Volume 125, Issue 19, 21 November 2006
 COMMUNICATIONS


Density functional theory reveals an increase in the amino chemical shift in guanine due to hydrogen bonding with water
View Description Hide DescriptionElectronic structure calculations underestimate the chemical shift of the non Hbonded amino proton in isolated Gquartet structures. The current work shows that this underestimation is due to the absence of a water environment in the calculations: coordination of at least two water molecules is required to obtain good agreement with experiment. The results indicate how improved agreement between calculated and experimental (solutionphase) NMR data can be obtained.

Magic alkalifullerene compound clusters of extreme thermal stability
View Description Hide DescriptionThe thermal stability of free pure , as well as alkali, and alkalineearth metalcompound clusters is investigated. We find that small clusters decay at comparatively low temperatures below , as a consequence of weak intermolecular van der Waals interaction. Adding barium or potassium to the clusters dramatically increases the decay temperatures for “magic” configurations of and , which reach values as high as . Contrary to common belief, the superstable compound clusters are not characterized by filled geometrical or electronic shells. Density functional calculations show that the delicate interplay of ionic (K, Ba) and covalent (Ba) interaction between and the metal atoms, on the one hand, and entropic contributions to the Gibbs free energy, on the other hand, determine the unusual stability.
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 ARTICLES

 Theoretical Methods and Algorithms

A new local density functional for maingroup thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions
View Description Hide DescriptionWe present a new local density functional, called M06L, for maingroup and transition element thermochemistry,thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchangecorrelation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniformelectrongas limit and to have good performance for both maingroup chemistry and transition metal chemistry. The M06L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06L functional gives the best overall performance for a combination of maingroup thermochemistry,thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderatesized and large systems and when long time scales must be addressed.

A local coherentstate approximation to systembath quantum dynamics
View Description Hide DescriptionA novel quantum method to deal with typical systembath dynamical problems is introduced. Subsystem discrete variable representation and bath coherentstate sets are used to write down a multiconfigurational expansion of the wave function of the whole system. With the help of the DiracFrenkel variational principle, simple equations of motion—a kind of SchrödingerLangevin equation for the subsystem coupled to (pseudo) classical equations for the bath—are derived. True dissipative dynamics at all times is obtained by coupling the bath to a secondary, classical Ohmic bath, which is modeled by adding a friction coefficient in the derived pseudoclassical bath equations. The resulting equations are then solved for a number of model problems, ranging from tunneling to vibrational relaxation dynamics. Comparison of the results with those of exact, multiconfiguration timedependent Hartree calculations in systems with up to 80 bath oscillators shows that the proposed method can be very accurate and might be of help in studying realistic problems with very large baths. To this end, its linear scaling behavior with respect to the number of bath degrees of freedom is shown in practice with model calculations using tens of thousands of bath oscillators.

Gradients of the polarization energy in the effective fragment potential method
View Description Hide DescriptionThe effective fragment potential (EFP) method is an ab initio based polarizable classical method in which the intermolecular interaction parameters are obtained from preparative ab initio calculations on isolated molecules. The polarization energy in the EFP method is modeled with asymmetric anisotropic dipole polarizabilitytensors located at the centroids of localized bond and lone pair orbitals of the molecules. Analytic expressions for the translational and rotational gradients (forces and torques) of the EFP polarization energy have been derived and implemented. Periodic boundary conditions (the minimum image convention) and switching functions have also been implemented for the polarization energy, as well as for other EFP interaction terms. With these improvements, molecular dynamics simulations can be performed with the EFP method for various chemical systems.

Calculation of nuclear magnetic resonance shieldings using frozendensity embedding
View Description Hide DescriptionWe have extended the frozendensity embedding (FDE) scheme within densityfunctional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem.97, 8050 (1993)] to include external magnetic fields and applied this extension to the nonrelativistic calculation of nuclear magnetic resonance(NMR) shieldings. This leads to a formulation in which the electron density and the induced current are calculated separately for the individual subsystems. If the current dependence of the exchangecorrelation functional and of the nonadditive kineticenergy functional are neglected, the induced currents in the subsystems are not coupled and each of them can be determined without knowledge of the induced current in the other subsystem. This allows the calculation of the NMR shielding as a sum of contributions of the individual subsystems. As a test application, we have calculated the solvent shifts of the nitrogen shielding of acetonitrile for different solvents using small geometryoptimized clusters consisting of acetonitrile and one solvent molecule. By comparing to the solvent shifts obtained from supermolecular calculations we assess the accuracy of the solvent shifts obtained from FDE calculations. We find a good agreement between supermolecular and FDE calculations for different solvents. In most cases it is possible to neglect the contribution of the induced current in the solvent subsystem to the NMR shielding, but it has to be considered for aromatic solvents. We demonstrate that FDE can describe the effect of induced currents in the environment accurately.

