Variational construction of diabatic states

The previously proposed local variational algorithm for generating diabatic states from adiabatic states is tested numerically for the simplest case of avoided potential curve crossing in a diatomic. The obtained results fully agree with those found by an interpolation scheme.     

Hamiltonian for diabatic molecular states

Hyperradial-adiabatic potential curves for (dt )⁺ molecular ions calculated for states with total three-body angular momentumJ=1 and total parityp=1, i.e. for the abnormal parity ground set, are demonstrated to be exactly diabatic-hyperradial potential curves for (J=1,p=–1) symmetry adiabatic curves. This could be thought of as a formal manifestation of the -doubling effect. The projection operator method of constructing a diabatic Hamiltonian that was suggested earlier can be naturally used in our case, too.     

Novel variational definition of diabatic states

The requirement that diabatic states be dominated by a single electronic configuration is transformed into a variational principle. A very simple algorithm for the adiabatic—diabatic transformation is found. It is equally applicable to avoided and to true potential crossing situations.     

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

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) 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-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). 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.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

A method for constructing diabatic states by interpolation on the reduced density matrix

Avoided crossing of adiabatic potential energy curves is considered. A new scheme for the adiabatic-diabatic transformation is developed that is based on an interpolation performed on reduced one-electron density matrices. The procedure is tested on the N₂ molecule.     

Determination of configurational isomers in cyclic polysulfides by Raman spectroscopy

Cyclic polysulfides such as trithiolanes, tetrathianes and their derivatives are found in natural sources like archaea, mushrooms and vegetables. They gained interest for research and industrial applications because of their pronounced flavors and biological activity. This study compares Raman spectra of reference compounds and cyclic polysulfides which were synthesized in-house and separated by preparative gas chromatography. The data show that the positions of the Raman bands due to SS stretching vibrations in the wavenumber region from 550 to 450 cm⁻¹ can determine the relative stereochemistry of 2,5-dialkyl trithiolanes and 4,6-dialkyl tetrathianes. Configurational cis isomers were distinguished from their corresponding trans isomers. In addition, 4,6-dialkyl-1,2,4,5-tetrathiane with disulfide bonds were distinguished from the constitutive isomer 3,6-dialkyl-1,2,3,5-tetrathiane with trisulfide bonds.     

Charge transfer ionic character illustration for strontium hydride ion through a diabatic investigation

Adiabatic and diabatic studies are performed for the strontium hydride ion (SrH)⁺. Potential energy surface and electric dipole moment for the ground and all excited states dissociating up to the charge transfer ionic limit Sr²⁺H⁻ have been investigated and analyzed in adiabatic and diabatic representations. The adiabatic approach uses the pseudo potential for the strontium atom complemented by core polarization potential operators, reducing the calculation to a two effective electrons system where full configuration interaction can be easily performed. The adiabatic results have been improved by a simple correction of the hydrogen electron affinity for all ¹Σ⁺ states. The diabatic results reveal the strong imprint of the charge transfer ionic state in the ¹Σ⁺ adiabatic states.     

Dynamics of bichromophoric compounds in the excited and ionic states: Conformational and configurational aspects

Absorption spectra of N-ethylcarbazole, 1,2-trans-di-N-carbazolylcyclobutane, 1,3-di-N-carbazolylpropane, rac(dd, 11)-2,4-di-N-carbazolylpentane and meso(dl)2,4-di-N-carbazolylpentane in the excited singlet, triplet, cationic and anionic states were measured with nanosecond and picosecond laser photolysis methods. The main conformations in the excited and ionic states were determined, which made it possible to establish a relation among adsorption spectrum, intersystem crossing, and relative geometrical structure of two carbazolyl groups. Fast conformational changes of these compounds were directly measured and compared with slow ones of bis[1-(1-pyrenyl)ethyl]ethers.     

The adiabatic‐to‐diabatic transformation angle and topological phases for strongly interacting states: Solution with four states

A few years back T. Vértesi et al. (J Phys Chem A 2005, 109, 3476) gave an elegant procedure to derive the adiabatic‐to‐diabatic transformation angle (ADT‐angle) for lowest two states, γ₁₂, in presence of their interaction with the higher states. In this article, we explicitly solved the coupled differential equations involving the ADT‐angles describing the mixing of four interacting states for the first time to get all the ADT‐angles, γ_ij's (including the γ₁₂) associated with well‐defined topological phases. In application to a suitable configuration space (CS) of a molecular system, we have demonstrated well‐defined Berry phases (Berry M. V., R Soc London Ser A 1984, 45, 392) for an isolated system with as many as four strongly interacting states. © 2012 Wiley Periodicals, Inc.     

Density of configurational states from first-principles calculations: the phase diagram of Al-Na surface alloys.

The structural phases of Al(x)Na(1-x) surface alloys have been investigated theoretically and experimentally. We describe the system using a lattice-gas Hamiltonian, determined from density functional theory, together with Monte Carlo (MC) calculations. The obtained phase diagram reproduces the experiment on a quantitative level. From calculation of the (configurational) density of states by the recently introduced Wang-Landau MC algorithm, we derive thermodynamic quantities, such as the free energy and entropy, which are not directly accessible from conventional MC simulations. We accurately reproduce the stoichiometry, as well as the temperature at which an order-disorder phase transition occurs, and demonstrate the crucial role, and magnitude, of the configurational entropy.     

Theoretical study of the He-HF+ complex. II. Rovibronic states from coupled diabatic potential energy surfaces

The bound rovibronic levels of the He-HF+ complex were calculated for total angular momentum J=1/2, 3/2, 5/2, 7/2, and 9/2 with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin-orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance R fixed at values ranging from 1.5 to 8.5 A and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer body-fixed (BF) frame with its z axis parallel to the intermolecular vector R and with respect to a molecule-fixed (MF) frame with its z axis parallel to the HF+ bond. The linear equilibrium geometry makes the He-HF+ complex a Renner-Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner-Teller effect in this system. In addition to the properties of a "normal" semirigid molecule Renner-Teller system it shows typical features caused by large-amplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin-orbit splittings, parity splittings, and rotational constants.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

Interpolation of diabatic potential energy surfaces

A method is presented for constructing diabatic potential energy matrices from ab initio quantum chemistry data. The method is similar to that reported previously for single adiabatic potential energy surfaces, but correctly accounts for the nuclear permutation symmetry of diabatic potential energy matrices and other complications that arise from the derivative coupling of electronic states. The method is tested by comparison with an analytic model for the two lowest energy states of H(3).     

Host-rotaxanes model proteins that promote ligand association through a favorable change in configurational entropy

Proteins can reduce the entropic penalty for ligand association through a favorable change in configurational entropy. To investigate this process, the Delta G(o), Delta H(o), and DeltaS(o) of complexes formed between host-rotaxanes and guests were determined and compared to discover the relationship between rotaxane-structure and the energies involved in guest-association in water and DMSO. Fluorescence quenching assays provided the association constants. Van't Hoff analysis of variable temperature assays gave the enthalpies of binding. The driving force for the association of a guest and a host-rotaxane can switch from being enthalpically to entropically driven with a change in the solvent or guest. This study shows that a dramatic increase in the entropy of binding can be obtained through the addition of a rotaxane-wheel to a synthetic host. An increased motion of the wheel appears to be the source of the positive binding entropy, which would be an example of favorable configurational entropy promoting complex formation.     

Interpolation of multidimensional diabatic potential energy matrices

A method for constructing diabatic potential energy matrices by interpolation of ab initio quantum chemistry data is described and tested. This approach is applicable to any number of interacting electronic states, and relies on a formalism and a computational procedure that are more general than those presented previously for the case of two electronic states. The method is tested against an analytic model for three interacting electronic states of NH(3) (+).     

Determination of equilibrium states in multi-phase systems

Volume corrections in calculation of equilibrium state for multi-phase systems, as an extension from one-phase systems, have been described. The algorithms can handle with one, two, three or more phases of different volumes. Several applications of the algorithms to calculation of equilibrium concentrations of all species in two- and three-phase systems have been presented. Different possibilities of the determination of equilibrium constants from extraction data have been discussed.