Volume 140, Issue 16, 28 April 2014

A set of seven conical intersections (CI’s) in methanol between vibrationally adiabatic surfaces is reported. The intersecting surfaces represent the energies of the two asymmetric CH stretch vibrations regarded as adiabatic functions of the torsion and COH bend angles. The ab initio data are well described by an extended Zwanziger and Grant (E ⊗ e) model [J. W. Zwanziger and E. R. Grant, J. Chem. Phys.87, 2954 (1987)] that might also be regarded as an extension of the XHL model [L.H. Xu, J. T. Hougen, and R. M. Lees, J. Mol. Spectrosc.293–294, 38 (2013)]. The CI's illuminate the role of geometric phase in methanol. More generally, they suggest the importance of energy transfer processes localized near the CI’s.
 COMMUNICATIONS


Communication: Conical intersections between vibrationally adiabatic surfaces in methanol
View Description Hide DescriptionA set of seven conical intersections (CI’s) in methanol between vibrationally adiabatic surfaces is reported. The intersecting surfaces represent the energies of the two asymmetric CH stretch vibrations regarded as adiabatic functions of the torsion and COH bend angles. The ab initio data are well described by an extended Zwanziger and Grant (E ⊗ e) model [J. W. Zwanziger and E. R. Grant, J. Chem. Phys.87, 2954 (1987)] that might also be regarded as an extension of the XHL model [L.H. Xu, J. T. Hougen, and R. M. Lees, J. Mol. Spectrosc.293–294, 38 (2013)]. The CI's illuminate the role of geometric phase in methanol. More generally, they suggest the importance of energy transfer processes localized near the CI’s.

Communication: On the origin of the surface term in the Ewald formula
View Description Hide DescriptionA transparent derivation of the Ewald formula for the electrostatic energy of a periodic threedimensional system of point charges is presented. The problem of the conditional convergence of the lattice sum is dealt with by separating off, in a physically natural and mathematically simple way, longrange nonabsolutely integrable contributions in the series. The general expression, for any summation order, of the surface (or dipole) term emerges very directly from those longrange contributions.

Communication: Electron transfer mediated decay enabled by spinorbit interaction in small krypton/xenon clusters
View Description Hide DescriptionIn this work we study the influence of relativistic effects, in particular spinorbit coupling, on electronic decay processes in KrXe2 clusters of various geometries. For the first time it is shown that inclusion of spinorbit coupling has decisive influence on the accessibility of a specific decay pathway in these clusters. The radiationless relaxation process is initiated by a Kr 4s ionization followed by an electron transfer from xenon to krypton and a final second ionization of the system. We demonstrate the existence of competing electronic decay pathways depending in a subtle way on the geometry and level of theory. For our calculations a fully relativistic framework was employed where omission of spinorbit coupling leads to closing of two decay pathways. These findings stress the relevance of an adequate relativistic description for clusters with heavy elements and their fragmentation dynamics.

Communication: Minimum in the thermal conductivity of supercooled water: A computer simulation study
View Description Hide DescriptionWe report the results of a computer simulation study of the thermodynamic properties and the thermal conductivity of supercooled water as a function of pressure and temperature using the TIP4P2005 water model. The thermodynamic properties can be represented by a twostructure equation of state consistent with the presence of a liquidliquid critical point in the supercooled region. Our simulations confirm the presence of a minimum in the thermal conductivity, not only at atmospheric pressure, as previously found for the TIP5P water model, but also at elevated pressures. This anomalous behavior of the thermal conductivity of supercooled water appears to be related to the maximum of the isothermal compressibility or the minimum of the speed of sound. However, the magnitudes of the simulated thermal conductivities are sensitive to the water model adopted and appear to be significantly larger than the experimental thermal conductivities of real water at low temperatures.

Communication: Spinboson model with diagonal and offdiagonal coupling to two independent baths: Groundstate phase transition in the deep subOhmic regime
View Description Hide DescriptionWe investigate a spinboson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep subOhmic regime there exists a novel secondorder phase transition between two types of doubly degenerate states, which is reduced to one of the usual types for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.

