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Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree–Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree–Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree–Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis. [ABSTRACT FROM AUTHOR]

A derivation of fourth-order vibrational perturbation theory (VPT4) based on the Watson Hamiltonian in dimensionless rectilinear normal coordinates is presented. Terms that are linear and cubic in the (nk + ½), with nk being the zeroth-order harmonic oscillator quantum numbers, appear in fourth order and extend the much simpler second-order vibrational perturbation theory model. The rather involved expressions for the fourth-order terms are derived with Rayleigh-Schröodinger perturbation theory, the process of verifying their correctness is described, and a computer code to generate the VPT4 constants from the potential energy surface derivatives is provided. The paper concludes with numerical examples featuring the H2O, Si2C, and cyclic-C3H2 molecules. [ABSTRACT FROM AUTHOR]

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs. [ABSTRACT FROM AUTHOR]

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model system wave function. According to nondegenerate ground state HKS-DFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKS-DFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrained-search version of HKS-DFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via Q-DFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlation-kinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of Q-DFT reaffirms that there can be no equivalent to the ground state HKS-DFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlation-kinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke’s atom. The work of others is also discussed. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) in HFCO initiated by an excitation of the out-of-plane bending vibration [nν6=2,4,6,...,18,20]. Using a full six-dimensional ab initio potential energy, the multiconfiguration time-dependent Hartree (MCTDH) method was exploited to propagate the corresponding six-dimensional wave packets. This study emphasizes the stability of highly excited states of the out-of-plane bending mode which exist even above the dissociation threshold. More strikingly, the structure of the IVR during the first step of the dynamics is very stable for initial excitations ranging from 2ν6 to 20ν6. This latter result is consistent with the analysis of the eigenstates obtained, up to 10ν6, with the aid of the Davidson algorithm in a foregoing paper [Iung and Ribeiro, J. Chem. Phys. 121, 174105 (2005)]. The present study can be considered as complementary to this previous investigation. This paper also shows how MCTDH can be used to predict the dynamical behavior of a strongly excited system and to determine the energies of the corresponding highly excited states. [ABSTRACT FROM AUTHOR]

In three recent publications it was predicted that an Al4C molecule is planar on the basis of nonhybrid density functional calculations. These conclusions contradict our earlier predictions that Al4C is tetrahedral. In order to resolve the controversy we probed in this paper a potential energy surface of Al4C using a large variety of theoretical methods including multiconfigurational methods and a variety of one-electron basis sets. We confirmed that the nonhybrid Becke’s exchange with Perdew–Wang 1991 correlation functional density functional method predicts that Al4C has a planar structure in agreement with the reports of the other three groups. However, in this paper we have shown that high level ab initio calculations at the coupled cluster with singles, doubles, and noniterative triples and at the complete active space self-consistent field followed by multireference configurational interaction levels of theory confirm our earlier prediction that Al4C is indeed tetrahedral. The failure of nonhybrid density functional methods to correctly characterize the global minimum structure of Al4C demonstrates that it is dangerous to rely solely on these density functional methods in characterization of new molecules and clusters, where experimental structure is not known. [ABSTRACT FROM AUTHOR]

This is the second in a series of papers detailing a MATLAB based implementation of the finite element method applied to collinear triatomic reactions. Here, we extend our previous work to reactions on coupled potential energy surfaces. The divergence of the probability current density field associated with the two electronically adiabatic states allows us to visualize in a novel way where and how nonadiabaticity occurs. A two-dimensional investigation gives additional insight into nonadiabaticity beyond standard one-dimensional models. We study the F(²P) + HCl and F(²P) + H2 reactions as model applications. Our publicly available code (http://www2.chem.umd.edu/groups/alexander/FEM) is general and easy to use. [ABSTRACT FROM AUTHOR]

Comparisons are presented of experimental and theoretical studies of the rotationally inelastic scattering of CD3 radicals with H2 and D2 collision partners at respective collision energies of 680 ± 75 and 640 ± 60 cm-1. Close-coupling quantum-mechanical calculations performed using a newly constructed ab initio potential energy surface (PES) provide initial-to-final CD3 rotational level (n, k → n', k') integral and differential cross sections (ICSs and DCSs). The DCSs are compared with crossed molecular beam and velocity map imaging measurements of angular scattering distributions, which serve as a critical test of the accuracy of the new PES. In general, there is very good agreement between the experimental measurements and the calculations. The DCSs for CD3 scattering from both H2 and D2 peak in the forward hemisphere for n' = 2-4 and shift more to sideways and backward scattering for n' = 5. For n' = 6-8, the DCSs are dominated by backward scattering. DCSs for a particular CD3 n→n' transition have a similar angular dependence with either D2 or H2 as collision partner. Any differences between DCSs or ICSs can be attributed to mass effects because the PES is unchanged for CD3-H2 and CD3-D2 collisions. Further comparisons are drawn between the CD3-D2 scattering and results for CD3-He presented in our recent paper [O. Tkáč, A. G. Sage, S. J. Greaves, A. J. Orr-Ewing, P. J. Dagdigian, Q. Ma, and M. H. Alexander, Chem. Sci. 4, 4199 (2013)]. These systems have the same reduced mass, but are governed by different PESs. [ABSTRACT FROM AUTHOR]

