Search

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In Paper I, focusing on adiabatic single surface processes, we derive the well-known double Herman–Kluk (DHK) approximation for real-time correlation functions in Wigner phase space and connect it to the linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important "system" degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the "bath") at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators and the decoherence of vibrational probability density of a model I2 Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign problem and employs reduced dimensional prefactors bringing calculations of complex system–bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes. [ABSTRACT FROM AUTHOR]

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field—the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperatures, quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this paper, we use the trajectory-ensemble reformulation of quantum mechanics, as recently proposed by one of the authors (Poirier) to compute adiabatic-channel capture probabilities and cross-sections for the highly exothermic reaction Li + CaH( v = 0, j = 0) → LiH + Ca, at low and ultra-low temperatures. Each captured quantum trajectory takes full account of tunneling and quantum reflection along the radial collision coordinate. Our approach is found to be very fast and accurate, down to extremely low temperatures. Moreover, it provides an intuitive and practical procedure for determining the capture distance (i.e., where the capture probability is evaluated), which would otherwise be arbitrary. [ABSTRACT FROM AUTHOR]

This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest 3A′ and 3A″ electronic states of the O(3P) + H2 system. For each of these states, ab initio electronic energies were calculated for more than 5000 geometries using internally contracted multireference configuration interaction methods. The calculated points were then fitted using the ansatz by Aguado et al. [Comput. Phys. Commun. 108, 259 (1998)] leading to very accurate analytical potentials well adapted to perform reaction dynamics studies. Overall, the topographies of both PESs are in good agreement with the benchmark potentials of Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)], but those presented in this work reproduce better the height and degeneracy of the two states at the saddle point. Moreover, the long range potential in the entrance channel does not require any cutoff. These features make the new PESs particularly suitable for a comparison of the dynamics on each of them. The new set of PESs was then used to perform quantum mechanics and quasiclassical trajectory calculations to determine differential and integral cross sections, which are compared to the experimental measurements by Garton et al. [J. Chem. Phys. 118, 1585 (2003)]. [ABSTRACT FROM AUTHOR]

Control of quantum systems via lasers has numerous applications that require fast and accurate numerical solution of the Schrödinger equation. In this paper, we present three strategies for extending any sixth-order scheme for the Schrödinger equation with time-independent potential to a sixth-order method for the Schrödinger equation with laser potential. As demonstrated via numerical examples, these schemes prove effective in the atomic regime as well as the semiclassical regime and are a particularly appealing alternative to time-ordered exponential splittings when the laser potential is highly oscillatory or known only at specific points in time (on an equispaced grid, for instance). These schemes are derived by exploiting the linear in space form of the time dependent potential under the dipole approximation (whereby commutators in the Magnus expansion reduce to a simpler form), separating the time step of numerical propagation from the issue of adequate time-resolution of the laser field by keeping integrals intact in the Magnus expansion and eliminating terms with unfavorable structure via carefully designed splittings. [ABSTRACT FROM AUTHOR]

Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However, it is often found that simple incoherent kinetic models of the radical pair singlet-triplet intersystem crossing provide an acceptable description of experimental measurements. In this paper, we outline the theoretical basis for this incoherent kinetic description, elucidating its connection to exact quantum mechanics. We show, in particular, how the finite lifetime of the radical pair spin states, as well as any additional spin-state dephasing, leads to incoherent intersystem crossing. We arrive at simple expressions for the radical pair spin state interconversion rates to which the functional form proposed recently by Steiner et al. [J. Phys. Chem. C 122, 11701 (2018)] can be regarded as an approximation. We also test the kinetic master equation against exact quantum dynamical simulations for a model radical pair and for a series of PTZ•+–Phn–PDI•− molecular wires. [ABSTRACT FROM AUTHOR]

