Volume 139, Issue 15, 21 October 2013

We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counteriononly system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counteriononly case and lead to important new insights into their properties that cannot be derived by any other means.
 PERSPECTIVES


Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond
View Description Hide DescriptionWe present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counteriononly system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counteriononly case and lead to important new insights into their properties that cannot be derived by any other means.
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 COMMUNICATIONS


Communication: The ionization spectroscopy of mixed carboxylic acid dimers
View Description Hide DescriptionWe report mass analyzed threshold ionization spectroscopy of supersonically cooled gas phase carboxylic complexes with 9hydroxy9fluorenecarboxylic acid (9HFCA), an analog of glycolic acid. The vibrationally resolved cation spectrum for the 9HFCA complex with formic acid allows accurate determination of its ionization potential (IP), 64 374 ± 8 cm^{−1}. This is 545 cm^{−1} smaller than the IP of 9HFCA monomer. The IPs of 9HFCA complexes with acetic acid and benzoic acid shift by −1133 cm^{−1} and −1438 cm^{−1}, respectively. Density functional calculations confirm that Cs symmetry is maintained upon ionization of the 9HFCA monomer and its acid complexes, in contrast to the drastic geometric rearrangement attending ionization in complexes of 9fluorene carboxylic acid. We suggest that the marginal geometry changes and small IP shifts are primarily due to the collective interactions among one intramolecular and two intermolecular hydrogen bonds in the dimer.

Communication: A tractable design for a thermal transistor
View Description Hide DescriptionWe propose a conceptual design for a logic device that is the thermal analog of a transistor. It has fixed hot (emitter) and cold (collector) temperatures, and a gate controls the heat current. Thermal logic could be applied for thermal digital computing, enhance energy conservation, facilitate thermal rheostats, and enable the transport of phononic data. We demonstrate such a device using molecular dynamics simulations that consider thermal transport across hot and cold solid Si regions that seal water within them. Changes in the hot side, or emitter, heat current are linear with respect to varying gate temperature but the corresponding variation in the collector current is nonlinear. This nonlinear variation in collector current defines the ON and OFF states of the device. In its OFF state, the thermal conductivity of the device is positive. In the ON state, however, more heat is extracted through the cold terminal than is provided at the hot terminal due to the intervention of the base terminal. This makes it possible to alter the transport factor by varying the gate conditions. When the device is ON, the transport factor is greater than unity, i.e., more heat is rejected at the collector than is supplied to the emitter.

Communication: Predictive partial linearized path integral simulation of condensed phase electron transfer dynamics
View Description Hide DescriptionA partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the fluxflux/fluxside quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between nonadiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semiclassical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the fluxflux correlation function that is responsible for the decreased rate in the inverted regime.

Communication: Hatom reactivity as a function of temperature in solid parahydrogen: The H + N_{2}O reaction
View Description Hide DescriptionWe present low temperature kinetic measurements for the H + N2O association reaction in solid parahydrogen (pH2) at liquid helium temperatures (1–5 K). We synthesize ^{15}N2 ^{18}O doped pH2 solids via rapid vapor deposition onto an optical substrate attached to the cold tip of a liquid helium bath cryostat. We then subject the solids to short duration 193 nm irradiations to generate Hatoms produced as byproducts of the in situ N2O photodissociation, and monitor the subsequent reaction kinetics using rapid scan FTIR. For reactions initiated in solid pH2 at 4.3 K we observe little to no reaction; however, if we then slowly reduce the temperature of the solid we observe an abrupt onset to the H + N2O → cisHNNO reaction at temperatures below 2.4 K. This abrupt change in the reaction kinetics is fully reversible as the temperature of the solid pH2 is repeatedly cycled. We speculate that the observed nonArrhenius behavior (negative activation energy) is related to the stability of the prereactive complex between the Hatom and ^{15}N2 ^{18}O reagents.
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 ARTICLES

 Theoretical Methods and Algorithms

Molecular density functional theory of water describing hydrophobicity at short and long length scales
View Description Hide DescriptionWe present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al. , J. Phys. Chem. Lett.4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the kdependent longitudinal and transverse dielectric susceptibilities. The fine threedimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation freeenergies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the LumChandlerWeeks theory, by complementing the functional with a truncated hardsphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the VanderWaals theory of liquidvapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volumedriven to a surfacedriven regime at the nanometer scale.

