Volume 138, Issue 22, 14 June 2013
 ARTICLES

 Theoretical Methods and Algorithms

Effects of extraneous surface charges on the enhanced Raman scattering from metallic nanoparticles
View Description Hide DescriptionMotivating by recent experiments on surface enhanced Raman scattering (SERS) from colloidal solutions, we present here a simple model to elucidate the effects of extraneous surface charges on the enhanced Raman signal. The model is based on the wellestablished GerstenNitzan model coupled to the modified Mie scattering theory of Bohren and Hunt in the long wavelength approximation. We further introduce corrections from the modified long wavelength approximation to the GerstenNitzan model for the improvement of its accuracy. Our results show that the surface charge will generally lead to a blueshift in the resonance frequency and greater enhancements in the SERS spectrum. Possible correlations with the recent experiments are elaborated.

On the connection of semiclassical instanton theory with Marcus theory for electron transfer in solution
View Description Hide DescriptionWe present a derivation of Marcus theory of electron transfer in solution starting from semiclassical instanton theory. The conventional semiclassical instanton theory provides an inadequate description of the electron transfer process in the inverted Marcus regime. This has been attributed to the lack of backscattering in the product region, which is represented as a semiinfinite continuum of states. For electron transfer processes in condensed phase, the electronic states in the acceptor well are bound, which violates the continuum assumption. We show by detailed analysis of the minimum action path of a model system for electron transfer that the proper tunneling coordinate is a delocalized, “beadcount” mode. The tunneling mode is analytically continued in the complex plane as in the traditional derivation. Unlike the traditional analysis where the method of steepest descent is used, the tunneling coordinate is treated as a quasizero mode. This feature allows including the influence of backscattering in the acceptor well and leads to the recovery of the Marcus formula for the rate of electron transfer. The results have implications on the performance of ring polymer molecular dynamics for the study of electron transfer dynamics.

Interpolation of multisheeted multidimensional potentialenergy surfaces via a linear optimization procedure
View Description Hide DescriptionSignificant progress has been achieved in recent years with the development of highdimensional permutationally invariant analytic BornOppenheimer potentialenergy surfaces, making use of polynomial invariant theory. In this work, we have developed a generalization of this approach which is suitable for the construction of multisheeted multidimensional potentialenergy surfaces exhibiting seams of conical intersections. The method avoids the nonlinear optimization problem which is encountered in the construction of multisheeted diabatic potentialenergy surfaces from ab initio electronicstructure data. The key of the method is the expansion of the coefficients of the characteristic polynomial in polynomials which are invariant with respect to the point group of the molecule or the permutation group of like atoms. The multisheeted adiabatic potentialenergy surface is obtained from the Frobenius companion matrix which contains the fitted coefficients. A threesheeted ninedimensional adiabatic potentialenergy surface of the 2 T 2 electronic ground state of the methane cation has been constructed as an example of the application of this method.

A novel construction of complexvalued Gaussian processes with arbitrary spectral densities and its application to excitation energy transfer
View Description Hide DescriptionThe recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open nonequilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complexvalued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the nonMarkovian effect without perturbation under the influence of different spectral densities of the linear systemphonon coupling coefficients. Its application in the study of EET in the FennaMatthewsOlson model Hamiltonian under four different spectral densities is discussed. Since the scaling of our algorithm is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.

Assessment of various natural orbitals as the basis of large active space densitymatrix renormalization group calculations
View Description Hide DescriptionIt is wellknown that not only the orbital ordering but also the choice of the orbitals itself as the basis may significantly influence the computational efficiency of densitymatrix renormalization group (DMRG) calculations. In this study, for assessing the efficiency of using various natural orbitals (NOs) as the DMRG basis, we performed benchmark DMRG calculations with different bases, which included the NOs obtained by various traditional electron correlation methods, as well as NOs acquired from preliminary moderate DMRG calculations (e.g., preserved states less than 500). The tested systems included N2, transition metal Cr2 systems, as well as 1D hydrogen polyradical chain systems under equilibrium and dissociation conditions and 2D hydrogen aggregates. The results indicate that a good compromise between the requirement for low computational costs of acquiring NOs and the demand for high efficiency of NOs as the basis of DMRG calculations may be very dependent on the studied systems’ diverse electron correlation characteristics and the size of the active space. It is also shown that a DMRGcomplete active space configuration interaction (DMRGCASCI) calculation in a basis of carefully chosen NOs can provide a less expensive alternative to the standard DMRGcomplete active space selfconsistent field (DMRGCASSCF) calculation and avoid the convergence difficulties of orbital optimization for large active spaces. The effect of different NO ordering schemes on DMRGCASCI calculations is also discussed.