The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function, which has led to a variety of numerically exact quantum methods for reduced density matrix propagation. Since spectral densities are often computed from classical molecular dynamics simulations, we investigate in this paper whether quantum effects should be accounted for in the calculations. Therefore, we reformulate the recently developed Fourier method for spectral density calculations from semiclassical simulations which approximately allow for quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested on a generic Calderra-Leggett model for the linearized semiclassical initial-value representation (LSC-IVR), the thawed Gaussian wave packet dynamics (TGWD), and hybrid schemes combining the two with the more accurate Herman-Kluk formula. Surprisingly, spectral densities from the LSC-IVR method, which treats the dynamics completely classically, are found to be extremely accurate, even in the quantum regime, where this method does not give a correct description of the correlation functions and expectation values. In contrast, the TGWD method turns out as too inaccurate for spectral density calculations, and the hybrid schemes perform well only if the system is close to the classical regime. This implies that, if the bath has a Caldeira-Leggett form, spectral densities are insensitive to quantum effects and any effort to approximately account for them rather leads to errors. Hence, in this case, spectral densities can be computed from classical simulations and used in a reduced quantum simulation as well. [ABSTRACT FROM AUTHOR]

A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters. [ABSTRACT FROM AUTHOR]

Multi-configurational Ehrenfest (MCE) approaches, which are intended to remedy the lack of correlations in the standard mean-field Ehrenfest method, have been proposed as coherent-state based ansätze for quantum propagation [D. V. Shalashilin, J. Chem. Phys. 130, 244101 (2009)] and also as the classical limit of the variational Gaussian-based multiconfiguration time dependent Hartree (G-MCTDH) method [S. Römer and I. Burghardt, Mol. Phys. 111, 3618 (2013)]. In the present paper, we establish the formal connection between these schemes and assess the performance of MCE for a coherent-state representation of the classical-limit subsystem. As a representative model system, we address the ultrafast, coherent charge transfer dynamics in an oligothiophene-fullerene donor-acceptor complex described by a two-state linear vibronic coupling model. MCE calculations are compared with reference calculations performed with the MCTDH method, for 10–40 vibrational modes. Beyond a dimensionality of 10 modes, it is shown that the correct representation of electronic coherence depends crucially on the sampling of initially unoccupied Gaussians. [ABSTRACT FROM AUTHOR]

In this paper, two levels of theory are developed to determine the role of scattering resonances in the process of ozone formation. At the lower theory level, we compute resonance lifetimes in the simplest possible way, by neglecting all couplings between the diabatic vibrational channels in the problem. This permits to determine the effect of "shape" resonances, trapped behind the centrifugal barrier and populated by quantum tunneling. At the next level of theory, we include couplings between the vibrational channels, which permits to determine the role of Feshbach resonances and interaction of different reaction pathways on the global PES of ozone. Pure shape resonances are found to contribute little to the overall recombination process since they occur rather infrequently in the spectrum, in the vicinity of the top of the centrifugal barrier only. Moreover, the associated isotope effects are found to disagree with experimental data. By contrast, Feshbach-type resonances are found to make dominant contribution to the process. They occur in a broader range of spectrum, and their density of states is much higher. The properties of Feshbach resonances are studied in detail. They explain the isotopic ζ -effect, giving theoretical prediction in good agreement with experiments for both singly and doubly substituted ozone molecules. Importantly, Feshbach resonances also contribute to the isotopic η -effect, moving theoretical predictions in the right direction. Some differences with experimental data remain, which indicates that there may be another additional source of the η -effect. [ABSTRACT FROM AUTHOR]

