Semiclassical time-correlation function approach to collisional energy transfer into many-atom systems

Cross sections for energy transfer into many-body systems can be expressed in terms of time-correlation functions (TCFS ) of transition operators. A semiclassical version is presented by treating internal motions as quantized and relative motions as classical. The time evolution of internal motions can be calculated in the Heisenberg picture and avoids expansions in target states. The decoupling of fast and slow internal motions is treated and applied to vibrational–rotational decoupling in polyatomic molecules. Results are presented for Li⁺-CO₂ collisions.     

An approach to the understanding of radiation chemistry in the condensed phase

This paper describes a purely electronic mechanism by which ≈ 20 eV excitations in condensed phases relax to lower energy states. The mechanism utilizes an “energy fission” process whereby an ionic or excitonic state splits into two lower energy states, at least one being localized. The mechanism explains not only the known rapidity of such processes but also suggests an explanation for the proportionation of the chemistry between ionic and electronically excited states.     

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.     

Non-markovian theory of molecular relaxation. I. Vibrational relaxation and dephasing in condensed phases

The cumulant expansion is used to derive two formally different master equations for a two-level molecular system interacting with a bath, starting wit The two master equations reduce to the same form in the markovian limit for the bath (where its correlation time is much shorter than the relaxation pr A detailed comparison is made between the predictions of the two approaches which enables us to understand their range of validity and limitations. We apply the formalism to the vibrational relaxation and dephasing of a molecular impurity in a solid matrix and obtain a closed expression for the vib In contrast to the simple stochastic approaches we predict that the line shape in the non-markovian limit contains information regarding the interactio However, the fluctuations in the mean interaction energy of the two-level system with the bath, if correlated with the frequency modulation, result in     

Semiquantal time-dependent Hartree approach to condensed phase chemical dynamics: application to the system-bath model

A semiquantal analysis of condensed phase chemical dynamics, outlined recently for a double-well linearly coupled to dissipative harmonic bath, is formulated in detail to clarify its general features as well as the specifics of the linear and quadratic coupling cases. The theory may be called a "semiquantal time-dependent Hartree (SQTDH)" approach, as it assumes a factorized product of the squeezed coherent state wave packets for the variational subspace of the many-dimensional time-dependent wave function. Due to this assumption, it straightforwardly satisfies the canonicity condition introduced by Marumori et al. is described by a set of Hamilton equations of motion in an extended phase space that includes auxiliary coordinates representing the wave packet widths. The potential in the extended phase space provides a pictorial understanding of the quantum effects affected due to the bath coupling, e.g., suppression of the wave packet spreading in terms of the potential wall developing along the auxiliary coordinates. The idea is illustrated by prototypical models of quartic double-well and cubic metastable potentials linearly and quadratically coupled to the bath. Further applications and extensions, where the SQTDH method will offer a practical approach for introducing quantum effects into realistic molecular dynamics simulations, are also discussed.     

On a fokker-planck type approach to molecular dynamics in condensed phase

A fast algorithm for dealing with multiplicative stochastic processes such as dielectric relaxation is developed. This technique allows us to get a straightforward evaluation of the effects of non-linearity, expecially non-Gaussian behaviour. Its use jointly to computer “experiments” on non-Gaussian behaviour is shown to be of basic importance for establishing a new approach to molecular dynamics in terms of non-linear models.     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

On the nature of intramolecular dephasing processes in polyatomic molecules

Intramolecular dephasing processes in polyatomic molecules are discussed with relation to coherent transient spectroscopy, radiationless transitions, multiphoton molecular processes, and overtone spectroscopy. A distinction is made between proper and improper dephasing processes (PDP, IDP) depending on whether they arise due to changes in populations or not. It is shown that the type of experiment and, consequently, the way we partition the hamiltonian are closely related to this distinction. We consider several experimental and theoretical approaches for studying intramolecular dynamics and discuss under what conditions it is necessary and useful to introduce explicitly dephasing interactions.     