Photodissociation of carbon dioxide in singlet valence electronic states. I. Six multiply intersecting ab initio potential energy surfaces
View Description Hide DescriptionThe global potential energy surfaces of the first six singlet electronic states of CO2, 1—31 A′, and 1—31 A″ are constructed using high level ab initio calculations. In linear molecule, they correspond to , 11Δ u , , and 11Π g . The calculations accurately reproduce the known benchmarks for all states and establish missing benchmarks for future calculations. The calculated states strongly interact at avoided crossings and true intersections, both conical and glancing. Near degeneracies can be found for each pair of six states and many intersections involve more than two states. In particular, a fivefold intersection dominates the FranckCondon zone for the ultraviolet excitation from the ground electronic state. The seam of this intersection traces out a closed loop. All states are diabatized, and a diabatic 5 × 5 potential matrix is constructed, which can be used in quantum mechanical calculations of the absorption spectrum of the five excited singlet valence states.

Photodissociation of carbon dioxide in singlet valence electronic states. II. Five state absorption spectrum and vibronic assignment
View Description Hide DescriptionThe absorption spectrum of CO2 in the wavelength range 120–160 nm is analyzed by means of quantum mechanical calculations performed using vibronically coupled potential energy surfaces of five singlet valence electronic states and the coordinate dependent transition dipole moment vectors. The thermally averaged spectrum, calculated for T = 190 K via Boltzmann averaging of optical transitions from many initial rotational states, accurately reproduces the experimental spectral envelope, consisting of a low and a high energy band, the positions of the absorption maxima, their FWHMs, peak intensities, and frequencies of diffuse structures in each band. Contributions of the vibronic interactions due to RennerTeller coupling, conical intersections, and the HerzbergTeller effect are isolated and the calculated bands are assigned in terms of adiabatic electronic states. Finally, diffuse structures in the calculated bands are vibronically assigned using wave functions of the underlying resonance states. It is demonstrated that the main progressions in the high energy band correspond to consecutive excitations of the pseudorotational motion along the closed loop of the CI seam, and progressions differ in the number of nodes along the radial mode perpendicular to the closed seam. Irregularity of the diffuse peaks in the low energy band is interpreted as a manifestation of the carbenetype “cyclic” OCO minimum.

Correlated onebody potential from secondorder MøllerPlesset perturbation theory: Alternative to orbitaloptimized MP2 method
View Description Hide DescriptionA meanfield (or oneparticle) theory to represent electron correlation at the level of the secondorder MøllerPlesset perturbation (MP2) theory is presented. Orbitals and associated energy levels are given as eigenfunctions and eigenvalues of the resulting onebody (or Focklike) MP2 Hamiltonian, respectively. They are optimized in the presence of MP2level correlation with the selfconsistent field procedure and used to update the MP1 amplitudes including their denominators. Numerical performance is illustrated in molecular applications for computing reaction energies, applying Koopmans’ theorem, and examining the effects of dynamic correlation on energy levels of metal complexes.

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission. II. Reactive collisions
View Description Hide DescriptionThe classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys.125, 184304 (Year: 2006)]10.1063/1.2371097 from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the internuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of interatomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multiexponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photodissociation experiments.

The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction
View Description Hide DescriptionThe BornOppenheimer approximation is a basic approximation in molecular science. In this approximation, the total molecular wavefunction is written as a product of an electronic and a nuclear wavefunction.Hunter [Int. J. Quantum Chem.9, 237 (Year: 1975)]10.1002/qua.560090205 has argued that the exact total wavefunction can also be factorized as such a product. In the present work, a variational principle is introduced which shows explicitly that the total wavefunction can be exactly written as such a product. To this end, a different electronic Hamiltonian has to be defined. The Schrödinger equation for the electronic wavefunction follows from the variational ansatz and is presented. As in the BornOppenheimer approximation, the nuclear motion is shown to proceed in a potential which is the electronic energy. In contrast to the BornOppenheimer approximation, the separation of the center of mass can be carried out exactly. The electronic Hamiltonian and the equation of motion of the nuclei resulting after the exact separation of the center of mass motion are explicitly given. A simple exactly solvable model is used to illustrate some aspects of the theory.

