Christophe Iung

Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach

An efficient pseudospectral method for performing fully-coupled six-dimensional bound state dynamics calculations is presented. A Lanczos-based iterative diagonalization scheme produces the energy levels in increasing energies. This scheme, which requires repetitively acting the Hamiltonian operator on a vector, circumvents the problem of constructing the full matrix. This permits the use of ultralarge molecular basis sets in order to fully converge the calculations. The Lanczos scheme was conducted in a symmetry adapted six-dimensional spectral representation. The Hamiltonian operator has been split into only four different terms, each being Hermitian and symmetry-adapted. The potential term is evaluated by a pseudospectral scheme of Gaussian accuracy, which guarantees the variational principle. Spectroscopic levels are computed with this method for one ammonia potential, and compared to experimental results. The results presented below are a direct application of our vector formulation. The latter has s...

Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method

A theoretical study of the vibrational spectrum of the CHF(3) molecule is carried out with the aid of the multiconfiguration time-dependent Hartree (MCTDH) algorithm. In order to obtain the eigenvalues and the eigenstates, recent developments in the MCTDH improved relaxation method in a block form are exploited. Around 80 eigenvalues are reported, which are converged with a very high accuracy. The results obtained with our study are compared with those of a previous work using the wave operator sorting algorithm approach. The present investigation exemplifies the robustness and the accuracy of the improved relaxation method.

A general expression of the exact kinetic energy operator in polyspherical coordinates

This paper aims at presenting a general and compact matrix expression of the exact kinetic energy operator in polyspherical coordinates adapted to the study of semirigid molecules. The internal coordinates of an N atom system are expressed by a set of N−1 relative position vectors. The operator can be applied to whatever the set of vectors (Jacobi, Radau, valence, satellite, etc., or a combination of these vectors), and whatever the number of atoms. It includes the rotation and the Coriolis coupling. Such a formulation gives the opportunity to develop a general code for calculating the ro-vibrational spectra in a curvilinear description including all the vibrational, rotational, and Coriolis couplings.

Quantum dynamics of overtone relaxation in benzene. II. 16 mode model for relaxation from CH(v=3)

This series is concerned with the quantum dynamics of overtone relaxation in planar benzene and in reduced mode planar benzene fragments. In these studies, ultralarge direct product primitive vibrational spaces (of dimension up to 1010) are contracted to active spaces of dimension 5000–10 000. The contractions are carried out via artificial intelligence tree pruning algorithms, or a new iterative wave operator pruning algorithm. The exact dynamics within the active space is then developed via the recursive residue generation method. In part I of this series, emphasis is placed upon v=3 CH overtone dynamics in the 5 and 9 mode benzene fragments C3H and C3H3. Neither system undergoes complete relaxation, but the survival probability in C3H undergoes large amplitude oscillations with a period characteristic of stretch–wag interaction in the CH chromophore. For C3H3, the two initially nonexcited CH stretch modes do not play a significant role in the dynamics for t<1 ps. However, modes in both systems that hav...

Vector parametrization of the N-atom problem in quantum mechanics. II. Coupled-angular-momentum spectral representations for four-atom systems

Within the framework of adapted coupled-angular-momentum spectral representations, the geometrical description of a four-atom molecular system by three Jacobi relative position vectors is shown to result in matrices representing the kinetic energy operator, prediagonalized to a very large extent. A fully diagonal representation is built for the angular (internal and rotational) part of the problem.

A Jacobi-Wilson description coupled to a block-Davidson algorithm: an efficient scheme to calculate highly excited vibrational levels.

We present a new approach based on the block-Davidson scheme which provides eigenvalues and eigenvectors of highly excited (ro) vibrational states of polyatomic molecules. The key ingredient is a prediagonalized-perturbative scheme applied to a subspace of a curvilinear normal-mode basis set. This approach is coupled to the Jacobi vector description recently developed by our group [C. Leforestier, A. Viel, F. Gatti, C. Munoz, and C. Iung, J. Chem. Phys. 114, 2099 (2001)], and applied to the HFCO and H2CO molecules, which represent the main difficulties of such calculations for any available method. The first one presents a significant state density because of its low symmetry and the presence of a fluorine atom, while strong resonances and intermode couplings occur in H2CO. This study establishes the robustness, the numerical efficiency, and the versatility of the method which is compared to the regular Lanczos and Davidson schemes. It is also shown that the eigenvectors can be obtained within a given accuracy easily set by the user. This point constitutes one of the main advantages of the method as very few potential-energy surfaces achieve an accuracy of the order of a wave number for highly excited states. Furthermore, this method allows one to restrict the calculations to selected energy levels based on their zero-order descriptions.

Intramolecular vibrational energy redistribution in the highly excited fluoroform molecule: A quantum mechanical study using the multiconfiguration time-dependent Hartree algorithm

The present paper is devoted to a detailed study of the intramolecular vibrational energy redistribution in fluoroform initiated by a local mode excitation of the CH stretch [nnu(CH) (n=1,...,4)]. All nine internal degrees of freedom are explicitly taken into account and the full quantum mechanical simulation is performed by means of the multiconfiguration time-dependent Hartree algorithm. The existence of different time scales considerably complicates the dynamics. The mode-to-mode energy transfer is analyzed by calculating the evolution of the partial energies of all vibrational modes. This study emphasizes the crucial role played by the two-dimensional FCH bending modes which act as an energy reservoir. The fast energy flow into these bending modes significantly hinders an energy flow from the CH chromophore. Finally, our results are compared with those obtained previously with the wave operator sorting algorithm approach.

The Jacobi-Wilson method: A new approach to the description of polyatomic molecules

We present a new method adapted to the calculation of excited rovibrational states of semirigid molecules. It first relies on a description of the molecule in terms of polyspherical coordinates of Jacobi vectors, in order to obtain a compact expression for the kinetic energy operator T(q). This general description is then adapted to the molecule considered by defining curvilinear normal modes from the corresponding zero order harmonic Hamiltonian Ĥ0=T(qeq)+Vharm(q), the solutions of which are being used as the working basis set. The residual kinetic term ΔT is treated mainly analytically in this basis, and displays no radial contribution. Anharmonic coupling ΔV(q) is handled by means of a pseudospectral scheme based on Gauss Hermite quadratures. This method is particularly adapted to direct iterative approaches which only require the action of Ĥ on a vector, without the need of the associated matrix, thus allowing ultralarge bases to be considered. An application to the excited vibrational states of th...

Calculation of highly excited vibrational levels: a prediagonalized Davidson scheme

Abstract We present a new approach based on the Davidson algorithm which provides eigenvalues and eigenvectors of selected highly excited (ro)vibrational states of polyatomic molecules. The key ingredient is a prediagonalization–perturbation scheme applied to a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of this method is illustrated by computing all vibrational states of the H 2 CO molecule, up to 9500 cm −1 of internal excitation. Convergence of the levels can be assessed during the iteration process by looking at the residual ||( H −E α )|Ψ α 〉|| .

EXACT AND CONSTRAINED KINETIC ENERGY OPERATORS IN POLYSPHERICAL COORDINATES

In this paper the derivation of exact and constrained kinetic energy operators in curvilinear coordinates is presented in a very general context. The polyspherical approach allows us to provide simple and explicit expressions of these operators which are well adapted to the numerical approaches used to solve the Schrodinger equation. These expressions can be exploited to treat a lot of problems such as the calculation of infrared or photoabsorption spectra as well as the study of intramolecular vibrational relaxation of molecules or the study of reactive scattering systems. Special emphasis is placed on concrete applications.