Using neural networks to represent potential surfaces as sums of products
View Description Hide DescriptionBy using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sumofproducts form. The sumofproducts form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sumofproducts potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.

An efficient molecular orbital approach for selfconsistent calculations of molecular junctions
View Description Hide DescriptionTo model electron transport through a molecular junction, we propose an efficient method using an ab initio selfconsistent nonequilibrium Green’s functiontheory combined with density functional theory. We have adopted a model close to the extended molecule approach, due to its flexibility, but have improved on the problems relating to moleculesurface couplings and the longrange potential via a systematic procedure for the same ab initio level as that of Green’s function. The resulting algorithm involves three main steps: (i) construction of the embedding potential; (ii) perturbation expansion of Green’s function in the molecular orbital basis; and (iii) truncation of the molecular orbital space by separating it into inactive, active, and virtual spaces. The above procedures directly reduce the matrix size of Green’s function for the selfconsistent calculation step, and thus, the algorithm is suitable for application to large molecular systems.

Quantum control mechanism analysis through field based Hamiltonian encoding
View Description Hide DescriptionOptimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlledsystem. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schrödinger’s equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment.

Spectral convergence of the quadrature discretization method in the solution of the Schrödinger and FokkerPlanck equations: Comparison with sinc methods
View Description Hide DescriptionSpectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the FokkerPlanck and Schrödinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers FokkerPlanck equations (and analogous Schrödinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrödinger equation for the vibrational states of with a Morse potential is also considered.

Linear scaling density fitting
View Description Hide DescriptionTwo modifications of the resolution of the identity (RI)/density fitting (DF) approximations are presented. First, we apply linear scaling and Jengine techniques to speed up traditional DF. Second, we develop an algorithm that produces local, accurate fits with effort that scales linearly with system size. The fits produced are continuous, differentiable, welldefined, and do not require preset fitting domains. This metricindependent technique for producing a priori local fits is shown to be accurate and robust even for large systems. Timings are presented for linear scaling RI/DF calculations on large one, two, and threedimensional carbon systems.

Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using timedependent density functional theory
View Description Hide DescriptionA comparison of two theoretical methods based on timedependent density functional theory for the calculation of the linear dispersive and absorptive properties of chiral molecules has been made. For this purpose, a recently proposed computational method for the calculation of circular dichroism (CD) spectra from the imaginary part of the optical rotation parameter has been applied to six rigid organic molecules. The results have been compared to the CD spectra obtained from the rotatory strengths and from the KramersKronig transformation of optical rotatory dispersion (ORD) curves. We have also investigated a criterion based on the KramersKronig integration formula to determine a number of excitations in truncated CD spectra which may yield a reasonable low frequency resonant ORD. It has been tested by calculating the ORD from the sumoverstates formula both in the nonresonant and resonant regions. Finally, we have applied these methods to model the resonant optical activity of proline at low .

Fourier decompositions and pulse sequence design algorithms for nuclear magnetic resonance in inhomogeneous fields
View Description Hide DescriptionIn this paper, we introduce algorithms based on Fourier synthesis for designing phase compensating rf pulse sequences for highresolution nuclear magnetic resonance(NMR)spectroscopy in an inhomogeneous field. We show that using radio frequency pulses and time varying linear gradients in three dimensions, it is possible to impart the transverse magnetization of spins phase, which is a desired function of the spatial location. Such a sequence can be used to precompensate the phase that will be acquired by spins at different spatial locations due to inhomogeneous magnetic fields. With this precompensation, the chemical shift information of the spins can be reliably extracted and high resolution NMR spectrum can be obtained.

