the infrared (IR) spectrum of formamide and thioformamide is investigated. The importance of triple potentials in the commonly used hierarchical expansion of the potential energy surface (PES) is studied in detail. The PES is expanded in terms of Cartesian as well as internal coordinate normal mode displacements. It is found that triples play an important role when using rectilinear coordinates. A VSCF computation based on rectilinear displacements exhibits serious shortcomings which are only remedied by a large vibrational configuration interaction (VCI) treatment including triple potentials. These limitations are partially removed when using curvilinear coordinates. The merits and disadvantages of either type of displacements for the generation of the PES are discussed.     

The hierarchical expansion of the kinetic energy operator in curvilinear coordinates extended to the vibrational configuration interaction method

The hierarchical expansion of the kinetic energy operator in curvilinear coordinates presented earlier for the vibrational self-consistent field technique is extended to the vibrational configuration interaction (VCI) method. The high accuracy of the modified VCI method is demonstrated by computing first excitation energies of the H(2)O(2) molecule using an analytic potential (PCPSDE) and showing convergence to accurate results from full dimensional discrete variable representation calculations.     

A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method

Full-dimensional quantum mechanical computations are carried out to investigate the photodissociation dynamics of A? state NH(3) and ND(3) using the multiconfiguration time-dependent Hartree (MCTDH) method with recently developed coupled ab initio potential energy surfaces (PESs) [Z. H. Li, R. Valero, and D. G. Truhlar, Theor. Chim. Acc. 118, 9 (2007)]. To use the MCTDH method efficiently the PESs are represented as based on the high-dimensional model representation. The A? ← X? absorption spectra for both isotopomers were calculated for the zeroth vibrational state of the ground electronic state. With a view to treating larger systems, Jacobi coordinates are used. Computations on the coupled PES are carried out for two-, three-, five-, and six-dimensional model systems to understand the validity of reduced-dimensional calculations. In addition to the fully coupled calculations, the effect of nonadiabatic coupling on absorption spectra is shown by propagating the initial wavepacket only in the A? electronic state. The calculated absorption spectra are shown to be in good agreement with available theoretical and experimental observations. Comparisons with calculations using Radau and valence coordinates show the effect of including the symmetry of the system explicitly. Finally, branching ratios for loss of a hydrogen atom via the two available channels are calculated. These predict that the nonadiabatic product increases with the dimension of the calculations and confirm the importance of the full-dimensional calculations.     

MULTIMODE quantum calculations of intramolecular vibrational energies of the water dimer and trimer using ab initio-based potential energy surfaces

We report vibrational configuration interaction calculations of the monomer fundamentals of (H(2)O)(2), (D(2)O)(2), (H(2)O)(3), and (D(2)O)(3) using the code MULTIMODE and full dimensional ab initio-based global potential energies surfaces (PESs). For the dimer the HBB PES [Huang et al., J. Chem. Phys 128, 034312 (2008)] is used and for the trimer a new PES, reported here, is used. The salient properties of the new trimer PES are presented and compared to previous single-point calculations and the vibrational energies are compared with experiments.     

Including anharmonicity in the calculation of rate constants. II. The OH+H2-->H2O+H reaction

A recently developed method for calculating anharmonic vibrational energy levels at nonstationary points along a reaction path that is based on second-order perturbation theory in curvilinear coordinates is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the title reaction. Two different potential energy surfaces were employed for these calculations, an improved version of the author's surface 5 and the WSLFH surface of Wu et al. [J. Chem. Phys. 113, 3150 (2000)]. We present detailed comparisons of rate constants computed for the two surfaces with and without anharmonicity and with various approximations for incorporating tunneling along the reaction path. The results for this system are quite sensitive to the surface employed, the choice of coordinates (curvilinear versus rectilinear), and the inclusion of anharmonicity. A comparison with experiment provides information on the accuracy of these surfaces.     

An adaptive potential energy surface generation method using curvilinear valence coordinates

An automatic Born-Oppenheimer potential energy surface (PES) generation method AGAPES is presented designed for the calculation of vibrational spectra of large rigid and semi-rigid polyatomic molecules within the mid-infrared energy range. An adaptive approach guided by information from intermediate vibrational calculations in connection with a multi-mode expansion of the PES in internal valence coordinates is used and its versatility is tested for a selection of molecules: HNO, HClCO, and formaldoxime. Significant computational savings are reported. The possibility of linear scaling of the sampling grid size with the molecular size due to decrease of correlation of remote coordinates in large molecules is examined and finally, possible improvements are suggested.     

Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics

The infrared absorption spectrum of the protonated water dimer (H5O2+) is simulated in full dimensionality (15 dimensional) in the spectral range of 0-4000 cm(-1). The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method for propagation of wavepackets. All the fundamentals and several overtones of the vibrational motion are computed. The spectrum of H5O2+ is shaped to a large extent by couplings of the proton-transfer motion to large amplitude fluxional motions of the water molecules, water bending and water-water stretch motions. These couplings are identified and discussed, and the corresponding spectral lines are assigned. The large couplings featured by H5O2+ do not hinder, however, to describe the coupled vibrational motion by well defined simple types of vibration (stretching, bending; etc.) based on well defined modes of vibration, in terms of which the spectral lines are assigned. Comparison of our results to recent experiments and calculations on the system is given. The reported MCTDH IR spectrum is in very good agreement to the recently measured spectrum by Hammer et al. [J. Chem. Phys. 122, 244301 (2005)].     

The ground state tunneling splitting of malonaldehyde: accurate full dimensional quantum dynamics calculations

Benchmark calculations of the tunneling splitting in malonaldehyde using the full dimensional potential proposed by Yagi et al. are reported. Two exact quantum dynamics methods are used: the multiconfigurational time-dependent Hartree (MCTDH) approach and the diffusion Monte Carlo based projection operator imaginary time spectral evolution (POITSE) method. A ground state tunneling splitting of 25.7+/-0.3 cm(-1) is calculated using POITSE. The MCTDH computation yields 25 cm(-1) converged to about 10% accuracy. These rigorous results are used to evaluate the accuracy of approximate dynamical approaches, e.g., the instanton theory.     

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.     

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.     

Multidimensional time-dependent discrete variable representations in multiconfiguration Hartree calculations

In the multiconfiguration time-dependent Hartree (MCTDH) approach, the wave function is expanded in time-dependent basis functions, called single-particle functions, to increase the efficiency of the wave-packet propagation. The correlation discrete variable representation (CDVR) approach, which is based on a time-dependent discrete variable representation (DVR), can be employed to evaluate matrix elements of the potential energy. The efficiency of the MCTDH method can be further enhanced by using multidimensional single-particle functions. However, up to now the CDVR approach could not be used in MCTDH calculations employing multidimensional single-particle functions, since this would require a general multidimensional non-direct-product DVR scheme. Recently, Dawes and Carrington presented a practical scheme to implement general non-direct-product multidimensional DVRs [R. Dawes and T. Carrington, Jr., J. Chem. Phys. 121, 726 (2004)]. The present work utilizes their scheme in the MCTDH/CDVR approach. The accuracy is tested using the photodissociation of NOCl as example. The results show that the CDVR scheme based on multidimensional time-dependent DVRs allows for an accurate evaluation of the potential in MCTDH calculations with multidimensional single-particle functions.     

Cumulative isomerization probability studied by various transition state wave packet methods including the MCTDH algorithm. Benchmark: HCN-->CNH isomerization

The 3D cumulative isomerization probability N(E) for the transfer of a light particle between two atoms is computed by one time-independent and two time-dependent versions of the transition state wave packet (TSWP) method. The time-independent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the time-dependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration time-dependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelberg MCTDH package [G. W. Worth, M. H. Beck, A. Jackle, and H.-D. Meyer, The MCDTH package, Version 8.2 (2000); H.-D Meyer, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/]. The benchmark is the HCN-->CNH isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the time-dependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of N(E) for the HCN-->CNH isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute N(E) for H-transfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited.     