Nonadiabatic excitedstate molecular dynamics: Treatment of electronic decoherence
View Description Hide DescriptionWithin the fewest switches surface hopping (FSSH) formulation, a swarm of independent trajectories is propagated and the equations of motion for the quantum coefficients are evolved coherently along each independent nuclear trajectory. That is, the phase factors, or quantum amplitudes, are retained. At a region of strong coupling, a trajectory can branch into multiple wavepackets. Directly following a hop, the two wavepackets remain in a region of nonadiabatic coupling and continue exchanging population. After these wavepackets have sufficiently separated in phase space, they should begin to evolve independently from one another, the process known as decoherence. Decoherence is not accounted for in the standard surface hopping algorithm and leads to internal inconsistency. FSSH is designed to ensure that at any time, the fraction of classical trajectories evolving on each quantum state is equal to the average quantum probability for that state. However, in many systems this internal consistency requirement is violated. Treating decoherence is an inherent problem that can be addressed by implementing some form of decoherence correction to the standard FSSH algorithm. In this study, we have implemented two forms of the instantaneous decoherence procedure where coefficients are reinitialized following hops. We also test the energybased decoherence correction (EDC) scheme proposed by Granucci et al. and a related version where the form of the decoherence time is taken from Truhlar's Coherent Switching with Decay of Mixing method. The sensitivity of the EDC results to changes in parameters is also evaluated. The application of these computationally inexpensive ad hoc methods is demonstrated in the simulation of nonradiative relaxation in two conjugated oligomer systems, specifically polyphenylene vinylene and polyphenylene ethynylene. We find that methods that have been used successfully for treating small systems do not necessarily translate to large polyatomic systems and their success depends on the particular system under study.

Accelerating MP2C dispersion corrections for dimers and molecular crystals
View Description Hide DescriptionThe MP2C dispersion correction of Pitonak and Hesselmann [J. Chem. Theory Comput.6, 168 (Year: 2010)]10.1021/ct9005882 substantially improves the performance of secondorder MøllerPlesset perturbation theory for noncovalent interactions, albeit with nontrivial computational cost. Here, the MP2C correction is computed in a monomercentered basis instead of a dimercentered one. When applied to a single dimer MP2 calculation, this change accelerates the MP2C dispersion correction severalfold while introducing only trivial new errors. More significantly, in the context of fragmentbased molecular crystal studies, combination of the new monomer basis algorithm and the periodic symmetry of the crystal reduces the cost of computing the dispersion correction by two orders of magnitude. This speedup reduces the MP2C dispersion correction calculation from a significant computational expense to a negligible one in crystals like aspirin or oxalyl dihydrazide, without compromising accuracy.
 Atoms, Molecules, and Clusters

Vibrationally induced charge transfer in a bimolecular model complex in vacuo
View Description Hide DescriptionWe report vibrationally induced charge transfer from nitromethane anion to methyliodide in a molecular complex. Excitation of a CH stretching vibrational transition in either of the molecular constituents results in dissociative electron transfer to the CH3I molecule, resulting in I− product anions. Solvation of the prereactive complex with more than two Ar atoms leads to complete quenching of the reaction and can be used to estimate the barrier for this reaction. We discuss the results in the framework of electronic structure calculations and compare the intracomplex electron transfer with vibrationally mediated electron emission in bare nitromethane anion.

Symmetry breaking in a nutshell: The odyssey of a pseudo problem in molecular physics. The BNB case revisited
View Description Hide DescriptionThe BNB state considered to be of symmetry broken (SB) character has been studied by high level multireference variational and full configuration interaction methods. We discuss in great detail the roots of the socalled SB problem and we offer an in depth analysis of the unsuspected reasons behind the double minimum topology found in practically all previous theoretical investigations. We argue that the true reason of failure to recover a D ∞h equilibrium geometry lies in the lack of the correct permutational symmetry of the wavefunctions employed and is by no means a real effect.

Methanol clusters (CH_{3}OH)_{ n }: Putative global minimumenergy structures from model potentials and dispersioncorrected density functional theory
View Description Hide DescriptionPutative global minima are reported for methanol clusters (CH3OH) n with n ⩽ 15. The predictions are based on global optimization of three intermolecular potential energy models followed by local optimization and singlepoint energy calculations using two variants of dispersioncorrected density functional theory. Recurring structural motifs include folded and/or twisted rings, folded rings with a short branch, and stacked rings. Many of the larger structures are stabilized by weak C–H⋯O bonds.

Binding sites and electronic states of group 3 metalaniline complexes probed by highresolution electron spectroscopy
View Description Hide DescriptionGroup 3 metalaniline complexes, M(aniline) (M = Sc, Y, and La), are produced in a pulsed laservaporization molecular beam source, identified by photoionization timeofflight mass spectrometry, and investigated by pulsedfield ionization zero electron kinetic energy (ZEKE) spectroscopy and quantum chemical calculations. Adiabatic ionization energies and several lowfrequency vibrational modes are measured for the first time from the ZEKE spectra. Metal binding sites and electronic states are determined by combining the ZEKE measurements with the theoretical calculations. The ionization energies of the complexes decrease down the metal group. An outofplane ring deformation mode coupled with an asymmetric metalcarbon stretch is considerably anharmonic. Although aniline has various possible sites for metal coordination, the preferred site is the phenyl ring. The metal binding with the phenyl ring yields syn and anti conformers with the metal atom and amino hydrogens on the same and opposite sides of the ring, respectively. The anti conformer is determined to be the spectral carrier. The ground electronic state of the anti conformer of each neutral complex is a doublet with a metalbased electron configuration of nd 2(n + 1)s 1, and the ground electronic state of each ion is a singlet with a metalbased electron configuration of nd 2. The formation of the neutral complexes requires the nd 2(n + 1)s 1 ← nd 1(n + 1)s 2 electron excitation in the metal atoms.