The role of vibrational excitation of reactants in driving reactions involving polyatomic species has been often studied by means of classical or quasi-classical trajectory simulations. We propose a different approach based on investigation of vibrational features of the Cl−⋯CH3Cl pre-reaction complex for the Cl− + CH3Cl SN2 reaction. We present vibrational power spectra and frequency estimates for the title pre-reaction complex calculated at the level of classical, semiclassical, and second-order vibrational perturbation theory on a pre-existing analytical potential energy surface. The main goals of the paper are the study of anharmonic effects and understanding of vibrational couplings that permit energy transfer between the collisional kinetic energy and the internal vibrations of the reactants. We provide both classical and quantum pictures of intermode couplings and show that the SN2 mechanism is favored by the coupling of a C–Cl bend involving the Cl− projectile with the CH3 rocking motion of the target molecule. We also illustrate how the routines needed for semiclassical vibrational spectroscopy simulations can be interfaced in a user-friendly way to pre-existing molecular dynamics software. In particular, we present an implementation of semiclassical spectroscopy into the VENUS suite of codes, thus providing a useful computational tool for users who are not experts of semiclassical dynamics. [ABSTRACT FROM AUTHOR]

Probabilities to find a chosen number of electrons in flexible domains of space are calculated for highly correlated wave functions. Quantum mechanics can produce higher probabilities for chemically relevant arrangements of electrons in these regions. However, the probability to have a given arrangement, e.g., that corresponding to chemical formulas (bonds or atoms), is low although being often maximal. Like in valence bond theory, it is useful to consider alternative distributions of electrons. Exchanges of electrons should be considered not only between atoms but also between other types of regions, such as those attributed to lone pairs. It is useful to have definitions flexible enough to allow users to find the most relevant representations. We tentatively suggest a tool (the effective number of parties) to help one make the choice. [ABSTRACT FROM AUTHOR]

The solid-solid and melting transitions that occur in Lennard-Jones LJn clusters have been both fascinating and challenging for the computational physics community over the last several decades. A number of attempts to extend these studies to the quantum case have also been made. Particularly interesting is the exploration of the parallel between the thermally induced and quantum-induced transitions. Yet, both numerically accurate and systematic studies of the latter are still lacking. In this paper, we apply the diffusion Monte Carlo method to the especially difficult case of LJ38. Starting with the truncated octahedral global minimum configuration, as the de Boer quantum delocalization parameterΛincreases, the system undergoes two consecutive solid-solid transitions, switching to anti-Mackay configurations. At sufficiently large values of Λ, the cluster is completely "melted" which is manifested by delocalization of the ground statewavefunction over a very large number of minima that represent several structural motifs. [ABSTRACT FROM AUTHOR]

This paper reports a time-dependent quantum mechanical wave packet study for bond-selective excitation and dissociation of HOD into the H + OD and D + OH channels in the first absorption band. Prior to excitation, the HOD molecule is randomly oriented with respect to a linearly polarized laser field and accurate static dipole moment and polarizability surfaces are included in the interaction potential. Vibrational excitation is obtained with intense, non-resonant 800 nm few-cycle excitation using dynamic Stark effect/impulsive Raman scattering. Dissociation is accomplished by another ultrashort vacuum ultraviolet-laser excitation. A laser control scheme is designed with a train of simple, non-resonant laser pulses in order to enhance the selectivity between the fragmentation channels. The effect of the carrier-envelope-phase of the ultrashort laser pulses is also investigated. [ABSTRACT FROM AUTHOR]

Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed. [ABSTRACT FROM AUTHOR]

Photodetachment spectroscopy of H2B-7 and its deuterated isotopomer probing the energetically low-lying electronic states of the respective neutral cluster is theoretically investigated in this paper. The theoretical methodology is based on detailed quantum chemistry calculations of electronic state energies, construction of a vibronic coupling model in the diabatic electronic basis, and nuclear dynamics calculations from first principles using time-dependent and time-independent quantum mechanical methods. The theoretical model consists of five coupled electronic states and fifteen vibrational modes. Several reduced dimensional calculations are performed to identify the relevant vibrational modes contributing to the vibronic structure of electronic bands and the impact of non-adiabatic coupling on them. The low-energy part of the spectrum of both H2B7 and its deuterated analogue is assigned by examining the vibronic wavefunctions and the results are compared with the experimental findings. The nonadiabatic decay dynamics of the electronic excited states of the neutral clusters is examined at length. [ABSTRACT FROM AUTHOR]

Ab initio quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulation is a useful tool to calculate thermodynamic properties such as potential of mean force for chemical reactions but intensely time consuming. In this paper, we developed a new method using the internal force correction for low-level semiempirical QM/MM molecular dynamics samplings with a predefined reaction coordinate. As a correction term, the internal force was predicted with a machine learning scheme, which provides a sophisticated force field, and added to the atomic forces on the reaction coordinate related atoms at each integration step. We applied this method to two reactions in aqueous solution and reproduced potentials of mean force at the ab initio QM/MM level. The saving in computational cost is about 2 orders of magnitude. The present work reveals great potentials for machine learning in QM/MM simulations to study complex chemical processes. [ABSTRACT FROM AUTHOR]

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches. [ABSTRACT FROM AUTHOR]

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term Hm and a field term Hf, and show that both Hm and Hf have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed study on the application of the quantum control technique of navigation in the energy spectrum to chemical isomerization processes, namely, CN-Li Li-CN. This technique is based on the controlled time variation of a Hamiltonian parameter, an external uniform electric field in our case. The main result of our work establishes that the navigation involved in the method is robust, in the sense that quite sizable deviations from a pre-established control parameter time profile can be introduced and still get good final results. This is specially relevant thinking of a experimental implementation of the method. [ABSTRACT FROM AUTHOR]

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self-consistent-Born-approximation improvements, should be transferable to their Heisenberg-picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable. [ABSTRACT FROM AUTHOR]

In this paper, we describe a new and fully coherent stochastic surface hopping method for simulating mixed quantum-classical systems. We illustrate the approach on the simple but unforgiving problem of quantum evolution of a two-state quantum system in the limit of unperturbed pure state dynamics and for dissipative evolution in the presence of both stationary and nonstationary random environments. We formulate our approach in the Liouville representation and describe the density matrix elements by ensembles of trajectories. Population dynamics are represented by stochastic surface hops for trajectories representing diagonal density matrix elements. These are combined with an unconventional coherent stochastic hopping algorithm for trajectories representing off-diagonal quantum coherences. The latter generalizes the binary (0,1) "probability" of a trajectory to be associated with a given state to allow integers that can be negative or greater than unity in magnitude. Unlike existing surface hopping methods, the dynamics of the ensembles are fully entangled, correctly capturing the coherent and nonlocal structure of quantum mechanics. [ABSTRACT FROM AUTHOR]

We developed a simple method to calculate exchange repulsion between a quantum mechanical (QM) solute and a molecular mechanical (MM) molecule in the QM/MM approach. In our method, the size parameter in the Buckingham type potential for the QM solute is directly determined in terms of the one-electron wave functions of the solute. The point of the method lies in the introduction of the exchange core function (ECF) defined as a Slater function which mimics the behavior of the exterior electron density at the QM/MM boundary region. In the present paper, the ECF was constructed in terms of the Becke-Roussel (BR) exchange hole function. It was demonstrated that the ECF yielded by the BR procedure can faithfully reproduce the radial behavior of the electron density of a QM solute. The size parameter of the solute as well as the exchange repulsion are, then, obtained using the overlap model without any fitting procedure. To examine the efficiency of the method, it was applied to calculation of the exchange repulsions for minimal QM/MM systems, hydrogen-bonded water dimer, and H3O+-H2O. We found that our approach is able to reproduce the potential energy curves for these systems showing reasonable agreements with those given by accurate full quantum chemical calculations. [ABSTRACT FROM AUTHOR]

Resonances are among the clearest quantum mechanical signatures of scattering processes. Previously, shape resonances and Feshbach resonances have been observed in inelastic and reactive collisions involving atoms or diatomic molecules. Structure in the integral cross section has been observed in a handful of elastic collisions involving polyatomic molecules. The present paper presents the observation of shape resonances in the reactive scattering of a polyatomic molecule, NH3. A merged-beam study of the gas phase He(³S1) + NH3 Penning ionization reaction dynamics is described in the collision energy range 3.3 μeV < Ecoll < 10 meV. In this energy range, the reaction rate is governed by long-range attraction. Peaks in the integral cross section are observed at collision energies of 1.8 meV and 7.3 meV and are assigned to l = 15,16 and l = 20,21 partial wave resonances, respectively. The experimental results are well reproduced by theoretical calculations with the short-range reaction probability Psr = 0.035. No clear signature of the orbiting resonances is visible in the branching ratio between NH3+ and NH2+ formation. [ABSTRACT FROM AUTHOR]

We present a full quantum-mechanical study of the laser control of the radiationless decay between the B3u(nπ*) and B2u(ππ*) states of pyrazine using the dynamic Stark effect. In contrast to our previous study [Sala et al., J. Chem. Phys. 140,194309 (2014)], where a four-dimensional model was used, all the 24 degrees of freedom are now included in order to test the robustness of the strategy of control. Using a vibronic coupling Hamiltonian model in a diabatic representation, the multilayer version of the multi-configuration time-dependent Hartree method is exploited to propagate the corresponding wave packets. We still observe a trapping of the wavepacket on the B2u(ππ*) potential energy surface due to the Stark effect for a longer time than the "non-resonant field-free" B2u(ππ*) lifetime. [ABSTRACT FROM AUTHOR]

Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems. [ABSTRACT FROM AUTHOR]

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 106 self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes. [ABSTRACT FROM AUTHOR]

With relevant chemical space growing larger and larger by the day, the ability to extend computational tractability over that larger space is of paramount importance in virtually all fields of science. The solution we aim to provide here for this issue is in the form of the generalized many-body expansion for building density matrices (GMBE-DM) based on the set-theoretical derivation with overlapping fragments, through which the energy can be obtained by a single Fock build. In combination with the purification scheme and the truncation at the one-body level, the DM-based GMBE(1)-DM-P approach shows both highly accurate absolute and relative energies for medium-to-large size water clusters with about an order of magnitude better than the corresponding energy-based GMBE(1) scheme. Simultaneously, GMBE(1)-DM-P is about an order of magnitude faster than the previously proposed MBE-DM scheme [F. Ballesteros and K. U. Lao, J. Chem. Theory Comput. 18, 179 (2022)] and is even faster than a supersystem calculation without significant parallelization to rescue the fragmentation method. For even more challenging systems including ion–water and ion–pair clusters, GMBE(1)-DM-P also performs about 3 and 30 times better than the energy-based GMBE(1) approach, respectively. In addition, this work provides the first overlapping fragmentation algorithm with a robust and effective binning scheme implemented internally in a popular quantum chemistry software package. Thus, GMBE(1)-DM-P opens a new door to accurately and efficiently describe noncovalent clusters using quantum mechanics. [ABSTRACT FROM AUTHOR]

Atomic description of electrochemical systems requires reactive interaction potential to explicitly describe the chemistry between atoms and molecules and the evolving charge distribution and polarization effects. Calculating Coulomb electrostatic interactions and polarization effects requires a better estimate of the partial charge distribution in molecular systems. However, models such as reactive force fields and charge equilibration (QEq) include Coulomb interactions up to a short-distance cutoff for better computational speeds. Ignoring long-distance electrostatic interaction affects the ability to describe electrochemistry in large systems. We studied the long-range Coulomb effects among charged particles and extended the QEq method to include long-range effects. By this extension, we anticipate a proper account of Coulomb interactions in reactive molecular dynamics simulations. We validate the approach by computing charges on a series of metal-organic frameworks and some simple systems. Results are compared to regular QEq and quantum mechanics calculations. The study shows slightly overestimated charge values in the regular QEq approach. Moreover, our method was combined with Ewald summation to compute forces and evaluate the long-range effects of simple capacitor configurations. There were noticeable differences between the calculated charges with/without long-range Coulomb interactions. The difference, which may have originated from the long-range influence on the capacitor ions, makes the Ewald method a better descriptor of Coulomb electrostatics for charged electrodes. The approach explored in this study enabled the atomic description of electrochemical systems with realistic electrolyte thickness while accounting for the electrostatic effects of charged electrodes throughout the dielectric layer in devices like batteries and emerging solid-state memory. [ABSTRACT FROM AUTHOR]

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively. The exact quantum propagator thereby becomes an expectation of the stochastic one in which the amplitude results from the potential with a fluctuating position: The particle moves with a constant velocity, subjected to a complex Brownian motion. We demonstrate that the stochastic Schrödinger equation can be feasibly used to derive the quantum propagators for the linear potential and the harmonic oscillator system. Novel semiclassical and other approximations may be developed from the new representation of quantum mechanics. [ABSTRACT FROM AUTHOR]

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local equation of motion for the reduced density operator, from which we can easily extract not only the reduced system but also hybrid bath dynamical information. The resulting steady-state heat current is found to be numerically consistent with another discrete imaginary-frequency method followed by Meir–Wingreen's formula. It is anticipated that the development in this work would constitute an indispensable component of nonequilibrium statistical mechanics for open quantum systems. [ABSTRACT FROM AUTHOR]

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum–classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available. [ABSTRACT FROM AUTHOR]

We present the coupling of two frameworks—the pseudo-open boundary simulation method known as constant potential molecular dynamics simulations (CμMD), combined with quantum mechanics/molecular dynamics (QMMD) calculations—to describe the properties of graphene electrodes in contact with electrolytes. The resulting CμQMMD model was then applied to three ionic solutions (LiCl, NaCl, and KCl in water) at bulk solution concentrations ranging from 0.5 M to 6 M in contact with a charged graphene electrode. The new approach we are describing here provides a simulation protocol to control the concentration of electrolyte solutions while including the effects of a fully polarizable electrode surface. Thanks to this coupling, we are able to accurately model both the electrode and solution side of the double layer and provide a thorough analysis of the properties of electrolytes at charged interfaces, such as the screening ability of the electrolyte and the electrostatic potential profile. We also report the calculation of the integral electrochemical double layer capacitance in the whole range of concentrations analyzed for each ionic species, while the quantum mechanical simulations provide access to the differential and integral quantum capacitance. We highlight how subtle features, such as the adsorption of potassium graphene or the tendency of the ions to form clusters contribute to the ability of graphene to store charge, and suggest implications for desalination. [ABSTRACT FROM AUTHOR]

Multicomponent density functional theory (DFT) enables the consistent quantum mechanical treatment of both electrons and protons. A major challenge has been the design of electron-proton correlation (epc) functionals that produce even qualitatively accurate proton densities. Herein an electron-proton correlation functional, epc17, is derived analogously to the Colle-Salvetti formalism for electron correlation and is implemented within the nuclear-electronic orbital (NEO) framework. The NEO-DFT/epc17 method produces accurate proton densities efficiently and is promising for diverse applications. [ABSTRACT FROM AUTHOR]

A traditional stochastic hierarchy equations of motion method is extended into the correlated realtime and imaginary-time propagations, in this paper, for its applications in calculating the equilibrium correlation functions. The central idea is based on a combined employment of stochastic unravelling and hierarchical techniques for the temperature-dependent and temperature-free parts of the influence functional, respectively, in the path integral formalism of the open quantum systems coupled to a harmonic bath. The feasibility and validity of the proposed method are justified in the emission spectra of homodimer compared to those obtained through the deterministic hierarchy equations of motion. Besides, it is interesting to find that the complex noises generated from a small portion of real-time and imaginary-time cross terms can be safely dropped to produce the stable and accurate position and flux correlation functions in a broad parameter regime. [ABSTRACT FROM AUTHOR]

Tryptophan synthase (TRPS) is a bifunctional enzyme consisting of α- and β-subunits that catalyzes the last two steps of L-tryptophan (L-Trp) biosynthesis. The first stage of the reaction at the β-subunit is called β-reaction stage I, which converts the β-ligand from an internal aldimine [E(Ain)] to an α-aminoacrylate [E(A-A)] intermediate. The activity is known to increase 3–10-fold upon the binding of 3-indole-D-glycerol-3′-phosphate (IGP) at the α-subunit. The effect of α-ligand binding on β-reaction stage I at the distal β-active site is not well understood despite the abundant structural information available for TRPS. Here, we investigate the β-reaction stage I by carrying out minimum-energy pathway searches based on a hybrid quantum mechanics/molecular mechanics (QM/MM) model. The free-energy differences along the pathway are also examined using QM/MM umbrella sampling simulations with QM calculations at the B3LYP-D3/aug-cc-pVDZ level of theory. Our simulations suggest that the sidechain orientation of βD305 near the β-ligand likely plays an essential role in the allosteric regulation: a hydrogen bond is formed between βD305 and the β-ligand in the absence of the α-ligand, prohibiting a smooth rotation of the hydroxyl group in the quinonoid intermediate, whereas the dihedral angle rotates smoothly after the hydrogen bond is switched from βD305-β-ligand to βD305-βR141. This switch could occur upon the IGP-binding at the α-subunit, as evidenced by the existing TRPS crystal structures. [ABSTRACT FROM AUTHOR]

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum–classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost. [ABSTRACT FROM AUTHOR]

The performance of different quantum mechanics/molecular mechanics embedding models to compute vacuo-to-water solvatochromic shifts is investigated. In particular, both nonpolarizable and polarizable approaches are analyzed and computed results are compared to reference experimental data. We show that none of the approaches outperform the others and that errors strongly depend on the nature of the molecular transition to be described. Thus, we prove that the best choice of embedding model highly depends on the molecular system and that the use of a specific approach as a black box can lead to significant errors and, sometimes, totally wrong predictions. [ABSTRACT FROM AUTHOR]

The main protease (Mpro) of SARS-CoV-2 is an essential enzyme for the replication of the virus causing the COVID-19 pandemic. Because there is no known homologue in humans, it has been proposed as a primary target for antiviral drug development. Here, we explore the potential of five acrylamide-based molecules as possible covalent inhibitors, leading to target MPro by docking, followed by polarizable molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) calculations. All calculations involving a classical potential were calculated with the AMOEBABIO18 polarizable force field, while electronic structure calculations were performed within the framework of density functional theory. Selected docking poses for each of the five compounds were used for MD simulations, which suggest only one of the tested leads remains bound in a catalytically active orientation. The QM/MM results for the covalent attachment of the promising lead to the catalytic serine suggest that this process is thermodynamically feasible but kinetically unlikely. Overall, our results are consistent with the low labeling percentages determined experimentally and may be useful for further development of acrylamide-based leads. [ABSTRACT FROM AUTHOR]

The vibrational spectra of condensed and gas-phase systems are influenced by thequantum-mechanical behavior of light nuclei. Full-dimensional simulations of approximate quantum dynamics are possible thanks to the imaginary time path-integral (PI) formulation of quantum statistical mechanics, albeit at a high computational cost which increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artifacts of standard PI approaches as well as eliminate the unfavorable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. Our simple, efficient, and accurate method has prospects for routine calculations of vibrational spectra for a wide range of molecular systems - with an explicit treatment of the quantum nature of nuclei. [ABSTRACT FROM AUTHOR]

This Perspective presents a comprehensive account of the dissipaton theories developed in our group since 2014, including the physical picture of dissipatons and the phase–space dissipaton algebra. The dissipaton–equation–of–motion–space (DEOM–space) formulations cover the Schrödinger picture, the Heisenberg picture, and further the imaginary–time DEOM. Recently developed are the dissipaton theories for studying equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski equality and Crooks relation are accurately reproduced numerically. It is anticipated that dissipaton theories would remain essential toward a maturation of quantum mechanics of open systems. [ABSTRACT FROM AUTHOR]

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4′-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs. [ABSTRACT FROM AUTHOR]

Dispersion interactions are one of the components of van der Waals (vdW) forces that play a key role in the understanding of intermolecular interactions in many physical, chemical, and biological processes. The theory of dispersion forces was developed by London in the early years of quantum mechanics. However, it was only in the 1960s that it was recognized that for molecules lacking an inversion center, such as chiral and helical molecules, there are chirality-sensitive corrections to the dispersion forces proportional to the rotatory power known from the theory of circular dichroism and with the same distance scaling law R−6 as the London energy. The discovery of the chirality-induced spin selectivity effect in recent years has led to an additional twist in the study of chiral molecular systems, showing a close relation between spin and molecular geometry. Motivated by it, we propose in this investigation to describe the mutual induction of charge and spin-density fluctuations in a pair A–B of chiral molecules by a simple physical model. The model assumes that the same fluctuating electric fields responsible for vdW forces can induce a magnetic response via a Rashba-like term so that a spin–orbit field acting on molecule B is generated by the electric field arising from charge density fluctuations in molecule A (and vice versa). Within a second-order perturbative approach, these contributions manifest as an effective intermolecular exchange interaction. Although expected to be weaker than the standard London forces, these interactions display the same R−6 distance scaling. [ABSTRACT FROM AUTHOR]

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings. [ABSTRACT FROM AUTHOR]

We present a density functional theory (DFT)-based, quantum mechanics/molecular mechanics (QM/MM) implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle-mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF4) ionic liquid were considered as "simple" and "complex" solvents, respectively, with water and p-phenylenediamine (PPD) solute molecules treated at the QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible errors for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe errors even at 2–3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms with our presented algorithm providing a general and robust approach. [ABSTRACT FROM AUTHOR]

The transport of free electrons in a water environment is still poorly understood. We show that additional insight can be brought about by investigating fragmentation patterns of finite-size particles upon electron impact ionization. We have developed a composite protocol aiming to simulate fragmentation of water clusters by electrons with kinetic energies in the range of up to 100 eV. The ionization events for atomistically described molecular clusters are identified by a kinetic Monte Carlo procedure. We subsequently model the fragmentation with classical molecular dynamics simulations, calibrated by non-adiabatic quantum mechanics/molecular mechanics simulations of the ionization process. We consider one-electron ionizations, energy transfer via electronic excitation events, elastic scattering, and also the autoionization events through intermolecular Coulombic decay. The simulations reveal that larger water clusters are often ionized repeatedly, which is the cause of substantial fragmentation. After losing most of its energy, low-energy electrons further contribute to fragmentation by electronic excitations. The simultaneous measurement of cluster size distribution before and after the ionization represents a sensitive measure of the energy transferred into the system by an incident electron. [ABSTRACT FROM AUTHOR]

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology. [ABSTRACT FROM AUTHOR]

In this paper, the ground state of para-hydrogen clusters for size regime N ≤ 40 has been studied by our variational path integral molecular dynamics method. Long molecular dynamics calculations have been performed to accurately evaluate ground state properties. The chemical potential of the hydrogen molecule is found to have a zigzag size dependence, indicating the magic number stability for the clusters of the size N = 13, 26, 29, 34, and 39. One-body density of the hydrogen molecule is demonstrated to have a structured profile, not a melted one. The observed magic number stability is examined using the inherent structure analysis. We also have developed a novel method combining our variational path integral hybrid Monte Carlo method with the replica exchange technique. We introduce replicas of the original system bridging from the structured to the melted cluster, which is realized by scaling the potential energy of the system. Using the enhanced sampling method, the clusters are demonstrated to have the structured density profile in the ground state. [ABSTRACT FROM AUTHOR]

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method. [ABSTRACT FROM AUTHOR]