Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

Abstract

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics ͑QWAIMD͒ method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD ͑xLag-QWAIMD͒ and diabatic extended Lagrangian-QWAIMD ͑DxLag-QWAIMD͒. In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

Accurate non-adiabatic quantum dynamics from pseudospectral sampling of time-dependent Gaussian basis sets

“…[1][2][3][4][5] Unfortunately, the ab initio description of nonadiabatic chemical processes is still a significant challenge for computation because of the accuracy and efficiency required for both the quantum molecular dynamics and the molecular electronic structure. 3,4,[6][7][8][9][10][11][12][13][14][15][16][17] Electronic structure calculations for nonadiabatic dynamics are computationally expensive because they must generate accurate excited electronic states with a balanced description of strong correlation. [18][19][20][21][22][23] A time-dependent (trajectory-guided) basis set circumvents the exponential scaling of traditional grid methods while being compatible with the direct determination of the potential energy surface from electronic structure calculations.…”

Gauging the Flexibility of the Active Site in Soybean Lipoxygenase-1 (SLO-1) through an Atom-Centered Density Matrix Propagation (ADMP) Treatment That Facilitates the Sampling of Rare Events

“…Such approaches have been combined 53–55 with extended-Lagrangian techniques 56–59 for (a) schemes that allow efficient treatment of systems having a large separation in time-scales 60–64 , and (b) simulations of other ensembles 56–59 . Another example of extended Lagrangian techniques is a growing class of strategies that allow the inclusion of electronic degrees of freedom with nuclear (classical and quantum) dynamics in real 65–67 and imaginary 68–73 time. Direct variational minimization of action to obtain long time-scale classical trajectories that sample rare events is another approach that was introduced by Elber and coworkers 74–78 .…”

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets

“…We also note that the recently published quantum trajectory Gaussian basis (QTGB) 9 method provides an interesting perspective in its application of Bohmian mechan-ics to its guiding trajectories; initial applications of this approach to two-dimensional problems have proven promising, while the applicability to more challenging higher-dimensional systems remains to be tested. Expanding the scope further beyond trajectory-guided methods for wavefunction propagation, there also exist a range of methods which employ mixed strategies whereby a quantum sub-system evolves in the presence of a classical environment; the quantum wavepacket ab initio molecular dynamics (QWAIMD) method 31,32 is a good example of such an approach which has found application to, for example, vibrational properties of hydrogen-bonded dihalide systems. 33 Of course, the idea of classical evolution of wavefunctions is also tied to the enormous range of work on semi-classical quantum dynamics methods, including the popular linearized-semi-classical initial value representation (LSC-IVR [34][35][36][37][38][39] ) and forwards-backwards IVR methods (FB-IVR 40,41 ) which have been successfully employed to study systems ranging from liquid water 42 to photosynthetic complexes.…”