The photochemistry of the water molecule has revealed a wealth of quantum phenomena, which arise from the involvement of several coupled electronic states with very different potential energy surfaces. Most recently, dissociation from single rotational levels of its C1B1 state near 124 nm has been attributed to a vibronically coupled decay via the lower Ã-state surface, despite a large vertical energy gap of 2.8 eV. Similar conclusions have been reached for subsequent experimental data for D2O. The present paper presents further experimental data for HOD and for both the H+OD(X) and D+OH(X) products. Unlike the cases for H2O and D2O, the vibrational populations for hydroxyl products do not follow a smooth distribution with v(OH/OD). In particular, for OH there is a clear alternation in population for all the strong peaks, with odd v favoured over even v. These experimental data are analysed using new MRCI+Q calculations, which have been used to generate potential surfaces and associated non-adiabatic matrix elements for transition from the adiabatic C-state to lower unbound potential surfaces; and hence, to guide dynamical calculations using time-dependent wavepackets. It is concluded that although there is a minor contribution from the C→ à decay route, the major route follows C→ 1A2 → Ã. This is mediated through two regions of near degeneracy of the elusive 1A2 surface with C for short bonds ca. 0.8 Å; and between 1A2 and à with long bonds ≥2 Å, thereby bridging the vertical energy gap. The striking population alternation for the D+OH(X) products is attributed to dynamic symmetry breaking on the 1A2 surface. [ABSTRACT FROM AUTHOR]

A theoretical study of the photoabsorption spectroscopy of hexafluorobenzene (HFBz) is presented in this paper. The chemical effect due to fluorine atom substitution on the electronic structure of benzene (Bz) saturates in HFBz. State- of-the-art quantum chemistry calculations are carried out to establish potential energy surfaces and coupling surfaces of five energetically low-lying electronic (two of them are orbitally degenerate) states of HFBz. Coupling of these electronic states caused by the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type of interactions are examined. The impact of these couplings on the nuclear dynamics of the participating electronic states is thoroughly investigated by quantum mechanical methods and the results are compared with those observed in the experiments. The complex structure of the S1 ← S0 absorption band is found to originate from a very strong nonadiabatic coupling of the S2 (of πσ* origin) and S1 (of ππ* origin) state. While S2 state is orbitally degenerate and JT active, the S1 state is nondegenerate. These states form energetically low-lying conical intersections (CIs) in HFBz. These CIs are found to be the mechanistic bottleneck of the observed low quantum yield of fluorescence emission, non overlapping absorption, and emission bands of HFBz and contribute to the spectral width. Justification is also provided for the observed two peaks in the second absorption (the unassigned 'c band') band of HFBz. The peaks observed in the third, fourth, and fifth absorption bands are also identified and assigned. [ABSTRACT FROM AUTHOR]

A common feature in computations of chemical and physical properties is the investigation of phenomena at different levels of computational accuracy. Less accurate computations are used to provide a relatively quick understanding of the behavior of a system and allow a researcher to focus on regions of initial conditions and parameter space where interesting phenomena are likely to occur. These inexpensive calculations are often discarded when more accurate calculations are performed. This paper demonstrates how computations at different levels of accuracy can be simultaneously incorporated to study chemical and physical phenomena with less overall computational effort than the most expensive level of computation. A smaller set of computationally expensive calculations is needed because the set of expensive calculations is correlated with the larger set of less expensive calculations. We present two applications. First, we demonstrate how potential energy surfaces can be fit by simultaneously using results from two different levels of accuracy in electronic structure calculations. In the second application, we study the optical response of metallic nanostructures. The optical response is generated with calculations at two different grid resolutions, and we demonstrate how using these two levels of computation in a correlated fashion can more efficiently optimize the response. [ABSTRACT FROM AUTHOR]

In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present a family of generally applicable schemes for updating the Hessian from electronic structure calculations based on an equation derived with compact finite difference (CFD). The CFD-based equation is of higher accuracy than the quasi-Newton equation on which existing generally applicable Hessian update schemes are based. Direct tests of Hessian update schemes, as well as dynamics simulations using an integrator incorporating Hessian update schemes, have shown four of the new schemes produce reliably higher accuracy than existing Hessian update schemes. [ABSTRACT FROM AUTHOR]