Communication: Radial distribution functions in a twodimensional binary colloidal hard sphere system
View Description Hide DescriptionTwodimensional hard disks are a fundamentally important manybody model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for twodimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a twodimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems.

Communication: Atomic force detection of singlemolecule nonlinear optical vibrational spectroscopy
View Description Hide DescriptionAtomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFMdetected signals closely resemble coherent heterodynedetected signals. Applications are made to AFMdetected and heterodynedetected vibrational resonances in Coherent AntiStokes Raman Spectroscopy (χ^{(3)}) and sum or difference frequency generation (χ^{(2)}).
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 ARTICLES

 Theoretical Methods and Algorithms

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: Effects of steric hindrance and ring formation
View Description Hide DescriptionIn this paper we develop a thermodynamic perturbation theory for two site associating fluids which exhibit bond cooperativity (system energy is nonpairwise additive). We include both steric hindrance and ring formation such that the equation of state is bond angle dependent. Here, the bond angle is the angle separating the centers of the two association sites. As a test, new Monte Carlo simulations are performed, and the theory is found to accurately predict the internal energy as well as the distribution of associated clusters as a function of bond angle.

Charge transfer excitations from excited state HartreeFock subsequent minimization scheme
View Description Hide DescriptionPhotoinduced chargetransfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initiomethods that allow for an accurate and computationally inexpensive treatment of chargetransfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations[M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem.113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys.138, 124107 (2013)] to allow for the description of intermolecular chargetransfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the HartreeFock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest chargetransfer excitation energies for a set of tetracyanoethylenehydrocarbon complexes that have been used earlier as a test set for such kind of excitations.

Describing longrange chargeseparation processes with subsystem densityfunctional theory
View Description Hide DescriptionLongrange chargetransfer processes in extended systems are difficult to describe with quantum chemical methods. In particular, costeffective (nonhybrid) approximations within timedependent density functional theory (DFT) are not applicable unless special precautions are taken. Here, we show that the efficient subsystem DFT can be employed as a constrained DFT variant to describe the energetics of longrange chargeseparation processes. A formal analysis of the energy components in subsystem DFT for such excitation energies is presented, which demonstrates that both the distance dependence and the longrange limit are correctly described. In addition, electronic couplings for these processes as needed for rate constants in Marcus theory can be obtained from this method. It is shown that the electronic structure of chargeseparated states constructed by a positively charged subsystem interacting with a negatively charged one is difficult to converge — charge leaking from the negative subsystem to the positive one can occur. This problem is related to the delocalization error in DFT and can be overcome with asymptotically correct exchange–correlation (XC) potentials or XC potentials including a sufficiently large amount of exact exchange. We also outline an approximate way to obtain chargetransfer couplings between locally excited and chargeseparated states.

Theoretical modeling of UVVis absorption and emission spectra in liquid state systems including vibrational and conformational effects: Explicit treatment of the vibronic transitions
View Description Hide DescriptionHere, we extend a recently introduced theoreticalcomputational procedure [M. D’Alessandro, M. Aschi, C. Mazzuca, A. Palleschi, and A. Amadei, J. Chem. Phys.139, 114102 (2013)] to include quantum vibrational transitions in modelling electronic spectra of atomic molecular systems in condensed phase. The method is based on the combination of Molecular Dynamics simulations and quantum chemical calculations within the Perturbed Matrix Method approach. The main aim of the presented approach is to reproduce as much as possible the spectral line shape which results from a subtle combination of environmental and intrinsic (chromophore) mechanicaldynamical features. As a case study, we were able to model the low energy UVvis transitions of pyrene in liquid acetonitrile in good agreement with the experimental data.

