Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution

An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.     

Theoretical study on infrared vibrational spectra of boric-acid in gas-phase using density functional methods

Density functional theory (DFT) methods with various exchange-correlation functionals such as SVWN, BVWN, BVWN5, BLYP, B1LYP, B3LYP, B3PW91, and BH and H are employed in a theoretical study of molecular boric-acid in gas-phase. In the calculations, the split valence 6-311++G** and 6-31G* basis sets were used. The geometry, zero-point vibrational energies (ZPVEs), and harmonic infrared vibrational (IR) frequencies are predicted. The calculated C_3h-symmetry geometrical parameters are compared with Hartree–Fock (HF) calculation results and experimental data. IR frequencies predicted by the BLYP, B3LYP, and B3PW91 calculations are in good agreement with experimental data. The frequency calculations presented here also suggest that the C_3h-symmetrical structure corresponds to a minimum in the potential energy surface, but neither is D_3h- or C₃-symmetrical structure.     

Theoretical study of vibrational wave-packet dynamics in electron-transfer systems

The vibrational wave-packet dynamics associated with ultrafast electron-transfer reactions in a condensed phase environment is studied. Applying the recently proposed self-consistent hybrid method to simulate the quantum dynamics of these reactions, we consider various electron-transfer systems including the spin-boson model with Debye spectral density, a reaction-coordinate model, as well as photoinduced electron-transfer reactions in a mixed valence compound. The results of the study demonstrate the interplay between electron-transfer dynamics and coherent vibrational motion of inner-sphere modes. Furthermore, the occurrence and quenching of electronic and vibrational coherence effects in electron-transfer reactions is discussed in some detail.     

Hypevirial theorem for open dynamical assemblies in the density matrix representation

The concepts of “open assembly” is defined, and the hypervirial theorem is derived in three steps: (i) An equation of motion of the reduced density matrix of the first order is derived. (ii) This equation is utilized to derive a general equation of continuity for single-particle properties. (iii) The hypervirial equation for open assemblies is obtained as a long-time average of the continuity equation. The hypervirial theorem is shown to be equivalent to a simple postulate: no physical property can keep on accumulating for ever in a limited volume. Finally, the hypervirial theorem is applied to the problems of force, torque, and virial balance in open dynamical assemblies, and the results are compared with the corresponding classical results.     

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.     

Electrostatic interactions in dissipative particle dynamics using the Ewald sums

The electrostatic interactions in dissipative particle dynamics (DPD) simulations are calculated using the standard Ewald [Ann. Phys. 64, 253 (1921)] sum method. Charge distributions on DPD particles are included to prevent artificial ionic pair formation. This proposal is an alternative method to that introduced recently by Groot [J. Chem. Phys. 118, 11265 (2003)] where the electrostatic field was solved locally on a lattice. The Ewald method is applied to study a bulk electrolyte and polyelectrolyte-surfactant solutions. The structure of the fluid is analyzed through the radial distribution function between charged particles. The results are in good agreement with those reported by Groot for the same systems. We also calculated the radius of gyration of a polyelectrolyte in salt solution as a function of solution pH and degree of ionization of the chain. The radius of gyration increases with the net charge of the polymer in agreement with the trend found in static light scattering experiments of polystyrene sulfonate solutions.     

Configurational temperature in membrane simulations using dissipative particle dynamics

The use of excessively long time steps in dissipative particle dynamics simulations may produce simulation artifacts due to the generation of configurations which are not representative of the desired canonical ensemble. The configurational temperature, among other quantities, may be used to assess the extent of the deviation from equilibrium. This paper presents results for simulations of models of water and lipid bilayer membranes to illustrate the nature of the problems.     

A spherically averaged representation of the atomic one-particle reduced density matrix

Summary A new way of representing the one-particle reduced density matrix (ODM) of closed-shell atoms in a spherically averaged manner is presented, and connections of this representation to the radial density distributionD(R) and the isotropic reciprocal form factorB(s) are shown. In this representation, certain characteristics of the angular nodal structure of the natural orbitals (NOs) are preserved. Examples of hydrogenic orbitals and near-Hartree-Fock wave functions for some closed-shell atoms are given.     

Parallel density matrix propagation in spin dynamics simulations

Several methods for density matrix propagation in parallel computing environments are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.     

Continuum limit frozen Gaussian approximation for the reduced thermal density matrix of dissipative systems

A continuum limit frozen Gaussian approximation is formulated for the reduced thermal density matrix for dissipative systems. The imaginary time dynamics is obtained from a novel generalized Langevin equation for the system coordinates. The method is applied to study the thermal density in a double well potential in the presence of Ohmic-like friction. We find that the approximation describes correctly the delocalization of the density due to quantization of the vibrations in the well. It also accounts for the friction induced reduction of the tunneling density in the barrier region.     