Franck–Condon factors in curvilinear coordinates: the photoelectron spectrum of ammonia

An approach to the calculation of Franck–Condon factors in curvilinear coordinates is outlined. The approach is based on curvilinear normal coordinates, which allows for an easy extension of Duschinsky’s transformation to the case of curvilinear coordinates, and on the power series expansion of the kinetic energy operator. Its usefulness in the case of molecules undergoing large displacements of their equilibrium nuclear configurations upon excitation is then demonstrated by an application to the vibrational structure of the photoelectron spectrum of ammonia, using an anharmonic potential only for the symmetric stretching and bending coordinates of the radical cation.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

An eight-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction on a new modified potential energy surface

An eight-dimensional time-dependent quantum dynamics wave packet approach is performed for the study of the H2+C2H-->H+C2H2 reaction system on a new modified potential energy surface (PES) [L.-P. Ju et al., Chem. Phys. Lett. 409, 249 (2005)]. This new potential energy surface is obtained by modifying Wang and Bowman's old PES [J. Chem. Phys. 101, 8646 (1994)] based on the new ab initio calculation. This new modified PES has a much lower transition state barrier height at 2.29 kcal/mol than Wang and Bowman's old PES at 4.3 kcal/mol. This study shows that the reactivity for this diatom-triatom reaction system is enhanced by vibrational excitations of H2, whereas the vibrational excitations of C2H only have a small effect on the reactivity. Furthermore, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. The comparison of the rate constant between this calculation and experimental results agrees with each other very well. This comparison indicates that the new modified PES corrects the large barrier height problem in Wang and Bowman's old PES.     

Discrete variable approaches to tetratomic molecules: part II: application to H2O2 and H2CO

We have carried out large-scale calculations for accurate vibrational energy levels of formaldehyde and hydrogen peroxide. The discrete variable representations of the radial and angular coordinates are employed together with the contraction scheme resulting from several diagonalization/truncation steps. The global potential energy surface due to Carter et al. [J. Mol. Spectrosc. 90 (1997) 729] is used for H2CO and due to Koput et al. [J. Phys. Chem. A 102 (1998) 6325] for H2O2. For both molecules, the calculated vibrational energy levels are characterized by combining vibrationally averaged geometries and expectation values of rotational constants with several adiabatic projection schemes for automatic quantum number assignments. The energy levels of H2CO involving the excited v2 and v3 vibrations appear as resonances beyond the zero-order picture consisting of uncoupled 3D stretching and 2D bending modes. The torsional energy levels of H2O2 are studied in great detail and different energy patterns occurring below and above the cis barrier are discussed. Our full dimensional calculations for H2O2 have shown that the OH triad levels, 2vOH, are symmetry adapted local mode states.     

Quantum dynamics of dissociative chemisorption of CH(4) on Ni(111): Influence of the bending vibration

Two-dimensional, three-dimensional, and four-dimensional quantum dynamic calculations are performed on the dissociative chemisorption of CH(4) on Ni(111) using the multiconfiguration time-dependent Hartree (MCTDH) method. The potential energy surface used for these calculations is 15-dimensional (15D) and was obtained with density functional theory for points which are concentrated in the region that is dynamically relevant to reaction. Many reduced dimensionality calculations were already performed on this system, but the molecule was generally treated as pseudodiatomic. The main improvement of our model is that we try to describe CH(4) as a polyatomic molecule by including a degree of freedom describing a bending vibration in our three-dimensional and four-dimensional models. Using a polyspherical coordinate system, a general expression for the 15D kinetic energy operator is derived, which discards all the singularities in the operator and includes rotational and Coriolis coupling. We use seven rigid constraints to fix the CH(3) umbrella of the molecule to its gas phase equilibrium geometry and to derive two-dimensional, three-dimensional, and four-dimensional Hamiltonians, which were used in the MCTDH method. Only four degrees of freedom evolve strongly along the 15D minimum energy path: the distance of the center of mass of the molecule to the surface, the dissociative C[Single Bond]H bond distance, the polar orientation of the molecule, and the bending angle between the dissociative C[Single Bond]H bond and the umbrella. A selection of these coordinates is included in each of our models. The polar rotation is found to be important in determining the mode selective behavior of the reaction. Furthermore, our calculations are in good agreement with the finding of Xiang et al. [J. Chem. Phys. 117, 7698 (2002)] in their reduced dimensional calculation that the helicopter motion of the umbrella symmetry axis is less efficient than its cartwheel motion for promoting the reaction. The effect of pre-exciting the bend modes is qualitatively incorrect at higher energies, suggesting the necessity of including additional rotational and vibrational degrees of freedom in the model.