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The multimode multistate vibronic interactions between the five lowest electronic states of all three isomers of the difluorobenzene radical cation are investigated theoretically, based on ab initio electronic structure data, and employing a well-established vibronic coupling model. The approach rests on the linear vibronic coupling scheme, augmented by quadratic coupling terms for the totally symmetric modes. The underlying ionization potentials and coupling constants are obtained from ab initio coupled-cluster calculations. Low-energy conical intersections and strong vibronic couplings are found to prevail within the sets of X-Ã and B-C-D cationic states, while the interactions between these two sets of states are found to be weaker and depend on the isomer. The inclusion of the aforementioned quadratic couplings is found to be essential to correctly reproduce the lowest-energy conical intersections between the two different sets of electronic states. Differences between the three isomers regarding these quantities are pointed out. The results will be used as basis for multidimensional wave-packet dynamical simulations for these coupled potential energy surfaces to be presented in the following paper (Paper II). [ABSTRACT FROM AUTHOR]

Several commonly used approximate methods for the calculation of vibration–rotation–tunneling spectra for (HCl)2 are described. These range from one-dimensional models to an exact coupled four-dimensional treatment of the intermolecular dynamics. Two different potential surfaces were employed—an ab initio and our ES1 experimental surface (determined by imbedding the four-dimensional calculation outlined here in a least-squares loop to fit the experimental data, which is described in the accompanying paper [J. Chem. Phys. 103, 933 (1995)]. The most important conclusion deduced from this work is that the validity of the various approximate models is extremely system specific. All of the approximate methods addressed in this paper were found to be sensitive to the approximate separability of the radial and angular degrees of freedom, wherein exists the primary difference between the two potentials. Of particular importance, the commonly used reversed adiabatic angular approximation was found to be very sensitive to the choice for fixed R; an improper choice would lead to results very much different from the fully coupled results and perhaps to false conclusions concerning the intermolecular potential energy surface. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recent ab initio calculations have focused on the minimum energy path region of this surface [J. Chem. Phys. 88, 6273 (1988), Paper I] and on the saddle point region for H atom exchange via a T-shaped HO2 complex (J. Chem. Phys. 91, 2373 (1989), Paper II). In this paper, the results of additional calculations are discussed that, combined with the previously reported results, provide a global representation of the potential energy surface for this reaction. Complete active space SCF/externally contracted configuration interaction calculations (CASSCF/CCI) were carried out using the same wave function employed in II. The new calculations presented here characterize the potential energy surface for a variety of H atom approach angles, ranging from perpendicular to collinear (measured with respect to the O2 bond) and for a variety of H atom to O2 center-of-mass distances. Additionally, a new collinear exchange saddle point is reported. Using the ab initio results from these new calculations, optimal geometries, and harmonic frequencies based on local polynomial representations of the potential energy surface are reported along the constrained energy minimum path, while anharmonic frequencies are calculated at both the O2 and OH asymptotes and at the HO2 intermediate. [ABSTRACT FROM AUTHOR]

This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest 3A′ and 3A″ electronic states of the O(3P) + H2 system. For each of these states, ab initio electronic energies were calculated for more than 5000 geometries using internally contracted multireference configuration interaction methods. The calculated points were then fitted using the ansatz by Aguado et al. [Comput. Phys. Commun. 108, 259 (1998)] leading to very accurate analytical potentials well adapted to perform reaction dynamics studies. Overall, the topographies of both PESs are in good agreement with the benchmark potentials of Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)], but those presented in this work reproduce better the height and degeneracy of the two states at the saddle point. Moreover, the long range potential in the entrance channel does not require any cutoff. These features make the new PESs particularly suitable for a comparison of the dynamics on each of them. The new set of PESs was then used to perform quantum mechanics and quasiclassical trajectory calculations to determine differential and integral cross sections, which are compared to the experimental measurements by Garton et al. [J. Chem. Phys. 118, 1585 (2003)]. [ABSTRACT FROM AUTHOR]

