Hans Jørgen Aa. Jensen

Integration of the classical equations of motion on ab initio molecular potential energy surfaces using gradients and Hessians: application to translational energy release upon fragmentation

Abstract A new method for calculating classical trajectories on molecular ab initio potential energy surfaces is presented. The equations of motion are integrated on a sequence of model surfaces constructed from analytically calculated molecular gradients and Hessians. The method avoids the explicit calculation of the total surface and is therefore applicable whenever the gradient and Hessian can be calculated. The method is applied to the unimolecular fragmentations of H 3 and CH 2 OH + , yielding the translational energy released upon separation of the products.

Nonlinear response theory with relaxation : The first-order hyperpolarizability

Based on the Ehrenfest theorem, an equation of motion that takes relaxation into account has been presented in wave-function theory, and the resulting response functions are nondivergent in the off-resonant as well as the resonant regions of optical frequencies. The derivation includes single- and multideterminant reference states. When applied to electric dipole properties, the response functions correspond to the phenomenological sum-over-states expressions of Orr and Ward [Mol. Phys. 20, 513 (1971)] for polarizabilities and hyperpolarizabilities of an isolated system. A universal dispersion formula is derived for the complex second-order response function. Response theory calculations are performed on lithium hydride and para-nitroaniline for off-resonant and resonant frequencies in the electro-optical Kerr effect and second-harmonic generation.

A direct, restricted-step, second-order MC SCF program for large scale ab initio calculations

Abstract A general purpose MC SCF program with a direct, fully second-order and step-restricted algorithm is presented. The direct character refers to the solution of an MC SCF eigenvalue equation by means of successive linear transformations where the norm-extended hessian matrix is multiplied onto a trial vector without explicitly constructing the hessian. This allows for applications to large wavefunctions. In the iterative solution of the eigenvalue equation a norm-extended optimization algorithm is utilized in which the number of negative eigenvalues of the hessian is monitored. The step control is based on the trust region concept and is accomplished by means of a simple modification of the Davidson—Liu simultaneous expansion method for iterative calculation of an eigenvector. Convergence to the lowest state of a symmetry is thereby guaranteed, and test calculations also show reliable convergence for excited states. We outline the theory and describe in detail an efficient implementation, illustrated with sample calculations.

Excitation energies, transition moments and dynamic polarizabilities for CH+. A comparison of multiconfigurational linear response and full configuration interaction calculations

Abstract Using a split valence with diffuse and polarization functions full configuration interaction excitation energies, transition moments and polarizabilities have been calculated for CH + . Comparisons have been made with multiconfiguration linear response calculations for various active orbital spaces and the active orbital space that gives results close to the full configuration interaction limit has been established.

MC SCF optimization using the direct, restricted step, second-order norm-extended optimization method

Abstract The potential of a direct, restricted step, second order MC SCF computer program is illustrated with a large configuration space calculation containing 24156 configuration state functions on the 3 B 1 state of methylene.

The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2

We present an implementation for large-scale relativistic electronic structure calculations including spin-dependent contributions and electron correlation in a fully variational procedure. The modular implementation of the double group configuration interaction (CI) program into a multiconfiguration self-consistent-field (MCSCF) code allows for the treatment of large CI expansions in both the spinor optimization step and the post-MCSCF dynamic electron correlation step. As an illustration of the potential of the new code, we calculate the spectroscopic properties of the UO2 molecule where we study the ground state and a few excited states in vertical and adiabatic calculations.

Relativistic effects on linear and nonlinear polarizabilities studied by effective-core potential, Douglas–Kroll, and Dirac–Hartree–Fock response theory

Relativistic calculations of electric dipole moments, linear polarizabilities, and first- and second-order hyperpolarizabilities have been carried out for the isovalent group VI dihydrides (O-Po) a ...

A gradient extremal walking algorithm

Gradient extremals define stream beds connecting stationary points on molecular potential energy surfaces. Using this concept we have developed an algorithm to determine transition states. We initiate walks at equilibrium geometries and follow the gradient extremals until a stationary point is reached. As an illustration we have investigated the mechanism for exchange of protons on carbon in methylenimine (H2C=NH) using a multi-reference self-consistent-field wave function.

Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline

We investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to the polarisable embedding scheme (PE-CCSD). We determine the amount of charge separation in the ground and excited charge-transfer state with both methods by calculating the electric dipole moments in the gas phase and for 100 solvent configurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic shift are found to be inverse proportional to the change in dipole moment upon excitation, we conclude that the flaws in the description of the solvatochromic shift of this excitation are related to TDDFT itself and how it responds to the solvent effects modelled by the PE scheme. We recommend therefore to benchmark results of TDDFT calculations with CAM-B3LYP for intramolecular charge-transfer excitations in molecular systems similar to pNA against higher level ab initio wave function methods, like, e.g. CCSD, prior to their use. Using the calculated change in dipole moment upon excitation as a measure for charge-transfer character, we furthermore confirm that the difference between excitation energies calculated with TDDFT and with the Tamm–Dancoff approximation (TDA) to TDDFT is indeed correlated with the charge-transfer character of a given electronic transition both in vacuo and in solution. This is supported by a corresponding correlation between the change in dipole moment and the size of the Λ index diagnostic for the investigated CT excitation.

Multi-configuration time-dependent density-functional theory based on range separation.

Multi-configuration range-separated density-functional theory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range Multi-Configuration-Self-Consistent Field (MCSCF) treatment with an adiabatic short-range density-functional (DFT) description, is then considered. The resulting time-dependent multi-configuration short-range DFT (TD-MC-srDFT) model is applied to the calculation of singlet excitation energies in H2, Be, and ferrocene, considering both short-range local density (srLDA) and generalized gradient (srGGA) approximations. As expected, when modeling long-range interactions with the MCSCF model instead of the adiabatic Buijse-Baerends density-matrix functional as recently proposed by Pernal [J. Chem. Phys. 136, 184105 (2012)], the description of both the 1(1)D doubly-excited state in Be and the 1(1)Σu(+) state in the stretched H2 molecule are improved, although the latter is still significantly underestimated. Exploratory TD-MC-srDFT/GGA calculations for ferrocene yield in general excitation energies at least as good as TD-DFT using the Coulomb attenuated method based on the three-parameter Becke-Lee-Yang-Parr functional (TD-DFT/CAM-B3LYP), and superior to wave-function (TD-MCSCF, symmetry adapted cluster-configuration interaction) and TD-DFT results based on LDA, GGA, and hybrid functionals.