Classical density functional theories usually separate the formulation of the excess Helmholtz free energy in hard-body and energetic contributions. Fundamental measure theories (FMTs) have emerged as the preferred choice to account for the former contribution. The evaluation of geometrically weighted densities (convolutions) arisen in FMT for hard spheres in long cylindrical cavities is addressed in this paper. Previously, Malijevský [J. Chem. Phys. 126, 134710 (2007)] reported expressions containing elliptic integrals for the kernels of the convolutions involving scalar and vectorial weights. Here, the set of kernels is extended to second and third order tensorial weights that introduce desirable dimensional crossover properties to the evaluation of the excess free energy. An alternative formulation for the convolutions, which greatly facilitates their computation, is also proposed. Integrals of the original kernels arise in this way and a set of expressions for them, again expressed in terms of elliptic integrals, is presented here. With the aim of providing a computationally simple framework to evaluate equilibrium density profile with cylindrical symmetry, a procedure based on direct minimization of the discretized grand potential energy, rather than employing the Euler–Lagrange equilibrium conditions, is discussed and used to identify differences between two FMT formulations, including or not second order tensorial kernels in very narrow cylindrical pores. [ABSTRACT FROM AUTHOR]

Structures, binding energies, and vibrational frequencies of (NH3)n (n=2–5) isomers and dynamical properties of liquid ammonia have been explored using a transferable intermolecular potential eight point model including fluctuating charges and flexible body based on a combination of the atom-bond electronegativity equalization and molecular (ABEEM) mechanics (ABEEM ammonia-8P) in this paper. The important feature of this model is to divide the charge sites of one ammonia molecule into eight points region containing four atoms, three σ bonds, and a lone pair, and allows the charges in system to fluctuate responding to the ambient environment. Due to the explicit descriptions of charges and special treatment of hydrogen bonds, the results of equilibrium geometries, dipole moments, cluster interaction energies, vibrational frequencies for the gas phase of small ammonia clusters, and radial distribution function for liquid ammonia calculated with the ABEEM ammonia-8P potential model are in good agreement with those measured by available experiments and those obtained from high level ab initio calculations. The properties of ammonia dimer are studied in detail involving the structure and one-dimensional, two-dimensional potential energy surface. As for interaction energies, the root mean square deviation is 0.27 kcal/mol, and the linear correlation coefficient reaches 0.994. [ABSTRACT FROM AUTHOR]

A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P,Q,G) or even three-index (T1,T2) conditions [H. Van Aggelen et al., Phys. Chem. Chem. Phys. 11, 5558 (2009)]. Heteronuclear molecules tend to dissociate into fractionally charged atoms. In this paper we introduce a general class of N-representability conditions, called subsystem constraints, and show that they cure the dissociation problem at little additional computational cost. As a numerical example the singlet potential energy surface of Be B+ is studied. The extension to polyatomic molecules, where more subsystem choices can be identified, is also discussed. [ABSTRACT FROM AUTHOR]

This paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing full-dimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a 2×2 electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction OH+H2→H2O+H and the hydrogen atom abstraction from a model of α-tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108-dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradient-based MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ high-level electronic structure calculations for dynamics at an affordable cost. [ABSTRACT FROM AUTHOR]

The multiscale coarse-graining (MS-CG) method, proposed by Izvekov and Voth [J. Phys. Chem. B 109, 2469 (2005); Izvekov and VothJ. Chem. Phys. 123, 134105 (2005)], is a method for determining the effective potential energy function for a coarse-grained model of a fluid using data obtained from molecular dynamics (MD) simulation of the corresponding atomically detailed model. The method has been given a rigorous statistical mechanical basis [Noid et al. J. Chem. Phys. 128, 244114 (2008); Noid et al.,J. Chem. Phys. 128, 244115 (2008)]. The coarse-grained (CG) potentials obtained using the MS-CG method are an approximate variational solution for the exact many-body potential of mean force for the coarse-grained sites. In this paper we apply this method to study the many-body potential of mean force among solutes in a simple model of a solution of Lennard-Jones particles. We use a new set of basis functions for the variational calculation that is useful when the coarse-grained potential is approximately equal to an arbitrarily complicated pairwise additive, central interaction among the sites of the coarse-grained model. For this model, pairwise additivity of the many-body potential of mean force is a very good approximation when the solute concentration is low, and it becomes less accurate for high concentrations, indicating the importance of many-body contributions to the coarse-grained potential. The best possible pairwise additive CG potential of the solute particles is found to be quite long ranged for all concentrations except those for which the mole fraction of solute is very close to unity. We discuss strategies for construction of short-ranged potentials for efficient but accurate CG MD simulation. We also discuss how the choice of basis functions for the variational calculation can be used to provide smoothing of the calculated CG potential function to overcome statistical sampling error in the atomistic simulation data used for the generation of the potential. [ABSTRACT FROM AUTHOR]

Recent experiments have shown convincing evidence for nonadiabatic energy transfer from adsorbate degrees of freedom to surface electrons during the interaction of molecules with metal surfaces. In this paper, we propose an independent-electron surface hopping algorithm for the simulation of nonadiabatic gas-surface dynamics. The transfer of energy to electron-hole pair excitations of the metal is successfully captured by hops between electronic adiabats. The algorithm is able to account for the creation of multiple electron-hole pairs in the metal due to nonadiabatic transitions. Detailed simulations of the vibrational relaxation of nitric oxide on a gold surface, employing a multistate potential energy surface fit to density functional theory calculations, confirm that our algorithm can capture the underlying physics of the inelastic scattering process. [ABSTRACT FROM AUTHOR]

Classical and quantum mechanical expressions for the j-j′ vector correlation (also referred to as the rotational tilt) are presented for the situation in which the initial and final relative velocity directions are unresolved. The quantum mechanical expressions are compared with previous descriptions in the literature. It is shown that in the case of 2S+1Σ radicals in collision with closed shell species, a tensor opacity formalism can be employed in quasiclassical trajectory calculations to provide classical estimates of both open shell spin-rotation state and nuclear hyperfine state changing (or conserving) cross sections. Polarization parameters are also obtained from the same formalism. The method is applied to calculations on the OH(A 2Σ+)–Ar system using a recently developed potential energy surface. The results of both the closed and open shell quasiclassical trajectory calculations are found to compare favorably with those from close-coupled closed and open shell quantum mechanical scattering calculations. The accompanying paper provides an experimental test of these calculations and of the potential energy surface they employ. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v=2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained. [ABSTRACT FROM AUTHOR]

A new semiempirical exchange-Coulomb model potential energy surface for the N2–He interaction was reported recently [A. K. Dham et al., J. Chem. Phys. 127, 054302 (2007)] and, using it, the temperature dependence of bulk gas properties of N2–He mixtures, such as the second virial coefficient and traditional transport phenomena, most of which depend primarily on the isotropic component of the interaction potential energy surface, was determined. Values of these properties, along with values calculated using two high-quality ab initio potential energy surfaces [C.-H. Hu and A. J. Thakkar, J. Chem. Phys. 104, 2541 (1996); K. Patel et al., ibid 119, 909 (2003)] were compared critically to available experimental data. The present paper reports on the ability of the same three potential energy surfaces to predict state-to-state and total differential cross sections, total integral cross sections, and the temperature dependence of bulk gas relaxation phenomena (including magnetic field effects on transport coefficients). While all three potential energy surfaces give total differential and higher speed integral scattering results that fall within the experimental uncertainties, integral scattering results and state-to-state differential cross section measurements consistently exceed the calculated values. All three surfaces give similar agreement with the relaxation properties of N2–He binary mixtures, with the semiempirical exchange-Coulomb model potential energy surface giving slightly better overall agreement with experiment than the two ab initio potential energy surfaces. [ABSTRACT FROM AUTHOR]

The frozen natural orbital (FNO) coupled-cluster method increases the speed of coupled-cluster (CC) calculations by an order of magnitude with no consequential error along a potential energy surface. This method allows the virtual space of a correlated calculation to be reduced by about half, significantly reducing the time spent performing the coupled-cluster (CC) calculation. This paper reports the derivation and implementation of analytical gradients for FNO-CC, including all orbital relaxation for both noncanonical and semicanonical perturbed orbitals. These derivatives introduce several new orbital relaxation contributions to the CC density matrices. FNO-CCSD(T) and FNO-ΛCCSD(T) are applied to a test set of equilibrium structures, verifying that these methods are capable of reproducing geometries and vibrational frequencies accurately, as well as energies. Several decomposition pathways of nitroethane are investigated using CCSD(T) and ΛCCSD(T) with 60% of the FNO virtual orbitals in a cc-pVTZ basis, and find differences on the order of 5 kcal/mol with reordering of the transition state energies when compared to B3LYP 6-311+G(3df,2p). [ABSTRACT FROM AUTHOR]

Several features and the performance of the recently published [P. Jankowski and M. Ziólkowski, Mol. Phys. 104, 2293 (2006)] three-dimensional intermolecular potential energy surface for the Ar–HF complex have been investigated. This full-dimensional surface has been obtained using the method of the local expansion of the exact interaction energy surface [P. Jankowski, J. Chem. Phys. 121, 1655 (2004)] in the Taylor series with respect to intramolecular coordinates. The interaction energies have been calculated with the coupled-cluster supermolecular method with single, double, and noniterative triple excitations. The convergence of the interaction energy with respect to the size of the basis set is discussed. The two-dimensional surfaces resulting from averaging of the full-dimensional surface over the intramolecular vibration of HF have been obtained and directly compared to the empirical H6(4,3,2) set of surfaces proposed by Hutson [J. Chem. Phys. 96, 6752 (1992)]. A very good agreement has been observed. The averaged potentials have been used to calculate the rovibrational energy levels of the Ar–HF and Ar–DF complexes and compared to the experimental data. The accuracy of rovibrational calculations achieved with the new surface is much better than with any of the ab initio surfaces available so far. Predictions of the rovibrational energy levels and spectroscopic constants have also been done for Ar–HF with HF in the v=4,5 vibrational states, and for Ar–DF and DF in the v=3,4 states. The full-dimensional surface studied in this paper is the first ab initio surface which is fully compatible with the empirical H6(4,3,2) surface proposed by Hutson. [ABSTRACT FROM AUTHOR]

Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view. [ABSTRACT FROM AUTHOR]

In this paper, the structure and spectroscopic parameters of the C5 cluster are determined using multiconfigurational quantum chemical methods as implemented in the MOLCAS software. A number of spectroscopic properties (band center positions, l-doubling parameters, and rotational constants) have been characterized. From the new results, the assignments of previous astrophysical observations [J. Goicoechea et al., Astrophys. J. 609, 225 (2004)] are discussed. A detailed exploration of the global potential energy surface confirms that C5 has a X 1Σg+ linear isomer of prominent stability and, at least, three minimum energy structures showing singlet electronic ground states. Two of them are cyclic and one has a nonplanar geometry. Vertical and adiabatic electronic transitions and vibrational spectroscopic parameters are determined for the most stable linear isomer using multiconfigurational second order perturbation theory (CASPT2) using an active space containing 12 valence orbitals with 12 active electrons and extended ANO-type basis sets. The infrared spectrum has been analyzed from an anharmonic force field derived form the local surface, determined from the energies of a grid of 1350 geometries. The force field includes four coupling terms. The CASPT2 band center position of the ν7(πu) anharmonic fundamental has been calculated to be at 102 cm-1, which validates the assignment to C5 of the pattern of bands centered at 102 cm-1 observed with the ISO telescope. [ABSTRACT FROM AUTHOR]

For the charge transfer and vibrational and electronic deexcitations between O2/O2++CO+/CO, O/O++CO2+/CO2, and C/C++O3+/O3, multistep reaction pathways are discussed in light of the theoretical data of this and previous paper together with close comparison with the experimental observations. Our calculations show that these pathways involve both the long range and molecular region ranges of the potential energy surfaces of the electronic states of the stable isomers of OOCO+ and mostly those of the weakly bound charge transfer complex OOCO+. The couplings between these electronic states such as vibronic, Renner-Teller, Jahn-Teller, and spin orbit are viewed to play crucial roles here. Moreover, the initial orientation of the reactants, in the entrance channels, strongly influences the reaction mechanisms undertaken. We propose for the first time a mechanism for the widely experimentally studied spin-forbidden exothermic O+(4Su)+CO2(X 1Σg+)→O2+(X 2Πg)+CO(X 1Σ+) reaction where the O turns around the OCO molecule. [ABSTRACT FROM AUTHOR]

In this paper, we present a calculation for the bound states of A1 symmetry on the spin-aligned Li3(1 4A′) potential energy surface. We apply a mixture of discrete variable representation and distributed approximating functional methods to discretize the Hamiltonian. We also introduce a new method that significantly reduces the computational effort needed to determine the lowest eigenvalues and eigenvectors (bound state energies and wave functions of the full Hamiltonian). In our study, we have found the lowest 150 energy bound states converged to less than 0.005% error, and most of the excited energy bound states converged to less than 2.0% error. Furthermore, we have estimated the total number of the A1 bound states of Li3 on the spin-aligned Li3(1 4A′) potential surface to be 601. [ABSTRACT FROM AUTHOR]

The thermodynamics and kinetics of a many-body system can be described in terms of a potential energy landscape in multidimensional configuration space. The partition function of such a landscape can be written in terms of a density of states, which can be computed using a variety of Monte Carlo techniques. In this paper, a new self-consistent Monte Carlo method for computing density of states is described that uses importance sampling and a multiplicative update factor to achieve rapid convergence. The technique is then applied to compute the equilibrium quench probability of the various inherent structures (minima) in the landscape. The quench probability depends on both the potential energy of the inherent structure and the volume of its corresponding basin in configuration space. Finally, the methodology is extended to the isothermal-isobaric ensemble in order to compute inherent structure quench probabilities in an enthalpy landscape. [ABSTRACT FROM AUTHOR]

This paper reports state-of-the-art ab initio calculations at the second order of Mo\ller-Plesset perturbation theory of molecular hydrogen interaction with polycyclic aromatic hydrocarbons (PAHs) up to coronene (C24H12). The effects of both H2 orientation with respect to the PAH plane and of PAH corrugation have been carefully investigated. It was found that the energetic preference for the perpendicular H2 orientation over the parallel one decreases rapidly as the PAH grows. The detailed study of coronene-H2 potential energy surface has made it possible to estimate from first principles the graphite-H2 binding energy. This ab initio estimate is shown to be in fair agreement with experiment. As revealed by the example of benzene-H2 dimer, the electrostatic energy component plays an important role in PAH-H2 interactions, that stems largely from the charge penetration effect and, therefore, cannot be reproduced by the simple quadrupole-quadrupole interaction model. [ABSTRACT FROM AUTHOR]

This paper presents a new ground state (1 2A′) electronic potential energy surface for the F(2P)+HCl→HF+Cl(2P) reaction. The ab initio calculations are done at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory by complete basis set extrapolation of the aug-cc-pVnZ (n=2,3,4) energies. Due to low-lying charge transfer states in the transition state region, the molecular orbitals are obtained by six-state dynamically weighted multichannel self-consistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple one-parameter correlation energy scaling to reproduce the experimental exothermicity (ΔE=-33.06 kcal/mol) for the reaction. Ab initio points are fitted to an analytical function based on sum of two- and three-body contributions, yielding a rms deviation of <0.3 kcal/mol for all geometries below 10 kcal/mol above the barrier. Of particular relevance to nonadiabatic dynamics, the calculations show significant multireference character in the transition state region, which is located 3.8 kcal/mol with respect to F+HCl reactants and features a strongly bent F–H–Cl transition state geometry (θ≈123.5°). Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the C∞v linear configuration that become avoided in Cs bent configurations of both the reactant and product, and should be a hallmark of all X–H–Y atom transfer reaction dynamics between (2P) halogen atoms. [ABSTRACT FROM AUTHOR]

We present several numerical applications based upon the effective-mode formulation for the short-time dynamics through conical intersections in macrosystems, as detailed in the preceding paper and first proposed by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)]. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective environmental modes are needed—together with the system’s modes—to accurately calculate the low resolution spectra and the short-time dynamics of the entire macrosystem. For the systems discussed here, results are compared to those of a full quantum wave-packet propagation. Some rules are extracted to provide general tendencies; these rules allow one to understand and predict the dynamical properties in more general situations where the exact quantum dynamics of the macrosystem is out of reach. [ABSTRACT FROM AUTHOR]

The short-time dynamics through a conical intersection of a macrosystem comprising a large number of nuclear degrees of freedom (modes) is investigated. The macrosystem is decomposed into a “system” part carrying a limited number of modes, and an “environment” part. An orthogonal transformation in the environment’s space is introduced, as a result of which a subset of three effective modes can be identified which couple directly to the electronic subsystem. Together with the system’s modes, these govern the short-time dynamics of the overall macrosystem. The remaining environmental modes couple, in turn, to the effective modes and become relevant at longer times. In this paper, we present the derivation of the effective Hamiltonian, first introduced by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)], and analyze its properties in some detail. Several special cases and topological aspects are discussed. [ABSTRACT FROM AUTHOR]

A method for constructing diabatic potential-energy matrices from ab initio quantum chemistry data is described and tested for use in exact quantum reactive scattering. The method is a refinement of that presented in a previous paper, in that it accounts for the presence of the nonremovable derivative coupling. The accuracy of quantum dynamics on this type of diabatic potential is tested by comparison with an analytic model and for an ab initio description of the two lowest-energy states of H3. [ABSTRACT FROM AUTHOR]

All the pure rotational transitions reported in the previous studies [J. Chem. Phys. 113, 10121 (2000); J. Mol. Spectrosc. 222, 22 (2003)] and newly observed rotation-vibration transitions, P=1/2←3/2, for Ar–SH and Ar–SD [J. Chem. Phys. (2005), the preceding paper] have been simultaneously analyzed to determine a new intermolecular potential-energy surface of Ar–SH in the ground state. A Schrödinger equation considering the three-dimensional freedom of motion for an atom-diatom complex in the Jacobi coordinate, R, θ, and r, was numerically solved to obtain energies of the rovibrational levels using the discrete variable representation method. A three-dimensional potential-energy surface is determined by a least-squares fitting with initial values of the parameters for the potential obtained by ab initio calculations at the RCCSD(T)/aug-cc-pVTZ level of theory. The potential well reproduces all the observed data in the microwave and millimeter wave regions with parity doublings and hyperfine splittings. Several low-lying rovibrational energies are calculated using the new potential-energy surface. The dependence of the interaction energy between Ar and SH(2Πi) on the bond length of the SH monomer is discussed. [ABSTRACT FROM AUTHOR]