Spurious fractional charge on dissociated atoms: Pervasive and resilient selfinteraction error of common density functionals
View Description Hide DescriptionSemilocal density functional approximations for the exchangecorrelation energy can improperly dissociate a neutral molecule to fractionally charged fragments with an energy significantly lower than . For example, NaCl can dissociate to . Generally, is positive when the lowestunoccupied orbital energy of atom lies below the highestoccupied orbital energy of atom . The first 24 open shell atoms of the Periodic Table can form 276 distinct unlike pairs , and in the local spin density approximation 174 of these display fractionalcharge dissociation. Finding these lowestenergy solutions with standard quantum chemistry codes, however, requires special care. Selfinteractioncorrected (SIC) semilocal approximations are exact for oneelectron systems and also reduce the spurious fractional charge. The original SIC of Perdew and Zunger typically reduces to 0. A scaleddown SIC with better equilibrium properties sometimes fails to reduce all the way to 0. The desideratum of “manyelectron selfinteraction freedom” is introduced as a generalization of the oneelectron concept.

Analysis on the contribution of molecular orbitals to the conductance of molecular electronic devices
View Description Hide DescriptionWe present a theoretical approach which allows one to extract the orbital contribution to the conductance of molecular electronic devices. This is achieved by calculating the scatteringwave functions after the Hamiltonian matrix of the extended molecule is obtained from a selfconsistent calculation that combines the nonequilibrium Green’s function formalism with density functional theory employing a finite basis of local atomic orbitals. As an example, the contribution of molecular orbitals to the conductance of a model system consisting of a 4,4bipyridine molecule connected to two semiinfinite gold monatomic chains is explored, illustrating the capability of our approach.

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: Treatment of exact exchange and role of correlation
View Description Hide DescriptionThe static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEPEXX) method developed by Yang and Wu [Phys. Rev. Lett.89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the KohnSham orbitals [molecular orbital (MO) basis]. Our results were compared to coupledperturbed HartreeFock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEPEXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finitebasisset HartreeFock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

A semiclassical theory for nonseparable rovibrational motions in curved space and its application to energy quantization of nonrigid molecules
View Description Hide DescriptionThe nonseparability of vibrational and rotational motions of a nonrigid molecule placed in the rotationally isotropic space induces several important effects on the dynamics of intramolecular energy flow and chemical reaction. However, most of these studies have been performed within the framework of classical mechanics. We present a semiclassical theory for the motions of such nonrigid molecules and apply to the energy quantization of three body atomic cluster. It is shown numerically that the semiclassical spectum given without the correct account of the rotational symmetry suffers from unnecessary broadening of the resultant spectral lines and moreover from spurious peaks.

Tunneling motions of argon on chlorofluoromethane
View Description Hide DescriptionThe rotational supersonic jet Fourier transform microwave spectra of the and species of the molecular complex chlorofluoromethaneargon show that, in its equilibrium conformation, the argon atom is located out of the ClCF plane, interacting with the F and Cl atoms. All rotational transitions are split into several quadrupole components, each of them further split into two lines, due to the tunneling motion of the Ar atom between two equivalent positions, below and above the ClCF plane. The feasible low energy pathway between the structurally degenerate conformations is described, in a first approximation, by a circular motion around the C–Cl bond, with barriers estimated to be about 61 and .

Wave packet interferometry and quantum state reconstruction by acoustooptic phase modulation
View Description Hide DescriptionStudies of wave packet dynamics often involve phaseselective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phaseselective measurements that combines acoustooptic phase modulation with ultrashort laser excitation to produce an intensitymodulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90°. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signaltonoise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system—atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.

Completing the metal fluoride series: The pure rotational spectrum of ZnF
View Description Hide DescriptionThe pure rotational spectrum of the ZnF radical has been recorded in the range of using millimeter/submillimeter direct absorption techniques. This study is the first gasphase spectroscopic investigation of this species. Between 5 and 11 transitions were measured for each of five isotopologues of this radical (, , , , and ) in the ground and several excited vibrational (, 2, and 3) states. Each transition consists of spinrotation doublets with a splitting of , indicating that the electronic ground state of ZnF is , as predicted by theory. Fluorine hyperfine splitting was observed in three isotopologues (, , and ), and hyperfine structure from the zinc67 nucleus was additionally resolved in . Rotational, fine structure, and and hyperfine constants were determined for ZnF, as well as equilibrium parameters. The bond length of the main isotopologue was calculated to be . Evaluation of the hyperfine constants indicates that the orbital containing the unpaired electron is in character with contributions from each of the and orbitals. These results imply that ZnF is somewhat less ionic than CaF, as suggested by theory.