In this paper, we performed a theoretical study on the influence of intramolecular bond lengths on the intermolecular interactions between H2 and AgCl molecules. Using four sets of bond lengths for the monomers of H2 and AgCl, four-dimensional intermolecular potential energy surfaces (PESs) were constructed from ab initio data points at the level of single and double excitation coupled cluster method with noniterative perturbation treatment of triple excitations. A T-shaped global minimum was found on the PES. Interestingly, both the binding energies and Ag–H2 distances present a linear relationship with the intramolecular bond lengths of H2–AgCl. The accuracy of these PESs was validated by the available spectroscopic data via the bound state calculations, and the predicted rotational transition frequencies can reproduce the experimental observations with a root-mean-squared error of 0.0003 cm−1 based on the PES constructed with r(H–H) and r(Ag–Cl) fixed at 0.795 and 2.261 Å, respectively. The intermolecular vibrational modes were assigned unambiguously with a simple pattern by analyzing the wave functions. Isotope effects were also investigated by the theoretical calculations, and the results are in excellent agreement with the available spectroscopic data. The transition frequencies for the isotopolog D2–AgCl are predicted with the accuracy of 0.3 MHz. [ABSTRACT FROM AUTHOR]

Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs. We introduce an MCTDH approach that uses a pruned basis and a collocation grid. Pruning the basis significantly reduces its size. Collocation makes it possible to do calculations using a potential that is not a SOP. The collocation point set is a Smolyak grid. Strategies using pruned MCTDH bases already exist, but they work only if the potential is a SOP. Strategies for using MCTDH with collocation also exist, but they work only if the MCTDH basis is a direct product. In this paper, we combine a pruned basis with collocation. This makes it possible to mitigate the direct-product basis size problem and do calculations when the potential is not a SOP. Because collocation is used, there are no integrals and no need for quadrature. All required matrix-vector products can be evaluated sequentially. We use nested sets of collocation points and hierarchical basis functions. They permit efficient inversion of the (large) matrix whose elements are basis functions evaluated at points, which is necessary to transform values of functions at points to basis coefficients. The inversion technique could be used outside of chemical physics. We confirm the validity of this new pruned, collocation-based (PC-)MCTDH approach by calculating the first 50 vibrational eigenenergies of CH2NH. [ABSTRACT FROM AUTHOR]

The infrared spectrum of proton-bound rare gas dimers has been extensively studied via matrix isolation spectroscopy. However, little attention has been paid on their spectrum in the gas phase. Most of the Rg2H+ has not been detected outside the matrix environment. Recently, ArnH+ (n = 3-7) has been first detected in the gas-phase [D. C. McDonald et al., J. Chem. Phys. 145, 231101 (2016)]. In that work, anharmonic theory can reproduce the observed vibrational structure. In this paper, we extend the existing theory to examine the vibrational signatures of Rg2H+, Rg = {Ne, Ar, Kr, and Xe}. The successive binding of Rg to H+ was investigated through the calculation of stepwise formation energies. It was found that this binding is anti-cooperative. High-level full-dimensional potential energy surfaces at the CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVQZ were constructed and used in the anharmonic calculation via discrete variable representation. We found that the potential coupling between the symmetric and asymmetric Rg-H+ stretch (ν1 and ν3 respectively) causes a series of bright n1ν1 + ν3 progressions. From Ne2H+ to Xe2H+, an enhancement of intensities for these bands was observed. [ABSTRACT FROM AUTHOR]

In this paper, we present a simple correction scheme to improve predictions of dielectric constants by classical non-polarisable models. This scheme takes into account electronic polarisation effects, through the experimental refractive index of the liquid, and a possible mismatch between the potential energy surface and the dipole moment surface. We have described the latter effect by an empirical scaling factor on the point charges, the value of which was determined by fitting the dielectric constant of methanol. Application of the same scaling factor to existing benchmark datasets, comprising four different models and a wide range of compounds, led to remarkable improvements in the quality of the predictions. In particular, the observed systematic underestimation of the dielectric constant was eliminated by accounting for the two missing terms in standard models. We propose that this correction term be included in future development and validation efforts of classical non-polarisable models. [ABSTRACT FROM AUTHOR]

This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach. [ABSTRACT FROM AUTHOR]

This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach. [ABSTRACT FROM AUTHOR]

The distinguishable cluster approximation proposed in Paper I [D. Kats and F. R. Manby, J. Chem. Phys. 139, 021102 (2013)] has shown intriguing abilities to accurately describe potential energy surfaces in various notoriously difficult cases. The question that still remained open is to what extend the accuracy and the stability of the method is due to the special choice of orbital-relaxation treatment. In this paper we introduce orbital relaxation in terms of Brueckner orbitals, orbital optimization, and projective singles into the distinguishable cluster approximation and investigate its importance in single- and multireference cases. All three resulting methods are able to cope with many multiple-bond breaking problems, but in some difficult cases where the Hartree-Fock orbitals seem to be entirely inadequate the orbital-optimized version turns out to be superior. [ABSTRACT FROM AUTHOR]

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields. [ABSTRACT FROM AUTHOR]

The role of vibrational excitation of reactants in driving reactions involving polyatomic species has been often studied by means of classical or quasi-classical trajectory simulations. We propose a different approach based on investigation of vibrational features of the Cl−⋯CH3Cl pre-reaction complex for the Cl− + CH3Cl SN2 reaction. We present vibrational power spectra and frequency estimates for the title pre-reaction complex calculated at the level of classical, semiclassical, and second-order vibrational perturbation theory on a pre-existing analytical potential energy surface. The main goals of the paper are the study of anharmonic effects and understanding of vibrational couplings that permit energy transfer between the collisional kinetic energy and the internal vibrations of the reactants. We provide both classical and quantum pictures of intermode couplings and show that the SN2 mechanism is favored by the coupling of a C–Cl bend involving the Cl− projectile with the CH3 rocking motion of the target molecule. We also illustrate how the routines needed for semiclassical vibrational spectroscopy simulations can be interfaced in a user-friendly way to pre-existing molecular dynamics software. In particular, we present an implementation of semiclassical spectroscopy into the VENUS suite of codes, thus providing a useful computational tool for users who are not experts of semiclassical dynamics. [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]

Potential energy surface (PES) holds the key in understanding a number of atomic clusters or molecular phenomena. However, due to the high dimension and incredible complexity of PES, only indirect methods can be used to characterize a PES of a given system in general. In this paper, a branched dynamic lattice searching method was developed to travel the PES, which was described in detail by a single-root network (SRN). The advantage of SRN is that it reflects the topological relation between different conformations and highlights the size of each structure energy trap. On the basis of SRN, to demonstrate how to transform one conformation to another, the transition path that connects two local minima in the PES was constructed. Herein, we take Lennard-Jones (LJ) clusters at the sizes of 38, 55, and 75 as examples. It is found that the PES of these three clusters have many local funnels and each local funnel represents one morphology. If a morphology is located more frequently, it will lie in a larger local funnel. Besides, certain steps of the transition path were generated successfully, such as changing from icosahedral to truncated octahedral of the LJ38-cluster. Though we do not exhibit all the parts of the PES or all transition paths, this method indeed works well in the local area and can be used more widely. [ABSTRACT FROM AUTHOR]

In this paper, the electronically nonadiabatic Landau-Zener (LZ) mechanism for the vibrational relaxation v = 1 → v = 0 of NO ( X 2 Π ) in collisions with Ar ( S 0 1 ) is discussed. It corresponds to nonadiabatic transitions between two crossing vibronic potential energy surfaces (PESs) originating from vibrational states of the collision complex and supported by two coupled electronic PESs. The LZ rate coefficients k 10 LZ are calculated within the uniform Airy approach in the reaction coordinate approximation with parameters derived from ab initio PESs and an asymptotic estimation of the Franck–Condon factor in the nonadiabatic coupling region. The rate coefficients are close to the experimental rate coefficients available over the range of 900–2500 K, where the electronically adiabatic Landau-Teller (LT) mechanism with the rate coefficients k 10 LT does not make a noticeable contribution to the total relaxation rate. The ratio k 10 LZ / k 10 LT increases with temperature and the LZ and LT mechanisms have comparable rates at about 4000 K. [ABSTRACT FROM AUTHOR]

Molecular fingerprints, i.e., feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we present the density-encoded canonically aligned fingerprint algorithm, which is robust and efficient, for fitting per-atom scalar and vector quantities. The fingerprint is essentially a continuous density field formed through the superimposition of smoothing kernels centered on the atoms. Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a local canonical coordinate frame computed from a kernel minisum optimization procedure. We show that this approach is superior over principal components analysis-based methods especially when the atomistic neighborhood is sparse and/or contains symmetry. We propose that the "distance" between the density fields be measured using a volume integral of their pointwise difference. This can be efficiently computed using optimal quadrature rules, which only require discrete sampling at a small number of grid points. We also experiment on the choice of weight functions for constructing the density fields and characterize their performance for fitting interatomic potentials. The applicability of the fingerprint is demonstrated through a set of benchmark problems. [ABSTRACT FROM AUTHOR]

The multiscale coarse-graining (MS-CG) method is a method for constructing a coarse-grained (CG) model of a system using data obtained from molecular dynamics simulations of the corresponding atomically detailed model. The formal statistical mechanical derivation of the method shows that the potential energy function extracted from an MS-CG calculation is a variational approximation for the true potential of mean force of the CG sites, one that becomes exact in the limit that a complete basis set is used in the variational calculation if enough data are obtained from the atomistic simulations. Most applications of the MS-CG method have employed a representation for the nonbonded part of the CG potential that is a sum of all possible pair interactions. This approach, despite being quite successful for some CG models, is inadequate for some others. Here we propose a systematic method for including three body terms as well as two body terms in the nonbonded part of the CG potential energy. The current method is more general than a previous version presented in a recent paper of this series [L. Larini, L. Lu, and G. A. Voth, J. Chem. Phys. 132, 164107 (2010)], in the sense that it does not make any restrictive choices for the functional form of the three body potential. We use hierarchical multiresolution functions that are similar to wavelets to develop very flexible basis function expansions with both two and three body basis functions. The variational problem is solved by a numerical technique that is capable of automatically selecting an appropriate subset of basis functions from a large initial set. We apply the method to two very different coarse-grained models: a solvent free model of a two component solution made of identical Lennard-Jones particles and a one site model of SPC/E water where a site is placed at the center of mass of each water molecule. These calculations show that the inclusion of three body terms in the nonbonded CG potential can lead to significant improvement in the accuracy of CG potentials and hence of CG simulations. [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]

The jet-cooled high resolution spectrum of the vibrationless Ã←X transition of the deuterated species of the methyl peroxy radical has been recently published in this journal (S. Wu, P. Dupré, P. Rupper, and T. A. Miller, J. Chem. Phys. 127, 224305 (2007)). The spectrum was analyzed using a rigid-rotor model with quadratic spin-rotation coupling. The analysis was based on the fit of ∼350 partially resolved line positions and was quite satisfactory. However, the full simulation of the spectral intensity clearly identifies a lack of ability to reproduce relatively small line clumps ('extra' lines) located between the two main central Q branches. This is indicating of an incomplete initial analysis. In the present paper we reanalyze this electronic transition by considering a reference-frame axis-switching resulting from the nuclear rearrangement associated to the electronic transition (spectra obtained at two different temperatures are considered). The potential energy hypersurfaces of the two electronic states are sufficiently dissimilar to induce changes in the molecule geometry, particularly, the angle COO⁁, which induces a rotation (∼1.7°) of the principal axes of inertia located in the molecule symmetry plane. The present analysis is supported by a global fitting of the spectrum intensity and gives rise to a slightly different set of molecular constants. Attention is paid to the wavefunction symmetry assignment of a non-orthorhombic molecule. Couplings due to the torsion of the methyl group are discussed in the following paper (P. Dupre, J. Chem. Phys. 134, 244309 (2011)). [ABSTRACT FROM AUTHOR]

The [H,C,N] molecular system is a very important model system to many fields of chemical physics and the experimental characterization of highly excited vibrational states of this molecular system is of special interest. This paper reports the experimental characterization of all 3822 eigenenergies up to 6880 cm-1 relative to the ground state in the HCN part of the potential surface using high temperature hot gas emission spectroscopy. The spectroscopic constants for the first 71 vibrational states including highly excited bending vibrations up to v2 = 10 are reported. The perturbed eigenenergies for all 20 rotational perturbations in the reported eigenenergy range have been determined. The 11 070 eigenenergies up to J = 90 for the first 123 vibrational substates are included as supplement to this paper. We show that a complete ab initio rovibrational analysis for a polyatomic molecule is possible. Using such an analysis we can understand the molecular physics behind the Schrödinger equation for problems for which perturbation theoretical calculations are no more valid. We show that the vibrational structure of the linear HCN molecule persists approximately up to the isomerization barrier and only above the barrier the accommodation of the vibrational states to the double well structure of the potential takes place. [ABSTRACT FROM AUTHOR]

Following our work on the study of helium droplets and film doped with one electronically excited rubidium atom Rb* (2P) [M. Leino, A. Viel, and R. E. Zillich, J. Chem. Phys. 129, 184308 (2008)], we focus in this paper on the second excited state. We present theoretical studies of such droplets and films using quantum Monte Carlo approaches. Diffusion and path integral Monte Carlo algorithms combined with a diatomics-in-molecule scheme to model the nonpair additive potential energy surface are used to investigate the energetics and the structure of Rb*Hen clusters. Helium films as a model for the limit of large clusters are also considered. As in our work on the first electronic excited state, our present calculations find stable Rb*Hen clusters. The structures obtained are however different with a He-Rb*-He exciplex core to which more helium atoms are weakly attached, preferentially on one end of the core exciplex. The electronic absorption spectrum is also presented for increasing cluster sizes as well as for the film. [ABSTRACT FROM AUTHOR]

The [H,C,N] system is one of the ideal candidate molecules to test new models aimed to calculate the manifold of the rotational, vibrational, and electronic states of a triatomic molecule. The isomerization reaction HCN<=>HNC is one of the most important model systems for the study of unimolecular reactions. This paper reports on the experimental characterization of all 1191 eigenenergies up to 3743 cm-1 relative to the ground state in the HNC part of the potential surface using high temperature hot gas emission spectroscopy. The spectroscopic constants for the first 27 vibrational states including highly excited bending vibrations up to v2=7 are reported. The first 14 rotational perturbations have been identified and the perturbed eigenenergies were determined. The 3200 eigenenergies up to J=70 for the first 47 vibrational substates are included as supplement to this paper. [ABSTRACT FROM AUTHOR]

In view of the initial success of the complete active space (CAS) based size-extensive state-specific multireference perturbation theory (SS-MRPT) [J. Phys. Chem. A 103, 1822 (1999)] for relatively diverse yet simple chemically interesting systems, in this paper, we present the computation of the potential energy curves (PEC) of systems with arbitrary complexity and generality such as HF, H2O, H2S, C2, and N2 molecules. The ground states of such systems (and also low-lying singlet excited states of C2) possess multireference character making the description of the state difficult with single-reference (SR) methods. In this paper, we have considered the Mo\ller–Plesset (MP) partitioning scheme [SS-MRPT(MP)] method. The accuracy of energies generated via SS-MRPT(MP) method is tested through comparison with other available results. Comparison with FCI has also been provided wherever available. The accuracy of this method is also demonstrated through the calculations of NPE (nonparallelism error) and the computation of the spectroscopic constants of all the above mentioned systems. The quality of the computed spectroscopic constants is established through comparison with the corresponding experimental and FCI results. Our numerical investigations demonstrate that the SS-MRPT(MP) approach provides a balanced treatment of dynamical and non-dynamical correlations across the entire PECs of the systems considered. [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 principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move—an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that deemphasizes the concept of potential barriers, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen [Phys. Rev. E 51, 4626 (1995)] of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its empirical mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper. [ABSTRACT FROM AUTHOR]

How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system’s dynamics. In this paper we show that, within what we call the potential-energy-landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics—the shortest paths through their landscapes within the special ensemble. The more convoluted and labyrinthine these geodesics are, the slower that dynamics is. Geodesics in the landscape ensemble have sufficiently well-defined characteristics that it is straightforward to search for them numerically, a point we illustrate by computing the geodesic lengths for an ordinary atomic liquid and a binary glass-forming atomic mixture. We find that the temperature dependence of the diffusion constants of these systems, including the precipitous drop as the glass-forming system approaches its empirical mode-coupling transition, is predicted quantitatively by the growth of the geodesic path lengths. [ABSTRACT FROM AUTHOR]

The nonrelativistic, valence-shell-only-correlated ab initio potential energy curve of the F2 molecule, which was reported in the preceding paper, is complemented by determining the energy contributions that arise from the electron correlations that involve the core electrons as well as the contributions that are due to spin-orbit coupling and scalar relativistic effects. The dissociation curve rises rather steeply toward the energy of the dissociated atoms because, at larger distances, the atomic quadrupole-quadrupole repulsion and spin-orbit coupling counteract the attractive contributions from incipient covalent binding and correlation forces including dispersion. [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]

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]

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]

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method. © 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]

The interaction of He with metastable CO(a[SUP3 п) gives rise to two adiabatic potential surfaces of reflection symmetry A' and A" which were calculated with the partially spin-restricted open-shell single and double excitation coupled cluster method with perturbative triples, RCCSD(T). Two diabatic potentials were constructed and fitted analytically; the appropriate form of the angular expansion functions was derived from general invariance properties. From variational calculations on these diabatic potential surfaces we obtained the quasibound vibration-rotation-spin levels of the CO-He complex in its lowest triplet state. Only the lower spin-orbit levels of this complex with approximate quantum number Ω = 0 of the CO(a[SUP3 п) monomer were found to be stable with respect to dissociation into He and triplet CO. The potential and the bound van der Waals levels of the ground state CO(X[SUP1]Σ[SUP+]) - He complex were recalculated and used in combination with the triplet excited state wave functions to compute the line strengths and the bound-bound part of the singlet-triplet excitation spectrum of the CO-He complex. The spin-forbidden singlet-triplet transitions access mainly the higher spin-orbit levels with &verbar;Ω&verbar; = 1, but these were found to undergo rapid predissociation. The companion Paper II explicitly studies this process, predicts the excited state lifetimes, and generates the bound-continuum part of the CO-He singlet-triplet spectrum. [ABSTRACT FROM AUTHOR]

The fourfold way is a general algorithm for generating diabatic electronic wave functions that span the same space as a small set of variationally optimized adiabatic electronic wave functions and for using the resulting diabatic wave functions to generate diabatic potential energy surfaces and their couplings. In this paper we extend the fourfold way so it is applicable to more complex polyatomic systems and in particular to the calculation of global potential energy surfaces for such systems. The extension involves partitioning the active space into three blocks, introducing restricted orbital rotation within two of the blocks, introducing a specific resolution of the subspace containing molecular orbitals that are doubly occupied in all dominant configuration state functions, and introducing specific orientations of the coordinate systems for reference molecular orbitals and resolution molecular orbitals. The major strength of the improved method presented in this paper is that it allows the diabatic molecular orbitals to exhibit a gradual change of chemical character with smooth deformation along the reaction coordinate for a change of chemical arrangement while preserving the orbital character required for a physical ordering of the orbitals. This feature is required for the convenient construction of global potential energy surfaces for non-BornOppenheimer rearrangements. The resulting extended algorithm is illustrated by calculating diabatic potential energy surfaces and couplings for the two lowest singlet potential energy surfaces of HNCO. [ABSTRACT FROM AUTHOR]

We report two new analytical fits of the ground potential energy surface (PES) (²A') and the first excited PES ([sup 4]A') involved into the title reaction and its reverse, using ab initio electronic structure calculations from Papers I and II along with new grids of ab initio points by means of the second-order perturbation theory on CASSCF wave function [CASPT2 (17,12) G2/aug-cc-pVTZ] reported here (1250 points for the ²A' PES and 910 points for the [sup 4]A' PES). Some experimental data were also introduced to better account for the exoergicity and the experimental rate constant at 300 K. The final root-mean-square deviations of the fits were 1.06 and 1.67 kcal/mol for ²A' and the [sup 4]A' PESs, respectively, for the NOO C[sub s] abstraction and insertion regions of the PESs. Thermal rate constants were calculated (300-5000 K) for both the direct and reverse reactions by means of the variational transition state theory with the inclusion of a microcanonical optimized multidimensional tunneling correction, obtaining a very good agreement with the experimental data within all the temperature range. The new analytical ²A' PES presents several stationary points not introduced in previous analytical surfaces, and describes accurately the NO[sub 2] (X²A[sub 1]) minimum, which seems to be very accessible according to the trajectories run in a preliminary quasiclassical trajectory study. The new analytical [sup 4]A' PES has a lower energy barrier than the previous one, which increases significantly the contribution of this PES to the total rate constant at high temperatures. Moreover, the new analytical PESs not only describe accurately the C[sub s] regions of the NOO system but also the ONO C[sub 2υ] or near C[sub 2υ] regions. [ABSTRACT FROM AUTHOR]

The potential-energy surface of the interstellar molecule C[sub 4]N is explored at the B3LYP/6-311G(d) level of theory. Thirteen isomers including the linear, three-membered ring, four-membered ring, A-like, Y-like, and cage-like structures are located as minima connected by 23 interconversion transition states. The structures of the most relevant isomers and transition states are further optimized at the QCISD/6-311G(d) level followed by single-point energy calculations at the MP4SDTQ, CCSD(T), and QCISD(T) levels with the 6-311G(2df) basis set. At the CCSD(T)/6-311G(2df)//QCISD/6-311G(d) level, the lowest-lying isomer is a linear structure CCCCN 1 followed by a CCC three-membered ring structure 4 with exocyclic CCN bonding that lies only 2.8 kcal/mol higher. The third and fourth low-lying isomers possess a CCC three-membered ring structure 5 with exocyclic CNC bonding at 21.4 kcal/mol and a linear structure CCCNC 2 at 23.4 kcal/mol, respectively. All the four isomers 1, 2, 4, and 5 and another high-lying isomer 3 with a linear CCNCC structure at 62.5 kcal/mol are shown to have considerable kinetic stability towards isomerization and dissociation. Thus, all the five isomers may be experimentally observable. Possible formation of these five stable C[sub 4]N isomers in interstellar space is discussed. Finally, our calculations show that the Møller-Plesset methods fail to predict even qualitatively the energetic properties between the four low-lying isomers 1, 2, 4, and 5, in comparison with the QCISD and CCSD results. This paper indicates that C[sub 4]N may be the first interstellar molecule with stable low-lying cyclic isomers among the C[sub n]N radical series to be detectable in near future. The results presented in this paper may provide useful information for future laboratory and interstellar identification of various C[sub 4]N isomers. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We compute four-dimensional diabatic potential energy surfaces and transition dipole moment surfaces of O2-O2, relevant for the theoretical description of collision-induced absorption in the forbidden X3∑-g → a1Δg and X3∑-g →b1∑+g bands at 7883 cm-1 and 13 122 cm-1, respectively. We compute potentials at the multi-reference configuration interaction (MRCI) level and dipole surfaces at the MRCI and complete active space self-consistent field (CASSCF) levels of theory. Potentials and dipole surfaces are transformed to a diabatic basis using a recent multiple-property-based diabatization algorithm. We discuss the angular expansion of these surfaces, derive the symmetry constraints on the expansion coefficients, and present working equations for determining the expansion coefficients by numerical integration over the angles. We also present an interpolation scheme with exponential extrapolation to both short and large separations, which is used for representing the O2-O2 distance dependence of the angular expansion coefficients. For the triplet ground state of the complex, the potential energy surface is in reasonable agreement with previous calculations, whereas global excited state potentials are reported here for the first time. The transition dipole moment surfaces are strongly dependent on the level of theory at which they are calculated, as is also shown here by benchmark calculations at high symmetry geometries. Therefore, ab initio calculations of the collision-induced absorption spectra cannot become quantitatively predictive unless more accurate transition dipole surfaces can be computed. This is left as an open question for method development in electronic structure theory. The calculated potential energy and transition dipole moment surfaces are employed in quantum dynamical calculations of collision-induced absorption spectra reported in Paper II [T. Karman et al., J. Chem. Phys. 147, 084307 (2017)]. [ABSTRACT FROM AUTHOR]

In this paper we extend our previous study (F. Schneider, F. Di Giacomo, and F. A. Gianturco, J. Chem. Phys. 104, 5153) on the topology of the electronic states of the neutral H2O molecule in C2v symmetry by examining the lowest ten potential energy surfaces of the water molecular cation in its doublet states. The relevant electronic energy surfaces of H2O+ are shown as 2D contour maps where possible reaction pathways for several low-lying potential energy surfaces of H2O+ are clearly seen and therefore can be discussed and analyzed in some detail. The present results were obtained using ab initio multireference configuration interaction calculations at 184 nuclear arrangements, as described in our previous paper dealing with the neutral H2O. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of ‘‘surface-hopping’’ MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the ‘‘molecular dynamics with quantum transitions’’ (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The nonbonding interaction of boron atoms, in their ground 2s22p 2P and excited 2s23s 2S states, with H2 and D2 has been investigated through laser fluorescence excitation spectroscopy in a supersonic free jet. For these isotopomeric complexes, an asymmetric, unstructured feature is observed, with maximum intensity ∼620 cm-1 to the blue of the 3s 2S–2p 2P atomic transition. The width of this feature is somewhat narrower for B–D2 than for B–H2. The fluorescence emission occurs in the same wavelength range as the boron atomic transition. These observations imply that the B(3s)–H2 interaction is repulsive in the Franck–Condon region. No evidence for chemical reaction on the excited BH2 potential energy surface was found. The observed formation of these complexes in the supersonic beam also suggests that there is a significant barrier to formation of the stable BH2 molecule from B(2p)+H2. These spectra have been interpreted with the help of ab initio calculations of the B(2p,3s)–H2 interactions and the bend–stretch energies of the complex, both reported in the preceding paper [M. H. Alexander and M. Yang, J. Chem. Phys. 103, 7956 (1995)]. From comparison with these calculations, our spectra can be assigned as electronic excitation from the lowest bend–stretch level of the B(2p)–H2/D2 complex to a repulsive region of the electronically excited potential energy surface. Spectral simulations based on the theoretical treatment of this nonbonding interaction reproduce quite well the observed spectra. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Chemical reactivity theory provides a basis for predicting the reactive proclivities of molecular or condensed systems. The frontier-orbital concepts of Fukui, as generalized by Parr and collaborators within the framework of density-functional theory, were developed further by us in a previous paper (I) [J. Chem. Phys. 101, 8988 (1994)]. Nevertheless, five aspects of the theory still require further development; the reactivities are defined as local responses to global stimuli instead of nonlocal responses to local stimuli; there are ambiguities associated with the existence of energy bands in condensed systems; the theory is static and does not properly incorporate the internal dynamics of the reacting systems; the theory focuses on responses without a corresponding definition of chemical stimuli; and no connection is made with the potential energy surface and the reaction pathway. In the present paper, we concentrate on gapless systems extended in at least one dimension, metals, semimetals, and insulators. We show that taking as measures of chemical reactivity the reactivity kernels of Nalewajski [J. Chem. Phys. 78, 6112 (1983); 81, 2088 (1984); 89, 2831 (1985)] and of Berkowitz and Parr [J. Chem. Phys. 88, 2554 (1988)] in the form introduced by the latter meets the first two requirements. We find an explicit expression for the softness kernel which is a natural generalization of that found for the local softness in I.The response functions entering it are calculable via the Kohn–Sham formalism. As recognized by Nalewajski and Koninski [Z. Naturforsch. 42a, 451 (1987)], there is an infinite set of modes of chemical reactivity with corresponding spectra of softness and hardness eigenvalues. The softness spectrum has an upper bound corresponding to the most reactive mode or set of degenerate modes [Z. Naturforsh. 42a, 451 (1987)] and a vanishing lower bound. The softness kernel itself can be expressed simply in terms of the static dielectric function.... [ABSTRACT FROM AUTHOR]

