Volume 139, Issue 24, 28 December 2013

In general, biomacromolecules are composed of hydrophilic and hydrophobic moieties and are confined within small cavities, such as cell membranes and intracellular organelles. Here, we studied the selforganization of macromolecules having groups with different affinities to solvents under spherical nanoscale confinement by means of computer modeling. It is shown that depending on the interaction parameters of monomer units composed of side and mainchain monomer groups along a single linear macromolecule and on cavity size, such amphiphilic polymers undergo the conformational transitions between hollow nanospheres, rodlike and folded cylindrical structures, and a necklace conformation with and without a particular ordering of beads. The diagram of the conformations in the variables the incompatibility parameter of monomer units and the cavity radius is constructed.
 COMMUNICATIONS


Communication: Nonmonotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules
View Description Hide DescriptionWe study the nucleation of model twodimensional crystals formed from anisotropically interacting molecules using kinetic Monte Carlo simulations and the forward flux sampling algorithm. The growth probability P(n) of a cluster of n molecules is measured while the supersaturation s and interaction anisotropy of the molecules are varied, in order to gain insight into the nucleation mechanism. It is found that with increasing degree of interaction anisotropy the nucleus size (defined as the cluster size at which P(n) = 0.5) can increase with increasing s, with sharp jumps at certain s values. Analysis of the cluster shape reveals that nucleation in the system studied is of a nonstandard form, in that it embodies elements of both the classical nucleation theory and the density functional theory frameworks.

 ARTICLES

 Theoretical Methods and Algorithms

Phonon interference effects in molecular junctions
View Description Hide DescriptionWe study coherent phonon transport through organic, πconjugated molecules. Using first principles calculations and Green's function methods, we find that the phonon transmission function in crossconjugated molecules, like metaconnected benzene, exhibits destructive quantum interference features very analogous to those observed theoretically and experimentally for electron transport in similar molecules. The destructive interference features observed in four different crossconjugated molecules significantly reduce the thermal conductance with respect to linear conjugated analogues. Such control of the thermal conductance by chemical modifications could be important for thermoelectric applications of molecular junctions.

Multicomponent dynamics of coupled quantum subspaces and fieldinduced molecular ionizations
View Description Hide DescriptionTo describe successive ionization steps of a manyelectron atom or molecule driven by an ultrashort, intense laser pulse, we introduce a hierarchy of successive twosubspace Feshbach partitions of the Nelectron Hilbert space, and solve the partitioned timedependent Schrödinger equation by a shorttime unitary algorithm. The partitioning scheme allows one to use different level of theory to treat the manyelectron dynamics in different subspaces. We illustrate the procedure on a simple twoactiveelectron model molecular system subjected to a fewcycle extreme UltraViolet (XUV) pulse to study channelresolved photoelectron spectra as a function of the pulse's central frequency and duration. We observe how the momentum and kineticenergy distributions of photoelectrons accompanying the formation of the molecular cation in a given electronic state (channel) change as the XUV fewcycle pulse's width is varied, from a form characteristic of an impulsive ionization regime, corresponding to the limit of a deltafunction pulse, to a form characteristic of multiphoton abovethreshold ionization, often associated with continuouswave infinitely long pulse.

Fixman compensating potential for general branched molecules
View Description Hide DescriptionThe technique of constraining high frequency modes of molecular motion is an effective way to increase simulation time scale and improve conformational sampling in molecular dynamics simulations. However, it has been shown that constraints on higher frequency modes such as bond lengths and bond angles stiffen the molecular model, thereby introducing systematic biases in the statistical behavior of the simulations. Fixman proposed a compensating potential to remove such biases in the thermodynamic and kinetic properties calculated from dynamics simulations. Previous implementations of the Fixman potential have been limited to only short serial chain systems. In this paper, we present a spatial operator algebra based algorithm to calculate the Fixman potential and its gradient within constrained dynamics simulations for branched topology molecules of any size. Our numerical studies on molecules of increasing complexity validate our algorithm by demonstrating recovery of the dihedral angle probability distribution function for systems that range in complexity from serial chains to protein molecules. We observe that the Fixman compensating potential recovers the free energy surface of a serial chain polymer, thus annulling the biases caused by constraining the bond lengths and bond angles. The inclusion of Fixman potential entails only a modest increase in the computational cost in these simulations. We believe that this work represents the first instance where the Fixman potential has been used for general branched systems, and establishes the viability for its use in constrained dynamics simulations of proteins and other macromolecules.

Propensity approach to nonequilibrium thermodynamics of a chemical reaction network: Controlling single Ecoli βgalactosidase enzyme catalysis through the elementary reaction steps^{a)}
View Description Hide DescriptionIn this work, we develop an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the elementary reaction propensities. The method is akin to the microscopic formulation of the dissipation function in terms of the KullbackLeibler distance of phase space trajectories in Hamiltonian system. The formalism is applied to a single oligomeric enzyme kinetics at chemiostatic condition that leads the reaction system to a nonequilibrium steady state, characterized by a positive total entropy production rate. Analytical expressions are derived, relating the individual reaction contributions towards the total entropy production rate with experimentally measurable reaction velocity. Taking a real case of Escherichia coli βgalactosidase enzyme obeying MichaelisMenten kinetics, we thoroughly analyze the temporal as well as the steady state behavior of various thermodynamic quantities for each elementary reaction. This gives a useful insight in the relative magnitudes of various energy terms and the dissipated heat to sustain a steady state of the reaction system operating farfromequilibrium. It is also observed that, the reaction is entropydriven at low substrate concentration and becomes energydriven as the substrate concentration rises.

Higherorder electric multipole contributions to retarded nonadditive threebody dispersion interaction energies between atoms: Equilateral triangle and collinear configurations
View Description Hide DescriptionThe theory of molecular quantum electrodynamics (QED) is used to calculate higher electric multipole contributions to the dispersion energy shift between three atoms or molecules arranged in a straight line or in an equilateral triangle configuration. As in twobody potentials, threebody dispersion interactions are viewed in the QED formalism to arise from exchange of virtual photons between coupled pairs of particles. By employing an interaction Hamiltonian that is quadratic in the electric displacement field means that thirdorder perturbation theory can be used to yield the energy shift for a particular combination of electric multipole polarizable species, with only six timeordered diagrams needing to be summed over. Specific potentials evaluated include dipoledipolequadrupole (DDQ), dipolequadrupolequadrupole (DQQ), and dipoledipoleoctupole (DDO) terms. For the geometries of interest, nearzone limiting forms are found to exhibit an R ^{−11} dependence on separation distance for the DDQ interaction, and an R ^{−13} behaviour for DQQ and DDO shifts, agreeing with an earlier semiclassical computation. Retardation weakens the potential in each case by R ^{−1} in the farzone. It is found that by decomposing the octupole moment into its irreducible components of weights1 and 3 that the former contribution to the DDO potential may be taken to be a higherorder correction to the leading triple dipole energy shift.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces
View Description Hide DescriptionWe develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTSMD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3DRISMKH molecular theory of solvation (threedimensional reference interaction site model complemented with the KovalenkoHirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3DRISMKH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete nonEckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best forcecoordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3DRISMKH at outer time steps over a broad time interval. The MTSMD integration with effective solvation forces obtained by converging 3DRISMKH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic NoséHoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTSMD/OIN/ASFE/3DRISMKH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100 to 500fold effective speedup in comparison to conventional MD with explicit solvent. With the statisticalmechanical 3DRISMKH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for “flipflop” conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

Analytical energy gradient based on spinfree infiniteorder DouglasKrollHess method with local unitary transformation
View Description Hide DescriptionIn this study, the analytical energy gradient for the spinfree infiniteorder DouglasKrollHess (IODKH) method at the levels of the HartreeFock (HF), density functional theory (DFT), and secondorder MøllerPlesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one, two, and threedimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.

Periodic boundary conditions for QM/MM calculations: Ewald summation for extended Gaussian basis sets
View Description Hide DescriptionAn implementation of Ewald summation for use in mixed quantum mechanics/molecular mechanics (QM/MM) calculations is presented, which builds upon previous work by others that was limited to semiempirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using “ChElPG” atomic charges, which are determined by fitting to the QM electrostatic potential evaluated on a realspace grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivatives of the ChElPG charges with respect to the QM density matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atomcentered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed analysis of the optimal choice of userselected Ewald parameters, as well as timing breakdowns, is presented.

Regularized orbitaloptimized secondorder perturbation theory
View Description Hide DescriptionOrbitaloptimized secondorder perturbation theory (OOMP2) optimizes the zeroth order wave function in the presence of correlations, removing the dependence of the method on Hartree–Fock orbitals. This is particularly important for systems where mean field orbitals spin contaminate to artificially lower the zeroth order energy such as open shell molecules, highly conjugated systems, and organometallic compounds. Unfortunately, the promise of OOMP2 is hampered by the possibility of solutions being drawn into divergences, which can occur during the optimization procedure if HOMO and LUMO energies approach degeneracy. In this work, we regularize these divergences through the simple addition of a level shift parameter to the denominator of the MP2 amplitudes. We find that a large level shift parameter of 400 mE h removes divergent behavior while also improving the overall accuracy of the method for atomization energies, barrier heights, intermolecular interactions, radical stabilization energies, and metal binding energies.

Twophoton spectroscopy of excitons with entangled photons
View Description Hide DescriptionThe utility of quantum light as a spectroscopic tool is demonstrated for frequencydispersed pumpprobe, integrated pumpprobe, and twophoton fluorescence signals which show Ramsey fringes. Simulations of the frequencydispersed transmission of a broadband pulse of entangled photons interacting with a threelevel model of matter reveal how the nonclassical timebandwidth properties of entangled photons can be used to disentangle congested spectra, and reveal otherwise unresolved features. Quantum light effects are most pronounced at weak intensities when entangled photon pairs are well separated, and are gradually diminished at higher intensities when different photon pairs overlap.

Frequencydomain multiscale quantum mechanics/electromagnetics simulation method
View Description Hide DescriptionA frequencydomain quantum mechanics and electromagnetics (QM/EM) method is developed. Compared with the timedomain QM/EM method [Meng et al. , J. Chem. Theory Comput.8, 1190–1199 (2012)], the newly developed frequencydomain QM/EM method could effectively capture the dynamic properties of electronic devices over a broader range of operating frequencies. The system is divided into QM and EM regions and solved in a selfconsistent manner via updating the boundary conditions at the QM and EM interface. The calculated potential distributions and current densities at the interface are taken as the boundary conditions for the QM and EM calculations, respectively, which facilitate the information exchange between the QM and EM calculations and ensure that the potential, charge, and current distributions are continuous across the QM/EM interface. Via Fourier transformation, the dynamic admittance calculated from the timedomain and frequencydomain QM/EM methods is compared for a carbon nanotube based molecular device.
 Advanced Experimental Techniques

Coherent transfer of nuclear spin polarization in fieldcycling NMR experiments
View Description Hide DescriptionCoherent polarization transfer effects in a coupled spin network have been studied over a wide field range. The transfer mechanism is based on exciting zeroquantum coherences between the nuclear spin states by means of nonadiabatic field jump from high to low magnetic field. Subsequent evolution of these coherences enables conversion of spin order in the system, which is monitored after field jump back to high field. Such processes are most efficient when the spin system passes through an avoided level crossing during the field variation. The polarization transfer effects have been demonstrated for Nacetyl histidine, which has five scalar coupled protons; the initial spin order has been prepared by applying RFpulses at high magnetic field. The observed oscillatory transfer kinetics is taken as a clear indication of a coherent mechanism; level crossing effects have also been demonstrated. The experimental data are in very good agreement with the theoretical model of coherent polarization transfer. The method suggested is also valid for other types of initial polarization in the spin system, most notably, for spin hyperpolarization.

Formation of ionic complexes in cryogenic matrices: A case study using codeposition of Cu^{−} with rare gas cations in solid argon
View Description Hide DescriptionMatrix isolation spectra have been obtained for ionic species formed from a beam of massselected ions, with a coincident beam of externally generated counterions used to provide charge balance. Infrared spectra were obtained for copper carbonyl complexes formed following deposition of Cu ^{−} ions with raregas countercations into COdoped argon matrices. Both anionic and neutral copper carbonyl complexes Cu(CO)n ^{q} (n = 1–3; q = 0, −1) were observed in the spectra, with peak positions corresponding to previously reported assignments; new partially resolved bands appearing in the range 1830–1845 cm^{−1} are assigned to larger [Cu(CO)3•(CO)n]^{−} aggregates, having additional CO ligands in the second solvation shell. The experimental geometry ensures that all Cucenters initially arrive at the matrix as anions, so the relative abundance of anionic relative to neutral complexes is much higher than in previous studies employing alternative methods for ion deposition; this allows for monitoring of electrontransfer processes between anions and cations in the matrix. Comparison of timedependent vs. temperaturedependent trends reveals that there are two distinct mechanisms by which the population of anionic complexes is converted into neutral complexes: shortrange electron transfer between a cationanion pair following diffusion, and longrange electron transfer involving photodetachment of an electron from the anion into the conduction band of solid argon, resulting in eventual recombination of the electron with a cation in a remote matrix site. The spectra also show a marked dependence on the deposition temperature and dopant concentration, in that 100fold higher CO concentrations were required during deposition with the sample window at 10 K compared to that used at 20 K, in order to obtain a similar distribution of copper carbonyl complexes. Furthermore, although no carbonyl complexes are observed initially when low concentrations of CO are used at 10 K, upon warming the matrix to 15 K, the neutral di and tricarbonyl peaks appear abruptly, which is attributed to fast diffusion of CO stimulated by the energy released upon shortrange electrontransfer between Cu ^{−}:countercation pairs.
 Atoms, Molecules, and Clusters

Fouriertransform spectroscopy of (4)^{1}Σ^{+} → A ^{1}Σ^{+} − b ^{3}Π, A ^{1}Σ^{+} − b ^{3}Π → X ^{1}Σ^{+}, and transitions in KCs and deperturbation treatment of A ^{1}Σ^{+} and b ^{3}Π states
View Description Hide DescriptionHigh resolution Fouriertransform spectroscopy data of term values in the spinorbit (SO) coupled first excited A ^{1}Σ^{+} and b ^{3}Π states in KCs were obtained from (4)^{1}Σ^{+} → A ^{1}Σ^{+} − b ^{3}Π, A ^{1}Σ^{+} − b ^{3}Π → X ^{1}Σ^{+}, and spectra of laserinduced fluorescence (LIF). About 3000 new rovibronic term values of the A ^{1}Σ^{+} and states were obtained with an uncertainty about 0.01 cm^{−1} and added to the previously obtained 3439 term values in Kruzins et al. [Phys. Rev. A81, 042509 (2010)] and 30 term values of the state levels below the A ^{1}Σ^{+} state in Tamanis et al. [Phys. Rev. A82, 032506 (2010)]. The data field was extended considerably, going down to vibrational level v b = 0 and up in energy to 13 814 cm^{−1}, as compared to previously achieved v b = 14 and E = 13 250 cm^{−1}. Overall 6431 esymmetry term values of ^{39}K^{133}Cs were included in 4 × 4 coupledchannel deperturbation analysis. The analytical MorseLongRange (MLR) function yielded empirical diabatic potentials for the A ^{1}Σ^{+} and states while the morphing of the SO ab initio points [J. T. Kim et al. , J. Mol. Spectrosc.256, 57 (2009)] provided the empirical diagonal and offdiagonal SO functions. Overall 98.5% of the fitted term values were reproduced with a rms (root mean square) uncertainty of 0.004 cm^{−1}. The reliability of the model is proved by a good agreement of predicted and measured term values of the ^{41}K^{133}Cs isotopologue, as well as of measured and calculated intensities of (4)^{1}Σ^{+} → A ^{1}Σ^{+} − b ^{3}Π LIF progressions. Directpotentialfit of lowlying v b levels of the component yielded the MLR potential which represents the 204 fsymmetry experimental term values with a rms uncertainty of 0.002 cm^{−1}. The Ωdoubling of the b ^{3}Π0 substate demonstrates a pronounced v b dependent increase.

A revisitation of the Förster energy transfer near a metallic spherical nanoparticle: (1) Efficiency enhancement or reduction? (2) The control of the Förster radius of the unbounded medium. (3) The impact of the local density of states
View Description Hide DescriptionThe central motivation of this theoretical revisitation comes from the fact that some experimental works about Förster energy transfer report improvement of the Förster efficiency when the donoracceptor molecular pair is in the vicinity of a metallic particle, while others found efficiency deterioration. In the presence of a nanoscale metallic sphere, we calculate contour plots of the Förster energy transfer rate K F and the Förster efficiency η as a function of the acceptor position r A for a fixed donor position. These contour plots clearly highlight the influence of the sphere on K F and η as the donor position, the orientations of donor and acceptor dipoles, and the particle size are varied; also the impact on K F(r A) and η due to the excitation of surface plasmons is easily noticeable from these contour plots. Moreover, we obtain the enhancement factor K F/K F0 (K F0 refers to the case without sphere) against the donorsurface separation for particular donoracceptor spatial distributions, several particle sizes, and distinct molecular dipole orientations. Therefore, our calculations provide a systematic analysis of the Förster energy transfer in the presence of a metallic nanosphere. Based on these results, we formulate hypotheses for explaining the aforementioned contradictory experimental results about η. To complement our study, we examine the impact of the local density of states ρ on K F. K F is practically unperturbed by sphere when the intermolecular separation R is ≲ 3 nm, since the direct donoracceptor electromagnetic interaction is dominant. On the contrary, when R ≳ 3 nm, the nanosphere perturbs K F and this perturbation is stronger if plasmonic resonances are excited. K F/K F0 can greatly be enhanced in certain regions, but these regions coincide with lowefficiency regions, compromising applications involving the Förster process. In the presence of the nanosphere, the high Förster efficiency region (η ⩾ 0.5) has the same shape as that for the case without sphere, but its extension (Förster radius R o) is reduced; this effect is a consequence of the large increase of the donor direct decay rate and R o depends strongly on donor position. Consequently, the sphere controls R o that is associated with the efficiency pattern that corresponds to the unbounded medium; this effect can be exploited in the measuring technique of nanoscale displacements of proteins that is based on the fluorescence resonant energy transfer. The functional form of K F(ρ) is determined by the intermolecular separation R, the spatial configuration and the dipole orientations of the molecular pair, and the donor proximity to the nanoparticle.

Probing the electronic structures of low oxidationstate uranium fluoride molecules UF_{ x } ^{−} (x = 2−4)
View Description Hide DescriptionWe report the experimental observation of gaseous UF x ^{−} (x = 2−4) anions, which are investigated using photoelectron spectroscopy and relativistic quantum chemistry. Vibrationally resolved photoelectron spectra are obtained for all three species and the electron affinities of UF x (x = 2−4) are measured to be 1.16(3), 1.09(3), and 1.58(3) eV, respectively. Significant multielectron transitions are observed in the photoelectron spectra of U(5f^{3}7s^{2})F2 ^{−}, as a result of strong electron correlation effects of the two 7s electrons. The U−F symmetric stretching vibrational modes are resolved for the ground states of all UF x (x = 2−4) neutrals. Theoretical calculations are performed to qualitatively understand the photoelectron spectra. The entire UF x ^{−} and UF x (x = 1−6) series are considered theoretically to examine the trends of U−F bonding and the electron affinities as a function of fluorine coordination. The increased U−F bond lengths and decreased bond orders from UF2 ^{−} to UF4 ^{−} indicate that the U−F bonding becomes weaker as the oxidation state of U increases from I to III.

A nonadiabatic dynamics study of octatetraene: The radiationless conversion from S _{2} to S _{1}
View Description Hide DescriptionSimulation of the excited state dynamics of alltrans1,3,5,7octatetraene has been performed to investigate the ultrafast radiationless S 2 → S 1 internal conversion process. Multireference configuration interaction with single excitation method has been employed to optimize the equilibrium structure of the excited states, as well as the S 2/S 1 conical intersection, and to investigate the nonadiabatic molecular dynamics of the S 2/S 1 state transition. At the conical intersection, the molecule is found to be distorted from the original planar trans structure to a nearly perpendicular conformation around C3−C4 bond, with the torsion angle being about 107°. Such structural change can result in mutual approaching of states S 2 and S 1 in energy, and drastically increase the nonadiabatic coupling between the two states by destroying the interstate symmetry prohibition in the electronic wavefunctions. Surfacehopping molecular dynamics simulations are performed to describe the nonadiabatic process. Upon the FranckCondon excitation to the S 2 state, the molecule quickly twists its C3−C4 bond and approaches the conical intersection region, where it can undergo efficient internal conversion to S 1. The decay time constant (τ) of S 2 state is estimated to be around 251 fs by fitting the occupation number of average fraction of trajectories using an exponential damping function. This value is reasonably consistent with previous experimental measurements of around 300–400 fs.

Synchrotronbased far infrared study of the rotationvibrationinversion spectrum of silacyclobutane below 500 cm^{−1}: The ν_{29} and ν_{30} bands
View Description Hide DescriptionFourier transform spectra of the fourmembered heterocycle silacyclobutane (cC3H8Si) were recorded in the far infrared region from 100 to 500 cm^{−1} with a maximum resolution of 0.000959 cm^{−1} using synchrotron radiation from the Canadian Light Source. The two fundamental bands observed in this region correspond to motions best described as the outofplane modes related to ring puckering (ν30) at ∼158 cm^{−1} and SiH2 rocking (ν29) at ∼410 cm^{−1}. Both bands exhibit complex, dense spectral patterns that arise from ring inversion tunneling of the puckered SCB ring through a planar (C2v) intermediate configuration. Analysis of these patterns revealed rotationvibration transitions between states of the same inversion symmetry as well as rotationvibrationinversion transitions that connect states of different inversion symmetry. Infrared ground state combination differences from 1871 pairs of P and R branch transitions were used to accurately determine the spectroscopic parameters for the tunnelingdoubled ground state based on a broad range of quantum levels. With the ground state energy levels welldetermined, 8255 infrared transitions were assigned and analyzed to derive the band centers, rotational and centrifugal distortion constants for the inversion split ν29 and ν30 vibrational states. Comparison with the band centers predicted via DFT (B3LYP) and MP2 calculations [6311++G(2d,2p)] suggests that anharmonic corrections found via perturbation theory typically agree within 2% when compared with the observed spectrum of SCB.

Density functional theory study of the interaction of vinyl radical, ethyne, and ethene with benzene, aimed to define an affordable computational level to investigate stability trends in large van der Waals complexes
View Description Hide DescriptionOur purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydrocarbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively lowlevel computational methods and compare them with higherlevel reference results. To this end, the interaction of three complexes between nonpolar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow highlevel reference calculations of the interaction energy ΔE AB. Counterpoisecorrected interaction energies ΔE AB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A−B complexes are carried out, using the B3LYPD, ωB97XD, and M062X functionals, with six basis sets: 631G(d), 6311 (2d,p), and 6311++G(3df,3pd); augccpVDZ and augccpVTZ; N07T. (2) Then, unconstrained optimizations by MøllerPlesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [E MP2/CBS] and (ii) the higherorder correlation energy effects in passing from MP2 to CCSD(T) at the augccpVTZ basis set, ΔE CCMP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔE AB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [631G(d) and N07T], exhibiting deviation from the computational reference of less than 1 kcal mol^{−1}. The zeropoint vibrational energy corrected estimates Δ(E AB+ZPE), obtained with the three functionals and the 631G(d) and N07T basis sets, are compared with experimental D0 measures, when available. In particular, this comparison is finally extended to the naphthalene and coronene dimers and to three π−π associations of different PAHs (R, made by 10, 16, or 24 C atoms) and P (80 C atoms).