Femtosecond vibrational nuclear dynamics in the electronically excited state of the I2 molecule

Dynamics of the nuclear motion in the bound electronic B-state of the I₂ molecule was studied in the real time scale. Experiments were performed by the femtosecond pump-probe technique, which measured the dependence of the intensity of fluorescenceP(t) in the highly excited f-state on the time delay between pump and probe pulses. TheP(t) dependence observed has an oscillating character with a period of –300 fs. The pump pulse was generated by a femtosecond dye laser and amplified in a pulse dye laser amplifier; its spectral width was 5.6 nm, the wavelength in the center of the spectrum was 614 nm, and the duration was 90 fs. The probe pulse was generated in a KDP crystal due to duplication of the light frequency; its spectral width was 1.2 nm, the wavelength in the center of the spectrum was 307 nm, and the duration was 120 fs. TheP(t) dependence on the parameters of the probe and pump pulses was theoretically analyzed in terms of the quantum model based on the known energies of electronic vibrational-rotational states in the X-, B-, and f-terms of the iodine molecule. Experimental and calculatedP(t) plots at time delays of up to l.5 ps and time resolution of less than 100 fs were compared. Values of potentials in the X-, B-, and f-terms of the iodine molecule, spectra, and durations of pump and probe pulses are sufficient data for quantitative calculation of the experimentally obtainedP(t) plot.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 594–600, March, 1996.     

Theoretical investigation of the molecular structure,vibrational spectra,and molecular docking of tramadol using density functional theory

The optimized molecular structures, harmonic vibrational wavenumbers, and the corresponding vibrational assignments of (1S,2S)-tramadol and (1R,2R)-tramadol are computationally examined using the B3LYP density functional theory method together with the standard 6–311++G(d,p) and def2-TVZP basis sets. The optimized structures show that phenolic rings of both 1R,2R and 1S,2S tramadol adopt planar geometry, which are slightly distorted due to the substitution at the meta-position; and the six-membered cyclohexane adopts a slightly distorted chair conformation. The 1S,2S enantiomer is energetically more favorable than 1R,2R with the energy differences of 1.32 and 1.03 kcal/mol obtained at B3LYP/6–311++G(d,p) and B3LYP/Def2-TVZP levels, respectively. The analysis of the binding pocket in the silico molecular docking with the m-opioid receptor shows that it originated two clusters with the 1S,2S enantiomer and one cluster with the 1R,2R enantiomer of tramadol. The results point to a more stable complex of the m-opioid receptor with the 1R,2R enantiomer of tramadol.     

A dissipative particle dynamics description of liquid-crystalline phases. I. Methodology and applications

Simulations of nematic and smectic mesophases based on a dissipative particle dynamics approach are discussed. Mesogenic units are built in the form of standard semirigid bead-spring chains. It is shown that nematic phases can be formed for chains containing at least eight beads, provided that the conservative soft-repulsive potential between nonconnected beads is sufficiently strong. Smectic phases are observed only by modifying the repulsive interaction between the main-chain and terminal beads. The simulations indicate that the smectic-nematic and smectic-isotropic phase transitions take place through the buckling of the smectic layering in the system.     

Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix

The intramolecular wave packet dynamics on the electronic B (3pi0) potential of Br2 in solid argon is induced and interrogated by femtosecond pump-probe spectroscopy. An effective potential of the chromophore in the solid is derived from the wave packet period for different excitation photon energies. Deep in the potential well, it is consistent with vibrational energies from wavelength-resolved spectra. It extends to higher energies, where the vibrational bands merge to a continuum, and even beyond the dissociation limit, thus quantifying the cage effect of the argon matrix. This advantage of pump-probe spectroscopy is related to a reduced contribution of homogeneous and inhomogeneous line broadenings. The vibrational energy relaxation rates are determined by a variation of the probe window spatial position via the probe quantum energy. A very large energy loss in the first excursion of the wave packet is observed near the dissociation limit. This strong interaction with the argon matrix is directly displayed in an experimental trajectory.     

Calculations of vibrational energy transfer using semi-classicals matrix theory

We utilize an extension of Miller's semi-classical S matrix theory to calculate resonant and non-resonant vibrational energy transfer probabilities. The collisions under study are collinear D₂D₂ interactions at energies below and above the classical dynamic transition threshold and collinear H₂D₂ interactions above the dynamic threshold. Below threshold we employ an initial angle representation. We find that the computed probabilities are in substantial agreement with exact quantum mechanical computations and represent a major improvement over quasi-classical results. At energies above threshold we apply the first order and the classical semi-classical versions of the theory. The results indicate fair agreement with quantum mechanical calculations, but no significant improvement over quasi-classical results.     

Reduced first order density matrix for the Be ground state

A reduced first order density matrix for the Be ground state is computed from an extensive configuration interaction (CI ) wave function. A sequence of increasingly accurate CI wave functions Φ_q converging towards the exact Ψ is used to assess the quality of the results which include approximate bounds for the overlaps 〈Φ_q|Ψ〉, electron–nuclear coalescence cusp data, Weinhold's overlap between density matrices, virial ratios, occupation number spectra, and some expectation values. The nuclear magnetic shielding constant and the molar diamagnetic susceptibility are determined with 2.0 and 1.5% of uncertainty, respectively.     

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.