Hybrid approach combining dissipative particle dynamics and finitedifference diffusion model: Simulation of reactive polymer coupling and interfacial polymerization
View Description Hide DescriptionA novel hybrid approach combining dissipative particle dynamics (DPD) and finite difference (FD) solution of partial differential equations is proposed to simulate complex reactiondiffusion phenomena in heterogeneous systems. DPD is used for the detailed molecular modeling of mass transfer, chemical reactions, and phase separation near the liquid/liquid interface, while FD approach is applied to describe the largescale diffusion of reactants outside the reaction zone. A smooth, selfconsistent procedure of matching the solute concentration is performed in the buffer region between the DPD and FD domains. The new model is tested on a simple model system admitting an analytical solution for the diffusion controlled regime and then applied to simulate practically important heterogeneous processes of (i) reactive coupling between immiscible endfunctionalized polymers and (ii) interfacial polymerization of two monomers dissolved in immiscible solvents. The results obtained due to extending the space and time scales accessible to modeling provide new insights into the kinetics and mechanism of those processes and demonstrate high robustness and accuracy of the novel technique.

Stateaveraged Monte Carlo configuration interaction applied to electronically excited states
View Description Hide DescriptionWe introduce stateaveraging into the method of Monte Carlo configuration interaction (SAMCCI) to allow the stable and efficient calculation of excited states. We show that excited potential curves for H3, including a crossing with the ground state, can be accurately reproduced using a small fraction of the full configuration interaction (FCI) space. A recently introduced error measure for potential curves [J. P. Coe and M. J. Paterson, J. Chem. Phys.137, 204108 (2012)] is also shown to be a fair approach when considering potential curves for multiple states. We demonstrate that potential curves for LiF using SAMCCI agree well with the FCI results and the avoided crossing occurs correctly. The seam of conical intersections for CH2 found by Yarkony [J. Chem. Phys.104, 2932 (1996)] is used as a test for SAMCCI and we compare potential curves from SAMCCI with FCI results for this system for the first three triplet states. We then demonstrate the improvement from using SAMCCI on the dipole of the 2 ^{1} A 1 state of carbon monoxide. We then look at vertical excitations for small organic molecules up to the size of butadiene where the SAMCCI energies and oscillator strengths are compared with CASPT2 values [M. Schreiber, M. R. SilvaJunior, S. P. A. Sauer, and W. Thiel, J. Chem. Phys.128, 134110 (2008)]. We finally see if the SAMCCI results for these excitation energies can be improved by using MCCIPT2 with approximate natural orbitals when the PT2 space is not onerously large.

A multistate fragment charge difference approach for diabatic states in electron transfer: Extension and automation
View Description Hide DescriptionThe electron transfer (ET) rate prediction requires the electronic coupling values. The Generalized MullikenHush (GMH) and Fragment Charge Difference (FCD) schemes have been useful approaches to calculate ET coupling from an excited state calculation. In their typical form, both methods use two eigenstates in forming the target chargelocalized diabatic states. For problems involve three or four states, a direct generalization is possible, but it is necessary to pick and assign the locally excited or chargetransfer states involved. In this work, we generalize the 3state scheme for a multistate FCD without the need of manual pick or assignment for the states. In this scheme, the diabatic states are obtained separately in the chargetransfer or neutral excited subspaces, defined by their eigenvalues in the fragment chargedifference matrix. In each subspace, the Hamiltonians are diagonalized, and there exist offdiagonal Hamiltonian matrix elements between different subspaces, particularly the chargetransfer and neutral excited diabatic states. The ET coupling values are obtained as the corresponding offdiagonal Hamiltonian matrix elements. A similar multistate GMH scheme can also be developed. We test the new multistate schemes for the performance in systems that have been studied using more than two states with FCD or GMH. We found that the multistate approach yields much better chargelocalized states in these systems. We further test for the dependence on the number of state included in the calculation of ET couplings. The final coupling values are converged when the number of state included is increased. In one system where experimental value is available, the multistate FCD coupling value agrees better with the previous experimental result. We found that the multistate GMH and FCD are useful when the original twostate approach fails.

The extended Koopmans' theorem for orbitaloptimized methods: Accurate computation of ionization potentials
View Description Hide DescriptionThe extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials (IPs) from any level of theory, in principle. However, for nonvariational methods, such as Møller–Plesset perturbation and coupledcluster theories, the EKT computations can only be performed as byproducts of analytic gradients as the relaxed generalized Fock matrix (GFM) and one and twoparticle density matrices (OPDM and TPDM, respectively) are required [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys.107, 6804 (1997)]. However, for the orbitaloptimized methods both the GFM and OPDM are readily available and symmetric, as opposed to the standard post Hartree–Fock (HF) methods. Further, the orbital optimized methods solve the Nrepresentability problem, which may arise when the relaxed particle density matrices are employed for the standard methods, by disregarding the orbital Zvector contributions for the OPDM. Moreover, for challenging chemical systems, where spin or spatial symmetrybreaking problems are observed, the abnormal orbital response contributions arising from the numerical instabilities in the HF molecular orbital Hessian can be avoided by the orbitaloptimization. Hence, it appears that the orbitaloptimized methods are the most natural choice for the study of the EKT. In this research, the EKT for the orbitaloptimized methods, such as orbitaloptimized second and thirdorder Møller–Plesset perturbation[U. Bozkaya, J. Chem. Phys.135, 224103 (2011)] and coupledelectron pair theories [OCEPA(0)] [U. Bozkaya and C. D. Sherrill, J. Chem. Phys.139, 054104 (2013)], are presented. The presented methods are applied to IPs of the second and thirdrow atoms, and closed and openshell molecules. Performances of the orbitaloptimized methods are compared with those of the counterpart standard methods. Especially, results of the OCEPA(0) method (with the augccpVTZ basis set) for the lowest IPs of the considered atoms and closedshell molecules are substantially accurate, the corresponding mean absolute errors are 0.11 and 0.15 eV, respectively.

Analytic evaluation of the dipole Hessian matrix in coupledcluster theory
View Description Hide DescriptionThe general theory required for the calculation of analytic third energy derivatives at the coupledcluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupledcluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations.

Proper and improper zero energy modes in HartreeFock theory and their relevance for symmetry breaking and restoration
View Description Hide DescriptionWe study the spectra of the molecular orbital Hessian (stability matrix) and randomphase approximation (RPA) Hamiltonian of brokensymmetry HartreeFock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected HartreeFock methods is also addressed.

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valleyridge inflection points
View Description Hide DescriptionWe study reaction dynamics on a model potential energy surface exhibiting posttransition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly nonmonotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.

Dynamical secondorder BetheSalpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation
View Description Hide DescriptionWe present a dynamical secondorder kernel for the BetheSalpeter equation to calculate electronic excitation energies. The derivation takes explicitly the functional derivative of the exact secondorder self energy with respect to the oneparticle Green's function. It includes naturally a frequency dependence, going beyond the adiabatic approximation. Perturbative calculations under the TammDancoff approximation, using the configuration interaction singles (CIS) eigenvectors, reveal an appreciable improvement over CIS, timedependent HartreeFock, and adiabatic timedependent density functional theory results. The perturbative results also compare well with equationofmotion coupledcluster and experimental results.

Modelfree simulation approach to molecular diffusion tensors
View Description Hide DescriptionIn the present work, we propose a simple modelfree approach for the computation of molecular diffusion tensors from molecular dynamics trajectories. The method uses a rigid body trajectory of the molecule under consideration, which is constructed a posteriori by an accumulation of quaternionbased superposition fits of consecutive conformations. From the rigid body trajectory, we compute the translational and angular velocities of the molecule and by integration of the latter also the corresponding angular trajectory. All quantities can be referred to the laboratory frame and a moleculefixed frame. The 6 × 6 diffusion tensor is computed from the asymptotic slope of the tensorial mean square displacement and, for comparison, also from the Kubo integral of the velocity correlation tensor. The method is illustrated for two simple model systems – a water molecule and a lysozyme molecule in bulk water. We give estimations of the statistical accuracy of the calculations.
 Advanced Experimental Techniques

Direct measurements of collisional Raman line broadening in the Sbranch transitions of acetylene (C_{2}H_{2})
View Description Hide DescriptionWe report direct measurements of the self and N2broadened Raman Sbranch linewidths of acetylene (C2H2), obtained by employing timeresolved picosecond rotational coherent antiStokes Raman scattering spectroscopy. Using broadband 115ps pump and Stokes pulses (∼135 cm^{−1} bandwidth) and a spectrally narrowed 90ps probe pulse (∼0.2 cm^{−1} bandwidth), Ramancoherence lifetimes are measured at room temperature for the Sbranch (ΔJ = +2) transitions associated with rotational quantum number J = 3–25. These directly measured Ramancoherence lifetimes, when converted to collisional linewidth broadening coefficients, differ from the previously reported broadening coefficients extracted from theoretical calculations by 6%–35% for selfbroadening for C2H2 and by up to 60% for N2broadened C2H2.

Stationary flow conditions in pulsed supersonic beams
View Description Hide DescriptionWe describe a generally applicable method for the experimental determination of stationary flow conditions in pulsed supersonic beams, utilizing timeresolved electron induced fluorescence measurements of high pressure jet expansions of helium. The detection of ultraviolet photons from electronically excited helium emitted very close to the nozzle exit images the valve opening behavior—with the decided advantage that a photon signal is not affected by beamskimmer and beamresidual gas interactions; it thus allows to conclusively determine those operation parameters of a pulsed valve that yield complete opening. The studies reveal that a “flattop” signal, indicating constant density and commonly considered as experimental criterion for continuous flow, is insufficient. Moreover, translational temperature and mean terminal flow velocity turn out to be significantly more sensitive in testing for the equivalent behavior of a continuous nozzle source. Based on the widely distributed EvenLavie valve we demonstrate that, in principle, it is possible to achieve quasicontinuous flow conditions even with fastacting valves; however, the two prerequisites are a minimum pulse duration that is much longer than standard practice and previous estimates, and a suitable tagging of the appropriate beam segment.

Perturbation facilitated twocolor fourwavemixing spectroscopy of C_{3}
View Description Hide DescriptionPerturbationfacilitated twocolor resonant fourwavemixing spectroscopy is realized to access the (dark) triplet manifold of the C3 molecule from the singlet ground state. The inherent nonlinear signal dependence and coherence of the technique result in a favorable detection of the excited triplet states of interest. The observation of a newly found ^{3}Δu electronic state is achieved by a twostep excitation via “gateway” levels (i.e., singlettriplet mixed levels). Additionally, by fixing the probe laser on a transition exhibiting mainly triplettriplet character and scanning the pump laser, we demonstrate an effective spinfiltering in a fourwave mixing measurement where only transitions to the perturber state appear exclusively in an otherwise congested spectral range of the Comet band. Ab initio calculations of excited triplet states complement our analysis with the electronic assignment of the observed resonances.
 Atoms, Molecules, and Clusters

Electronic transitions in liquid amides studied by using attenuated total reflection farultraviolet spectroscopy and quantum chemical calculations
View Description Hide DescriptionAttenuated total reflection farultraviolet (ATRFUV) spectra in the 140–260 nm region were measured for several types of liquid amides (formamide, FA; Nmethylformamide, NMF; Nmethylacetamide, NMA; N,Ndimethylformamide, NdMF; and N,Ndimethylacetamide, NdMA) to investigate their electronic transitions in the FUV region. The spectra were compared with the corresponding gasphase spectra to examine the shift in the major absorption band in the 180–200 nm region going from the gas phase to the liquid phase, and it was found that the peak shift was dependent on the particular amide. FA and NMF, which exhibit intermolecular C=O…H–N hydrogen bonding, show a large shift of ∼0.60 eV to lower energy; however, NMA, which also exhibits hydrogen bonding, shows only a small shift. In NdMF and NdMA, C=O groups seem to be coupled, which results in a small peak shift. Two types of quantum chemical calculations, timedependent density functional theory (TDDFT) and symmetryadaptedcluster configuration interaction (SACCI) method, were performed to elucidate the origin of the shifts and the band assignments. The shift estimated by the monomer and dimer models with TDDFT reproduced well the observed shift from the gas phase to the liquid phase. This suggests that the intermolecular hydrogenbonding interaction significantly affects the magnitude of the shift. The manybody effects were also considered using the larger cluster models (trimer to pentamer). The energy shift calculated using SACCI with the monomer and the statespecific polarizable continuum model was also accurate, indicating that the nonlinear polarization effect appears to be important. As for the band assignments, it was found that though the major band can be mainly attributed to the ππ^{*} transition, several types of Rydberg transitions also exist in its vicinity and mixing of orbitals with the same symmetry occurs. The number and type of Rydberg transitions in the spectra depend upon the type of amide molecules. The valenceRydberg coupling of the ππ* transition is more significant than nπ* transition, which also holds in the pure liquid phase.

Topology of conical/surface intersections among five lowlying electronic states of CO_{2}: Multireference configuration interaction calculations
View Description Hide DescriptionMultireference configuration interaction with single and double excitation method has been utilized to calculate the potential energy surfaces of the five lowlying electronic states ^{1}A1, ^{1}A2, ^{3}A2, ^{1}B2, and ^{3}B2 of carbon dioxide molecule. Topology of intersections among these five states has been fully analyzed and is associated with doublewell potential energy structure for every electronic state. The analytical potential energy surfaces based on the reproducing kernel Hilbert space method have been utilized for illustrating topology of surface crossings. Double surface seam lines between ^{1}A1 and ^{3}B2 states have been found inside which the ^{3}B2 state is always lower in potential energy than the ^{1}A1 state, and thus it leads to an angle bias collision dynamics. Several conical/surface intersections among these five lowlying states have been found to enrich dissociation pathways, and predissociation can even prefer bentgeometry channels. Especially, the dissociation of O(^{3}P) + CO can take place through the intersection between ^{3}B2 and ^{1}B2 states, and the intersection between ^{3}A2 and ^{1}B2 states.