Electron dynamics in complex environments with realtime time dependent density functional theory in a QMMM framework
View Description Hide DescriptionThis article presents a time dependent density functional theory (TDDFT) implementation to propagate the KohnSham equations in real time, including the effects of a molecular environment through a QuantumMechanics MolecularMechanics (QMMM) hamiltonian. The code delivers an allelectron description employing Gaussian basis functions, and incorporates the Amber forcefield in the QMMM treatment. The most expensive parts of the computation, comprising the commutators between the hamiltonian and the density matrix—required to propagate the electron dynamics—, and the evaluation of the exchangecorrelation energy, were migrated to the CUDA platform to run on graphics processing units, which remarkably accelerates the performance of the code. The method was validated by reproducing linearresponse TDDFT results for the absorption spectra of several molecular species. Two different schemes were tested to propagate the quantum dynamics: (i) a leapfrog Verlet algorithm, and (ii) the Magnus expansion to firstorder. These two approaches were confronted, to find that the Magnus scheme is more efficient by a factor of six in small molecules. Interestingly, the presence of iron was found to seriously limitate the length of the integration time step, due to the high frequencies associated with the coreelectrons. This highlights the importance of pseudopotentials to alleviate the cost of the propagation of the inner states when heavy nuclei are present. Finally, the methodology was applied to investigate the shifts induced by the chemical environment on the most intense UV absorption bands of two model systems of general relevance: the formamide molecule in water solution, and the carboxyheme group in Flavohemoglobin. In both cases, shifts of several nanometers are observed, consistently with the available experimental data.

Assessing the accuracy of the isotropic periodic sum method through Madelung energy computation
View Description Hide DescriptionWe tested the isotropic periodic sum (IPS) method for computing Madelung energies of ionic crystals. The performance of the method, both in its nonpolar (IPSn) and polar (IPSp) forms, was compared with that of the zerocharge and Wolf potentials [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys.110, 8254 (1999)]. The results show that the IPSn and IPSp methods converge the Madelung energy to its reference value with an average deviation of ∼10^{−4} and ∼10^{−7} energy units, respectively, for a cutoff range of 18–24a (a/2 being the nearestneighbor ion separation). However, minor oscillations were detected for the IPS methods when deviations of the computed Madelung energies were plotted on a logarithmic scale as a function of the cutoff distance. To remove such oscillations, we introduced a modified IPSn potential in which both the localregion and longrange electrostatic terms are damped, in analogy to the Wolf potential. With the dampedIPSn potential, a smoother convergence was achieved. In addition, we observed a better agreement between the dampedIPSn and IPSp methods, which suggests that damping the IPSn potential is in effect similar to adding a screening potential in IPSp.

Vibrational solvatochromism. II. A firstprinciple theory of solvationinduced vibrational frequency shift based on effective fragment potential method
View Description Hide DescriptionVibrational solvatochromism is a solvationinduced effect on fundamental vibrational frequencies of molecules in solutions. Here we present a detailed firstprinciple coarsegrained theory of vibrational solvatochromism, which is an extension of our previous work [B. Błasiak, H. Lee, and M. Cho, J. Chem. Phys.139(4), 044111 (2013)] by taking into account electrostatic, exchangerepulsion, polarization, and chargetransfer interactions. By applying our theory to the model Nmethylacetamidewater clusters, solutesolvent interactioninduced effects on amide I vibrational frequency are fully elucidated at HartreeFock level. Although the electrostatic interaction between distributed multipole moments of solute and solvent molecules plays the dominant role, the contributions from exchange repulsion and induced dipoleelectric field interactions are found to be of comparable importance in short distance range, whereas the chargetransfer effect is negligible. The overall frequency shifts calculated by taking into account the contributions of electrostatics, exchangerepulsion, and polarization terms are in quantitative agreement with ab initio results obtained at the HartreeFock level of theory.