Water polarizability in condensed phase: ab initio evaluation by cluster approach

The polarizability of a water molecule in liquid is evaluated via ab initio and density functional calculations for water clusters. This work has considerably improved our previous effort [J Chem Phys 1999, 110, 11987] to attain quantitative accuracy for polarizability. The calculations revealed that the water polarizability in the liquid is reduced from that in the gaseous phase by 7-9%. These results suggest significant implications for polarizable water models.     

New approach to indole alkaloids based on the intramolecular Pauson-Khand reaction

The synthesis of indoles bearing alkenyl and alkynyl moieties in different positions of the nucleus is described. These compounds are used as substrates for the intermolecular Pauson-Khand reaction leading to tetracyclic cyclopentenones with formation of additional five- to seven-membered rings. Products are related to alkaloids such as mitosenes, clausines, ergotamines, or apogeissochizines.     

The theory of atomic-molecular transformations in condensed phase at low temperatures

The probability of the elementary act of a nonadiabatic chemical reaction in condensed medium at low temperature is calculated. General results are illustrated by the formulas for Debye-type and resonance-type absorption spectra of the medium. For the reactions involving the reorganization of the intramolecular structure of the reactants the limiting cases of both weak and strong coupling of the reactants with the medium are considered.     

New approach to unsymmetrical 1,3-diazatriphenylenes through intramolecular oxidative cyclodehydrogenation

An efficient synthetic route towards previously inaccessible dibenzo[f,h]quinazolines and [1]benzothieno[3,2-f]benzo[h]quinazolines through FeCl₃-mediated intramolecular oxidative cyclodehydrogenation of readily available 5-([1,1′-biphenyl]-2-yl)pyrimidines and 5-(2-phenylbenzo[b]thiophen-3-yl)pyrimidines is described. Molecular orbital calculations (DFT), as well as redox and photophysical measurements for all new compounds have been performed. The data show that the reported polycyclic systems have a potential to use in organic electronic applications.     

Vibrational relaxation in the condensed phase

A modified Landau-Teller equation for vibrational relaxation in the condensed phase is proposed. This equation differs from previous approaches by accounting for the fluctuations of the energies of the vibrational levels that result from the interactions with the surroundings (bath). In the conventional approach the effects of the bath are only included in the coupling between the relaxing and accepting vibrational modes. It is shown that the additional inclusion of the fluctuations of the energy levels can lead to a dramatic change of the vibrational relaxation rate.     

eQE: An open‐source density functional embedding theory code for the condensed phase

In this work, we present the main features and algorithmic details of a novel implementation of the frozen density embedding (FDE) formulation of subsystem density functional theory (DFT) that is specifically designed to enable ab initio molecular dynamics (AIMD) simulations of large‐scale condensed‐phase systems containing 1000s of atoms. This code (available at http://eqe.rutgers.edu ) has been given the moniker of embedded Quantum ESPRESSO (eQE) as it is a generalization of the open‐source Quantum ESPRESSO (QE) suite of programs. The strengths of eQE reside in a hierarchical parallelization scheme that allows for an efficient and fully self‐consistent treatment of the electronic structure (via the addition of an additional DIIS extrapolation layer) while simultaneously exploiting the inherent symmetries and periodicities in the system (via sampling of subsystem‐specific first Brillouin zones and utilization of subsystem‐specific basis sets). While bulk liquids and molecular crystals are two classes of systems that exemplify the utility of the FDE approach (as these systems can be partitioned into weakly interacting subunits), we show that eQE has significantly extended this regime of applicability by outperforming standard semilocal Kohn–Sham DFT (KS‐DFT) for large‐scale heterogeneous catalysts with quite different layer‐specific electronic structure and intrinsic periodicities. eQE features very favorable strong parallel scaling for a model system of bulk liquid water composed of 256 water molecules, which allows for a significant decrease in the overall time to solution when compared to KS‐DFT. We show that eQE achieves speedups greater than one order of magnitude ( ) when performing AIMD simulations of such large‐scale condensed‐phase systems as: (1) molecular liquids via bulk liquid water represented by 1024 independent water molecules (3072 atoms with a 25.3× speedup over KS‐DFT), (2) polypeptide/biomolecule solvation via (gly )₆ solvated in (H₂O)₃₉₅ (1230 atoms with a 38.6× speedup over KS‐DFT), and (3) molecular crystals via a 3 × 3 × 3 periodic supercell of pentacene (1940 atoms with a 12.0× speedup over KS‐DFT). These results represent a significant improvement over the current state‐of‐the‐art and now enable subsystem DFT‐based AIMD simulations of realistically sized condensed‐phase systems of interest throughout chemistry, physics, and materials science.     