Fundamental issues associated with the application of the nuclear-electronic orbital (NEO) approach to hydrogen transfer systems are addressed. In the NEO approach, specified nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wavefunctions are calculated with molecular orbital methods. The positions of the nuclear basis function centers are optimized variationally. In the application of the NEO approach to hydrogen transfer systems, the hydrogen nuclei and all electrons are treated quantum mechanically. Within the NEO framework, the transferring hydrogen atom can be represented by two basis function centers to allow delocalization of the proton vibrational wavefunction. In this paper, the NEO approach is applied to the [He-H-He]+ and [He-H-He]++ model systems. Analyses of technical issues pertaining to flexibility of the basis set to describe both single and double well proton potential energy surfaces, linear dependency of the hydrogen basis functions, multiple minima in the basis function center optimization, convergence of the number of hydrogen basis function centers, and basis set superposition error are presented. The accuracy of the NEO approach is tested by comparison to grid calculations for these model systems. [ABSTRACT FROM AUTHOR]

In this paper we report a combined experimental and theoretical study on the dynamics of the insertion reaction C(1D)+D2 at 15.5 kJ mol-1 collision energy. Product angular and velocity distributions have been obtained in crossed beam experiments and quasiclassical trajectory (QCT) and rigorous statistical calculations have been performed on the recent and accurate ab initio potential energy surface of Bussery-Honvault, Honvault, and Launay at the energy of the experiment. The molecular-beam results have been simulated using the theoretical calculations. Good agreement between experiment and both QCT and statistical predictions is found. [ABSTRACT FROM AUTHOR]

The paper presents a theoretical study of the low-energy dynamics of radiative association processes in the He++H2 collision system. Formation of the triatomic HeH2+ ion in its bound rotation-vibration states on the potential-energy surfaces of the ground and of the first excited electronic states is investigated. Close-coupling calculations are performed to determine detailed state-to-state characteristics (bound←free transition rates, radiative and dissociative widths of resonances) as well as temperature-average characteristics (rate constants, photon emission spectra) of the two-state (X←A) reaction He+(2S)+H2(X1Σg+)→HeH2+(X2A′)+hν and of the single-state (A←A) reaction He+(2S)+H2(X1Σg+)→HeH2+(A2A′)+hν. The potential-energy surfaces of the X- and A-electronic states of HeH2+ and the dipole moment surfaces determined ab initio in an earlier work [Kraemer, Sˇpirko, and Bludsky, Chem. Phys. 276, 225 (2002)] are used in the calculations. The rate constants k(T) as functions of temperature are calculated for the temperature interval 1≤T≤100 K. The maximum k(T) values are predicted as 3.3×10-15 s-1 cm3 for the X←A reaction and 2.3×10-20 s-1 cm3 for the A←A reaction at temperatures around 2 K. Rotationally predissociating states of the He+-H2 complex, correlating with the υ=0, j=2 state of free H2, are found to play a crucial role in the dynamics of the association reactions at low temperatures; their contribution to the k(T) function of the X←A reaction at T<30 K is estimated as larger than 80%. The calculated partial rate constants and emission spectra show that in the X←A reaction the HeH2+(X) ion is formed in its highly excited vibrational states. This is in contrast with the vibrational state population of the ion when formed via the (X←X) reaction He(1S)+H2+(X2Σg+)→HeH2+(X2A′)+hν. [ABSTRACT FROM AUTHOR]

A method for incorporating strong electric field polarization effects into optimal control calculations is presented. A Born–Oppenheimer-type separation, referred to as the electric-nuclear Born–Oppenheimer (ENBO) approximation, is introduced in which variations of both the nuclear geometry and the external electric field are assumed to be slow compared with the speed at which the electronic degrees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei but also on the electric field strength and on the orientation of the molecule with respect to the electric field. The range of validity of the ENBO approximation is discussed in the paper. A two-stage toolkit implementation is presented to incorporate the polarization effects and reduce the cost of the optimal control dynamics calculations. As an illustration of the method, it is applied to optimal control of vibrational excitation in a hydrogen molecule aligned along the field direction. Ab initio configuration interaction calculations with a large orbital basis set are used to compute the H–H interaction potential in the presence of the electric field. The significant computational cost reduction afforded by the toolkit implementation is demonstrated. [ABSTRACT FROM AUTHOR]