Calculation of statetostate cross sections for triatomic reaction by the multiconfiguration timedependent Hartree method
View Description Hide DescriptionA framework for quantum statetostate integral and differential cross sections of triatomic reactive scattering using the MultiConfiguration TimeDependent Hartree (MCTDH) method is introduced, where a modified version of the Heidelberg MCTDH package is applied. Parity of the system is adopted using only nonnegative helicity quantum numbers, which reduces the basis set size of the single particle functions in angular degree of freedom almost by half. The initial wave packet is constructed in the spacefixed frame, which can accurately account for the centrifugal potential. By using the reactantcoordinatebased method, the product stateresolved information can be accurately extracted. Test calculations are presented for the H + H2 reactive scattering. This work demonstrates the capability of the MCTDH method for extracting accurate statetostate integral and differential cross sections. As an efficient scheme for highdimensional problems, the MCTDH method may be promising for the study of product stateresolved cross sections for polyatomic reactive systems.

Sampling saddle points on a free energy surface
View Description Hide DescriptionMany problems in biology, chemistry, and materials science require knowledge of saddle points on free energy surfaces. These saddle points act as transition states and are the bottlenecks for transitions of the system between different metastable states. For simple systems in which the free energy depends on a few variables, the free energy surface can be precomputed, and saddle points can then be found using existing techniques. For complex systems, where the free energy depends on many degrees of freedom, this is not feasible. In this paper, we develop an algorithm for finding the saddle points on a highdimensional free energy surface “onthefly” without requiring a priori knowledge the free energy function itself. This is done by using the general strategy of the heterogeneous multiscale method by applying a macroscale solver, here the gentlest ascent dynamics algorithm, with the needed force and Hessian values computed onthefly using a microscale model such as molecular dynamics. The algorithm is capable of dealing with problems involving many coarsegrained variables. The utility of the algorithm is illustrated by studying the saddle points associated with (a) the isomerization transition of the alanine dipeptide using two coarsegrained variables, specifically the Ramachandran dihedral angles, and (b) the betahairpin structure of the alanine decamer using 20 coarsegrained variables, specifically the full set of Ramachandran angle pairs associated with each residue. For the alanine decamer, we obtain a detailed network showing the connectivity of the minima obtained and the saddlepoint structures that connect them, which provides a way to visualize the gross features of the highdimensional surface.

Twolevel system in spin baths: Nonadiabatic dynamics and heat transport
View Description Hide DescriptionWe study the nonadiabatic dynamics of a twostate subsystem in a bath of independent spins using the noninteracting blip approximation, and derive an exact analytic expression for the relevant memory kernel. We show that in the thermodynamic limit, when the subsystembath coupling is diluted (uniformly) over many (infinite) degrees of freedom, our expression reduces to known results, corresponding to the harmonic bath with an effective, temperaturedependent, spectral density function. We then proceed and study the heat current characteristics in the outofequilibrium spinspinbath model, with a twostate subsystem bridging two thermal spinbaths of different temperatures. We compare the behavior of this model to the case of a spin connecting boson baths, and demonstrate pronounced qualitative differences between the two models. Specifically, we focus on the development of the thermal diode effect, and show that the spinspinbath model cannot support it at weak (subsystembath) coupling, while in the intermediatestrong coupling regime its rectifying performance outplays the spinboson model.

Development of multicomponent hybrid density functional theory with polarizable continuum model for the analysis of nuclear quantum effect and solvent effect on NMR chemical shift
View Description Hide DescriptionWe have developed the multicomponent hybrid density functional theory [MC_(HF+DFT)] method with polarizable continuum model (PCM) for the analysis of molecular properties including both nuclear quantum effect and solvent effect. The chemical shifts and H/D isotope shifts of the picolinic acid Noxide (PANO) molecule in chloroform and acetonitrile solvents are applied by B3LYP electron exchangecorrelation functional for our MC_(HF+DFT) method with PCM (MC_B3LYP/PCM). Our MC_B3LYP/PCM results for PANO are in reasonable agreement with the corresponding experimental chemical shifts and isotope shifts. We further investigated the applicability of our method for acetylacetone in several solvents.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore
View Description Hide DescriptionSimulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, parahydroxybenzylidene imidazolinone, in reference to its allatom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Local CC2 response method based on the Laplace transform: Analytic energy gradients for ground and excited states
View Description Hide DescriptionA multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, statespecific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest.