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.
 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.

Modespecific tunneling using the Q _{im} path: Theory and an application to fulldimensional malonaldehyde
View Description Hide DescriptionWe present a theory of modespecific tunneling that makes use of the general tunneling path along the imaginaryfrequency normal mode of the saddle point, Q im, and the associated relaxed potential, V(Q im) [Y. Wang and J. M. Bowman, J. Chem. Phys.129, 121103 (2008)]. The novel aspect of the theory is the projection of the normal modes of a minimum onto the Q im path and the determination of turning points on V(Q im). From that projection, the change in tunneling upon mode excitation can be calculated. If the projection is zero, no enhancement of tunneling is predicted. In that case vibrationally adiabatic (VA) theory could apply. However, if the projection is large then VA theory is not applicable. The approach is applied to modespecific tunneling in fulldimensional malonaldehyde, using an accurate fulldimensional potential energy surface. Results are in semiquantitative agreement with experiment for modes that show large enhancement of the tunneling, relative to the ground state tunneling splitting. For the six outofplane modes, which have zero projection on the planar Q im path, VA theory does apply, and results from that theory agree qualitatively and even semiquantitatively with experiment. We also verify the failure of simple VA theory for modes that show large enhancement of tunneling.

High resolution spectroscopy of HCl–water clusters: IR bands of undissociated and dissociated clusters revisited
View Description Hide DescriptionWe report a detailed study on the IR spectroscopy of HClwater complexes in superfluid helium nanodroplets in the frequency range from 2660 to 2675 cm^{−1}. We have recorded spectra of O as well as of O complexes and compared these results with theoretical predictions. In addition, we have carried out massselective intensity measurements as a function of partial pressure of HCl as well as of O (pickup curves). The results support a scenario where the IRabsorption in this part of the spectrum contains contributions from undissociated as well as from dissociated clusters with Cl^{−}(H2O)3(H3O)^{+} being the smallest dissociated complex. These findings are corroborated by additional electric field measurements yielding the orientation of the vibrational transition moment with respect to the permanent dipole moment. As a result we are able to assign a broad absorption band starting at 2675 cm^{−1} to dissociated HClwater clusters (HCl)1(H2O) n with n ⩾ 4. The two narrow absorption lines at 2667.9 cm^{−1} and 2670 cm^{−1} are assigned to an undissociated cluster, in agreement with previous studies.

Accurate ab initiobased adiabatic global potential energy surface for the 2^{2} A″ state of NH_{2} by extrapolation to the complete basis set limit
View Description Hide DescriptionA full threedimensional global potential energy surface is reported first time for the title system, which is important for the photodissociation processes. It is obtained using double manybody expansion theory and an extensive set of accurate ab initio energies extrapolated to the complete basis set limit. Such a work can be recommended for dynamics studies of the N(^{2} D) + H2 reaction, a reliable theoretical treatment of the photodissociation dynamics and as building blocks for constructing the double manybody expansion potential energy surface of larger nitrogen/hydrogen containing systems. In turn, a preliminary theoretical study of the reaction has been carried out with the method of quasiclassical trajectory on the new potential energy surface. Integral cross sections and thermal rate constants have been calculated, providing perhaps the most reliable estimate of the integral cross sections and the rate constants known thus far for such a reaction.

Corresponding states principle and van der Waals potentials of Zn_{2}, Cd_{2}, and Hg_{2}
View Description Hide DescriptionBased on the assumptions that the corresponding states principle is valid for the group 12 dimers and that the interaction potentials of these dimers can be described by the TangToennies potential model, a set of correlation relations between the spectroscopic constants of these dimers are derived. Some recently measured spectroscopic constants satisfy these relations quite well, but older experimental data do not. These recent spectroscopic constants and the newly available dispersion coefficients are used to construct the entire van der Waals potentials of Zn 2, Cd2, and Hg 2. There are indications that the ground state Hg 2 potential predicted by the present study is possibly the most accurate to date. No unequivocal conclusion can be made for Zn 2 and Cd2 potentials. Compared with the recent experiments, the present Zn 2 bond length is eight percent too small, and the present Cd2 bond length is eight percent too large. However, both Zn 2 and Cd2 bond lengths predicted by the present study are in good agreement with the quantum Monte Carlo results.

Theoretical study on reaction mechanism and kinetics of HNCS with CN
View Description Hide DescriptionWe presented a theoretical study on the detailed reaction mechanism and kinetics of the CN radical with the HNCS molecule. The barrierless minimum energy path and the most favorable entrance channel have been determined by constructing a twodimensional potential energy surface of the C atom of CN attacking the HNCS molecule. The reaction of the C atom attacking the S atom was finally identified as the dominant entrance channel based on the rate constants' results calculated with the canonical variational transition state theory. The master equation method was employed to calculate the products' branching ratios, the overall rate constant, and the pressure dependence of the title reaction. The B3LYP/6311+G(2d,p) method was employed for all the geometrical optimizations and a multilevel extrapolation method based on the CCSD(T) and MP2(FC) energies was employed for further energy refinements.