Quantum defects at the critical charge
View Description Hide DescriptionThe quantum defect is an empirically introduced notion that has allowed convenient interpolations of spectral data along atomic isoelectronic sequences and their extrapolation with respect to the principal quantum number. Both yield valuable spectral information, the latter providing estimates of lowenergyelectron elastic scattering phase shifts as well. We examine a recently proposed conjecture concerning the extrapolated value of the quantum defect along an isoelectronic sequence: If the binding energy of the outermost electron vanishes in the singly negative ion, then its asymptotic quantum defect is an integer whose value is equal to the number of occupied shells with the same orbital angular momentum. This behavior is associated with the fact, established by means of appropriate electronic structure calculations, that—asymptotically—the outermost orbital becomes an infinitely diffuse hydrogenlike orbital. In most cases explored the asymptotic behavior can be ascertained by analysis of spectral data along the appropriate isoelectronic sequence, but in some cases the approach to the asymptotic value takes place over a very narrow range of nuclear charge in the vicinity of that of the negative ion.

The influence of translational and vibrational energy on the reaction of Cl with CH_{3}D
View Description Hide DescriptionThe reaction of Cl atoms with CH3D proceeds either by abstraction of hydrogen to produce HCl + CH2D or by abstraction of deuterium to produce DCl + CH3. Using Cl atoms with different amounts of translational energy, produced by photolysis of Cl2 with 309, 355, or 416 nm light, reveals the influence of translational energy on the relative reaction probability for the two channels. These measurements give an estimate of the energy barrier for the reaction for comparison to theory and indicate that tunneling is the dominant reaction mechanism at low collision energies. Adding two quanta of C–H stretching vibration causes the reaction to proceed readily at all collision energies. Detecting the vibrational state of the CH2D product shows that vibrational energy initially in the surviving C–H bond appears as vibrational excitation of the product, an example of spectator behavior in the reaction. The reaction produces both stretch and stretchbend excited products except at the lowest collision energy. A subtle variation in the reaction probability of the lowest energy rotational states with translational energy may reflect the presence of a van der Waals well in the entrance channel.

Gasphase electronic spectroscopy of the indene cation (C_{9}H_{8} ^{+})
View Description Hide DescriptionThe electronic spectrum of the indene radical cation has been investigated through resonanceenhanced photodissociation of the weakly bound C9H8 +–He and C9H8 +–Ar n (n = 1, 2) complexes in a tandem mass spectrometer. The D2 ← D0 band origin for indene+–He is observed at 17 379 ± 15 cm−1, while the D2 ← D0 and D4 ← D0 band origins for indene+–Ar appear at 17 353 ± 15 cm−1 and 28 254 ± 15 cm−1, respectively. The vibronic structure of the D2 ← D0 band system is assigned by comparison with a simulated spectrum based on timedependent density functional theory calculations, and is due mainly to progressions in ring deformation vibrational modes. Possible correspondences between the stronger visible transitions of the indene cation and diffuse interstellar bands observed towards the heavily reddened star HD 204827 are discussed.

Solvatochromism and the solvation structure of benzophenone
View Description Hide DescriptionMany complex molecular phenomena, including macromolecular association, protein folding, and chemical reactivity, are determined by the nuances of their electrostatic landscapes. The measurement of such electrostatic effects is nonetheless difficult, and is typically accomplished by exploiting a spectroscopic probe within the system of interest, such as through the vibrational Stark effect. Raman spectroscopy and solvatochromism afford an alternative to this method, circumventing the limitations of infrared spectroscopy, providing a lower detection limit, and permitting measurement in a native chemical environment. To explore this possibility, the solvatochromism of the C=O and aromatic C–H stretching modes of benzophenone are investigated using Raman spectroscopy. In conjunction with density functional theory calculations, these observations are sufficient to determine the probe electrostatic environment as well as contributions from halogen and hydrogen bonding. Further analysis using a detailed Kubo–Anderson lineshape model permits the detailed assignment of distinct hydrogen bonding configurations for water in the benzophenone solvation shell. These observations reinforce the use of benzophenone as an effective electrostatic probe for complex chemical systems.