Density functional theory study of 1,2‐dioxetanone decomposition in condensed phase

The decomposition of 1,2‐dioxetanone into a CO₂ molecule and into an excited state formaldehyde molecule was studied in condensed phase, using a density functional theory approach. Singlet and triplet ground and excited states were all included in the calculations. The calculations revealed a novel mechanism for the chemiluminescence of this compound. The triplet excitation can be explained by two intersystem crossings (ISCs) with the ground state, while the singlet excitation can be accounted by an ISC with the triplet state. The experimentally verified small excitation yield can then be explained by the presence of an energy barrier present in the potential energy surface of the triplet excited state, which will govern both triplet and singlet excitation. It was also found that the triplet ground state interacts with both the triplet excited and singlet ground states. A MPWB1K/mPWKCIS approach provided results in agreement with the existent literature. © 2012 Wiley Periodicals, Inc.     

New approach to the first-order phase transition of Lennard-Jones fluids

The multicanonical Monte Carlo method is applied to a bulk Lennard-Jones fluid system to investigate the liquid-solid phase transition. We take the example of a system of 108 argon particles. The multicanonical weight factor we determined turned out to be reliable for the energy range between -7.0 and -4.0 kJ/mol, which corresponds to the temperature range between 60 and 250 K. The expectation values of the thermodynamic quantities obtained from the multicanonical production run by the reweighting techniques exhibit the characteristics of first-order phase transitions between liquid and solid states around 150 K. The present study reveals that the multicanonical algorithm is particularly suitable for analyzing the transition state of the first-order phase transition in detail.     

Application of the group function theory to infinite systems

We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill‐defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A “linked‐AD” theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long‐range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 511–534, 2000     

New approach to calculation of the leaky aquifer function

The leaky aquifer function W(x,y), an incomplete Bessel function which has had application in hydrology, is now also arising in electronic-structure calculations on periodic systems. This work presents an expansion which improves the efficiency of calculation of W in the range where x and y are comparable and both are larger than unity. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 913–916, 1997     

Momentum representation of the solute/bath interaction in the dynamic theory of chemical processes in condensed phase

For the system consisting of the chemically reactive solute immersed in the oscillator bath, we consider an approach based on the solute/medium interaction expressed in terms of momenta rather than coordinates. In the adiabatic representation the medium reorganization effects are suppressed, being hidden in the solute renormalized potential and new spectral density function. The advantage proposed by the bilinear interaction in momentum representation is its spatial uniformity important for approximate dynamical treatments. The procedure of explicit transforming a standard spectral density (coordinate representation of interaction) into the spectral density in adiabatic representation (momentum representation of interaction) is the main new result of the present study. Illustrative calculations for several types of spectral functions are performed. Special discussion is devoted to clarifying the nature of the slow diffusion coordinate, to which the present approach is mainly addressed.     

Application of the unitary group approach to crystal field theory

An analytical treatment for a strong crystal field in an octahedral symmetry by using the unitary group approach is given. It shows that the convenience of the unitary group approach is comparable with that of the Racah method.