The recently developed completely renormalized (CR) coupled-cluster (CC) methods with singles, doubles, and noniterative triples or triples and quadruples [CR-CCSD(T) or CR-CCSD(TQ), respectively], which are based on the method of moments of CC equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], eliminate the failures of the standard CCSD(T) and CCSD(TQ) methods at larger internuclear separations, but they are not rigorously size extensive. Although the departure from strict size extensivity of the CR-CCSD(T) and CR-CCSD(TQ) methods is small, it is important to examine the possibility of formulating the improved CR-CC methods, which are as effective in breaking chemical bonds as the existing CR-CCSD(T) and CR-CCSD(TQ) approaches, which are as easy to use as the CR-CCSD(T) and CR-CCSD(TQ) methods, and which can be made rigorously size extensive. This may be particularly useful for the applications of CR-CC methods and other MMCC approaches in calculations of potential energy surfaces of large many-electron systems and van der Waals molecules, where the additive separability of energies in the noninteracting limit is very important. In this paper, we propose different types of CR-CC approximations, termed the locally renormalized (LR) CCSD(T) and CCSD(TQ) methods, which become rigorously size extensive if the orbitals are localized on nointeracting fragments. The LR-CCSD(T) and LR-CCSD(TQ) methods rely on the form of the energy expression in terms of the generalized moments of CC equations, derived in this work, termed the numerator-denominator-connected MMCC expansion. The size extensivity and excellent performance of the LR-CCSD(T) and LR-CCSD(TQ) methods are illustrated numerically by showing the results for the dimers of stretched HF and LiH molecules and bond breaking in HF and H2O. [ABSTRACT FROM AUTHOR]

A potential energy surface is retrieved for the Ar-CO complex by carrying out a global analysis of its high-resolution spectroscopic data. The data set consists of already published microwave and infrared data and of new microwave transitions which are presented in the paper. The theoretical approach used to reproduce the spectrum is based on a model Hamiltonian which accounts simultaneously for the two large amplitude van der Waals modes and for the overall rotation of the complex. Only the vCO=0 state is considered. The root-mean-square deviation of the analysis is 18 MHz for the microwave data and 1.4×10-3 cm-1 for the infrared energy difference data. Fifteen parameters corresponding to the potential energy function are determined in addition to two kinetic energy parameters and two distortion-type parameters. The potential energy surface derived is in good agreement with the one obtained by Shin, Shin, and Tao [J. Chem. Phys. 104, 183 (1996)]. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The bound rovibronic levels of the He–HF[sup +] complex were calculated for total angular momentum J=1/2, 3/2, 5/2, 7/2, and 9/2 with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin–orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance R fixed at values ranging from 1.5 to 8.5 Å and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer body-fixed (BF) frame with its z axis parallel to the intermolecular vector R and with respect to a molecule-fixed (MF) frame with its z axis parallel to the HF[sup +] bond. The linear equilibrium geometry makes the He–HF[sup +] complex a Renner–Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner–Teller effect in this system. In addition to the properties of a “normal” semirigid molecule Renner–Teller system it shows typical features caused by large-amplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin–orbit splittings, parity splittings, and rotational constants. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Shapes of the potential energy surfaces (PES) of ‘‘floppy’’ molecules can be represented by graphs in which vertices denote global minima and edges connecting the vertices describe energetically accessible paths connecting such global minima. Such graphical representations of PESs are characterized by (i) the number of vertices; (ii) edges that connect (or do not) various vertices; and (iii) the symmetry of the PES, which may be obtained from the graphical figure. These characteristics are shown in this paper to be reflected in the vibration–rotation wave function’s symmetry. Such a symmetry analysis reduces to that provided by the conventional point group for rigid molecules, but provides a useful tool for characterizing vibrations of floppy molecules. In particular, it is shown that for so-called connected graphs, the nonrigid group of the molecule is its full permutation-inversion group. PESs with connected graphs having three and six global minima are examined as examples, and relevant character tables are provided. PESs with disconnected graphs (which characterize species containing some inaccessible barriers), are also considered. The flexible molecules ArH3+, C2H3+, CH4+, and LiBH4 are considered as examples of the tools presented here. [ABSTRACT FROM AUTHOR]

We demonstrate in this Comment that the quantum mechanical absorption spectrum of the Hartley band of ozone, calculated using the diabatic B state potential energy surface constructed from the ab initio data of the title paper, is strongly structured. This result, which is in agreement with previous theoretical studies of the Hartley band, contradicts the findings of Baloïtcha and Balint-Kurti and questions the accuracy of their calculations. [ABSTRACT FROM AUTHOR]

We comment on a paper [J. R. Stine and J. T. Muckerman, J. Chem. Phys. 65, 3975 (1976)] of the same title. We point out that their attempted reduction of a locally avoided intersection of two potential energy surfaces to a one-dimensional problem is incorrect. [ABSTRACT FROM AUTHOR]

Reports that in the article 'Theoretical characterization of the potential energy surface for H+O[sub2]...HO[sub2]...OH+O. IIII. Computed points to define a global potential energy surface,' from the Journal of Chemical Physics volume 94, p. 7068, the CASSCF/CCI calculations described in the paper were incorrectly identified as [4s3p2d1f/3s*2p] instead of [4s3p2d1f/3s*2p1d].