Electronic Spectra

Ballhausen, C. J.; Hansen, Aage E.

doi:10.1146/annurev.pc.23.100172.000311

Cited by 179 publications

(85 citation statements)

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“…For completeness, we also discuss the so-called "diabatic" representation. [5] This representation is defined by having time-or geometry-independent basis functions (also called "crude adiabatic" basis [173] ), which means that a diabatic basis has T diab 5 0 and likewise K diab 5 0. The coupling between diabatic states is described by off-diagonal terms in the Hamiltonian.…”

Section: Representationsmentioning

confidence: 99%

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Mai

Marquetand

González

2015

Int J of Quantum Chemistry

266

406

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Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV‐Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different methods to describe intersystem crossing dynamics, paying attention to semiclassical trajectory theories, which are especially interesting because they can be applied to large systems with many degrees of freedom. In particular, a general trajectory surface hopping methodology recently developed by the authors, which is able to include nonadiabatic and spin‐orbit couplings in excited‐state dynamics simulations, is explained in detail. This method, termed SHARC, can in principle include any arbitrary coupling, what makes it generally applicable to photophysical and photochemical problems, also those including explicit laser fields. A step‐by‐step derivation of the main equations of motion employed in surface hopping based on the fewest‐switches method of Tully, adapted for the inclusion of spin‐orbit interactions, is provided. Special emphasis is put on describing the different possible choices of the electronic bases in which spin‐orbit can be included in surface hopping, highlighting the advantages and inconsistencies of the different approaches. © 2015 Wiley Periodicals, Inc.

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Section: Representationsmentioning

confidence: 99%

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Mai

Marquetand

González

2015

Int J of Quantum Chemistry

266

406

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“…For other systems, approximations must be introduced to calculate numerical solutions with the aid of computers. The most common and perhaps the mildest approximation often made is the Born-Oppenheimer approximation [19,[24][25][26][27][35][36][37][38]. It decouples internuclear motions from electrons so that nuclei effectively move on a potential energy surface (PES) obtained by solving the electronic part of Schrödinger equation.…”

Section: Origin Of Potential Energy Surface: Born-oppenheimer Approximentioning

confidence: 99%

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Wong

2014

Commun. comput. phys.

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Abstract. Feynman's path integral reformulates the quantum Schrödinger differential equation to be an integral equation. It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems. In this Review, the molecular Schrödinger equation will first be introduced, together with the BornOppenheimer approximation that decouples electronic and internuclear motions. Some effective semiclassical potentials, e.g., centroid potential, which are all formulated in terms of Feynman's path integral, will be discussed and compared. These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger's energy eigenvalues. As a result, path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques. To complement these techniques, we will examine how Kleinert's variational perturbation (KP) theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential. To enable the powerful KP theory to be practical for many-body molecular systems, we have proposed a new path-integral method: automated integrationfree path-integral (AIF-PI) method. Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method, we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions. The computational procedure of using our AIF-PI method, along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy (AMAZE), are also highlighted in this review.

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“…In Equation (2) and in the ones that follow, atomic units are used, except for the reduced Planck's constant, , that will be kept for clarity.…”

Section: Nonadiabatic Dynamics With Classical and Quantum Trajectoriesmentioning

confidence: 99%

“…Within this approximation, one usually solves the time-independent electronic Schrödinger equation for a given nuclear configuration [2] and then computes the quantum mechanical forces acting on the nuclei from the gradient of the corresponding eigenvalues, which depend parametrically on the nuclear coordinates and form the so-called potential energy surfaces (PES). However, in the description of most photophysical and photochemical processes, the electronic and nuclear dynamics become entangled, and therefore, more accurate nonadiabatic molecular dynamics schemes that go beyond the Born-Oppenheimer (BO) approximation are required.…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic Molecular Dynamics Based on Trajectories

Carvalho

Bouduban

Curchod

et al. 2013

Entropy

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Performing molecular dynamics in electronically excited states requires the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes an interesting compromise between accuracy and efficiency for the simulation of medium-to large-scale molecular systems. This approach is, however, based on non-rigorous approximations that could compromise, in some cases, the correct description of the nonadiabatic effects under consideration and hamper a systematic improvement of the theory. With the help of an in principle exact description of nonadiabatic dynamics based on Bohmian quantum trajectories, we will investigate the origin of the main approximations in trajectory surface hopping and illustrate some of the limits of this approach by means of a few simple examples.

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Electronic Spectra

Cited by 179 publications

References 0 publications

A general method to describe intersystem crossing dynamics in trajectory surface hopping

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Nonadiabatic Molecular Dynamics Based on Trajectories

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