Jean Christophe Tremblay

Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term Lanczos eigensolver

We use a contracted basis+Lanczos eigensolver approach to compute vinylidene-like vibrational states of the acetylene-vinylidene system. To overcome problems caused by loss of orthogonality of the Lanczos vectors we reorthogonalize Lanczos vector and use a coupled two-term approach. The calculations are done in CC-HH diatom-diatom Jacobi coordinates which make it easy to compute states one irreducible representation at a time. The most costly parts of the calculation are parallelized and scale well. We estimate that the vinylidene energies we compute are converged to approximately 1 cm(-1).

Calculation of zero-field splitting parameters: Comparison of a two-component noncolinear spin-density-functional method and a one-component perturbational approach

Two different sets of approaches for the density-functional calculation of the spin-orbit contributions to zero-field splitting (ZFS) parameters of high-spin systems have been implemented within the same quantum chemistry code ReSpect and have been validated and compared for a series of model systems. The first approach includes spin-orbit coupling variationally in a two-component calculation, using either an all-electron Douglas-Kroll-Hess ansatz or two-component relativistic pseudopotentials. The ZFS parameters are computed directly from energy differences between different relativistic states. Additionally, an approximate second-order perturbation theory approach has been implemented, based on nonrelativistic or scalar relativistic wave functions. For a series of group 16 triplet diatomics and for the octet GdH3 molecules, two-component density functional calculations underestimate the zero-field splitting D systematically by a factor of 2. This may be rationalized readily by the incomplete description of states with absolute value MJ < J by a single-determinantal wave function built from two-component spinors. In the case of two 3d transition metal complexes and for GdH3, the results depend furthermore sensitively on exchange-correlation functional. Results of the alternative one-component approach agree strikingly with the two-component data for systems with small spin-orbit effects and start to deviate from them only for heavier systems with large spin-orbit effects. These results have fundamental implications for the achievable accuracy of one-component density-functional approaches used widely to compute ZFS parameters in the field of molecular magnetism. Possible refinements of both one-and two-component approaches are discussed.

ORBKIT: A modular python toolbox for cross‐platform postprocessing of quantum chemical wavefunction data

ORBKIT is a toolbox for postprocessing electronic structure calculations based on a highly modular and portable Python architecture. The program allows computing a multitude of electronic properties of molecular systems on arbitrary spatial grids from the basis set representation of its electronic wavefunction, as well as several grid‐independent properties. The required data can be extracted directly from the standard output of a large number of quantum chemistry programs. ORBKIT can be used as a standalone program to determine standard quantities, for example, the electron density, molecular orbitals, and derivatives thereof. The cornerstone of ORBKIT is its modular structure. The existing basic functions can be arranged in an individual way and can be easily extended by user‐written modules to determine any other derived quantity. ORBKIT offers multiple output formats that can be processed by common visualization tools (VMD, Molden, etc.). Additionally, ORBKIT possesses routines to order molecular orbitals computed at different nuclear configurations according to their electronic character and to interpolate the wavefunction between these configurations. The program is open‐source under GNU‐LGPLv3 license and freely available at https://github.com/orbkit/orbkit/. This article provides an overview of ORBKIT with particular focus on its capabilities and applicability, and includes several example calculations.

Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene

Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.

Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schrödinger equation

If the Hamiltonian is time dependent it is common to solve the time-dependent Schrödinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.

Imaging the Ultrafast Photoelectron Transfer Process in Alizarin-TiO2

In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO2 nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO2 nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.

Selective excitation of coupled CO vibrations on a dissipative Cu(100) surface by shaped infrared laser pulses

In a previous paper [Beyvers et al., J. Chem. Phys. 124, 234706 (2006)], the possibility to mode and state selectively excite various vibrational modes of a CO molecule adsorbed on a dissipative Cu(100) surface by shaped IR pulses was examined. Reduced-dimensionality models with stretching-only coordinates were employed to do so. This model is now extended with the goal to include rotational modes. First, we present an analysis of the bound states of the adsorbed CO molecule in full dimension; i.e., six-dimensional eigenstates are obtained by diagonalizing the six-dimensional Hamiltonian containing the semiempirical potential of Tully et al. [J. Vac. Sci. Technol. A 11, 1914 (1993)]. This is achieved by using a contracted iterative eigensolver based on the coupled two-term Lanczos algorithm with full reorthogonalization. Reduced-dimension subsystem eigenvectors are also computed and then used to study the selective excitation of the molecule in the presence of dissipation within the density matrix formalism for open systems. In the density matrix propagations, up to four degrees of freedom were included, namely, r (the C-O distance), Z (the molecule-surface distance), and phi and theta (the azimuthal and polar angles of the molecular axis with respect to the surface). Short, intense laser pulses are rationally engineered and further refined with optimal control theory, again with the goal for mode and state selective excitation. Also, IR-laser induced desorption is studied. For the calculations, the previous two-mode (r,Z) dipole surface is extended to include the angular dependence and the model for the coupling of the molecule to the surface electronic degrees of freedom is refined.

Dissipative many-electron dynamics of ionizing systems

In this paper, we perform many-electron dynamics using the time-dependent configuration-interaction method in its reduced density matrix formulation (ρ-TDCI). Dissipation is treated implicitly using the Lindblad formalism. To include the effect of ionization on the state-resolved dynamics, we extend a recently introduced heuristic model for ionizing states to the ρ-TDCI method, which leads to a reduced density matrix evolution that is not norm-preserving. We apply the new method to the laser-driven excitation of H(2) in a strongly dissipative environment, for which the state-resolve lifetimes are tuned to a few femtoseconds, typical for dynamics of adsorbate at metallic surfaces. Further testing is made on the laser-induced intramolecular charge transfer in a quinone derivative as a model for a molecular switch. A modified scheme to treat ionizing states is proposed to reduce the computational burden associated with the density matrix propagation, and it is thoroughly tested and compared to the results obtained with the former model. The new approach scales favorably (∼N(2)) with the number of configurations N used to represent the reduced density matrix in the ρ-TDCI method, as compared to a N(3) scaling for the model in its original form.

Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.

Adiabatic electronic flux density: A Born-Oppenheimer broken-symmetry ansatz

The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise anti-symmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from non-adiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is applied to the