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This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.
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We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S1/T2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.
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We present a preliminary extension of the fewest switches surface hopping (FSSH) algorithm to the case of complex Hamiltonians as appropriate for modeling the dynamics of photoexcited molecules in magnetic fields. We make ansätze for the direction of momentum rescaling, and we account for Berry's phase effects through "magnetic" forces as applicable in the adiabatic limit. Because Berry's phase is a nonlocal, topological characteristic of a set of entangled potential energy surfaces, we find that Tully's local FSSH algorithm can only partially capture the correct physics.
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Although the quantum classical Liouville equation (QCLE) arises by cutting off the exact equation of motion for a coupled nuclear-electronic system at order 1 (1 = â0), we show that the QCLE does include Berry's phase effects and Berry's forces (which are proportional to a higher order, â = â1). Thus, the fundamental equation underlying mixed quantum-classical dynamics does not need a correction for Berry's phase effects and is valid for the case of complex (i.e., not just real) Hamiltonians, where exotic features can arise in the course of electronic relaxation. Furthermore, we also show that, even though Tully's surface hopping model ignores Berry's phase, Berry's phase effects are included automatically within Ehrenfest dynamics. These findings should be of great importance if we seek to model coupled nuclear-electronic dynamics for systems with odd numbers of electrons and spin-orbit coupling, where the complex nature of the Hamiltonian is paramount.
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For future use in modeling photoexcited dynamics and intersystem crossing, we calculate spin-adiabatic states and their analytical nuclear gradients within configuration interaction singles theory. These energies and forces should be immediately useful for surface hopping dynamics, which are natural within an adiabatic framework. The resulting code has been implemented within the Q-Chem software and preliminary results suggest that the additional cost of including spin-orbit coupling within the singles-singles block is not large.
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We present a current, up-to-date review of the surface hopping methodology for solving nonadiabatic problems, 25 years after Tully published the fewest switches surface hopping algorithm. After reviewing the original motivation for and failures of the algorithm, we give a detailed examination of modern advances, focusing on both theoretical and practical issues. We highlight how one can partially derive surface hopping from the Schrödinger equation in the adiabatic basis, how one can change basis within the surface hopping algorithm, and how one should understand and apply the notions of decoherence and wavepacket bifurcation. The question of time reversibility and detailed balance is also examined at length. Recent applications to photoexcited conjugated polymers are discussed briefly.
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We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton's [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-fieldtheory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.
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In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of N2O, singlet-triplet conversion in CH2, and CO addition to Fe(CO)4], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.