A simple formula for the canonical flexible transition state theory expression for the thermal reaction rate constant is derived that is exact in the limit of the reaction path being well approximated by the distance between the centers of mass of the reactants. This formula evaluates classically the contribution to the rate constant from transitional degrees of freedom (those that evolve from free rotations in the limit of infinite separation of the reactants). As a result of this treatment, the formula contains the product of two factors: one that exclusively depends on the collision kinematics and one that exclusively depends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classical limit, from harmonic oscillator to hindered rotor to free rotor partition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orientation angles of the fragments. An application to the recombination of CH3+H essentially demonstrates exact agreement with a previous flexible transition state theory study in which all integrals are carried out numerically. The simple formulas presented in this paper allow the classical inclusion of large amplitude motion of arbitrary complexity in the determination of the canonical rate constant for reactions whose reaction path is dominated by the distance between the centers of mass of the reactants. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

When the nascent products of a three-atom reaction governed by chemical forces separate, energy transfers may occur between vibrational, rotational, and translational motions. In the first part of the paper, we show from quasiclassical trajectory calculations on a model potential energy surface that (a) the vibrational energy is adiabatic on average as usually assumed in statistical theories, (b) rotational-translational energy transfer mainly favors translational motion (as was initially suggested by Marcus), but that (c) this transfer is inefficient when the product atom is sufficiently light with respect to the other two. A qualitative analysis of these findings is proposed based on arguments differing from those of Marcus, and Quack and Troe. In the second part of the paper, we extend the classical statistical formalism proposed recently by ourselves, initially limited to reactions governed by long-range forces, to the present more general case of reactions involving tight transition states and for which energy transfers are inefficient. In such a case, energy distributions at the exit transition state and in the products are the same. We focus our developments on the recoil energy distribution. Agreement between our theoretical result and the quasiclassical trajectory approach is shown to be very satisfactory. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An intermolecular potential energy surface was derived for the hydrogen-bonded water trimer as a function of the three torsional angles ω1, ω2, ω3, for energies up to 1300 cm-1 (3.7 kcal/mol) above the global minimum. The O...O distances and the intramolecular geometry of the H2O molecules are held fixed. This surface is based on the ab initio calculations presented in a companion paper [W. Klopper et al., J. Chem. Phys. 103, 1085 (1995)], which involve very large basis sets and the most extensive treatment of correlation energy for calculations of (H2O)3 so far. The 70 ab initio interaction energies, multiplied by six due to the S6 symmetry of the surface, were fitted using an analytical potential function, with an average error of ≊11 cm-1. This potential provides a rapidly computable analytical expression for use in calculations of torsional eigenfunctions and -values and other properties of this cluster. Also given is a classification of the low-lying torsional wave functions according to nodal properties. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Ab initio calculations are used to explore the ground-state potential energy surface for the syn–anti photoisomerization reaction of 5-hydroxytropolone (5-HOTrOH). Two reaction coordinates are identified, involving 2-OH tunneling and 5-OH torsion. Hartree–Fock (HF) and perturbation theory (at the MP2 level) have been used to calculate the stationary points on the two-dimensional surface associated with these coordinates. Similar calculations on the parent molecule tropolone are carried out for comparison. As observed in previous studies, the 2-OH tunneling barrier drops dramatically at the MP2 level which includes electron correlation. Vibrational frequency calculations are carried out for both tropolone and 5-HOTrOH at the HF/6-31G** and MP2/6-31G** levels in order to correlate the modes with those observed experimentally. A method is introduced for evaluating which normal coordinates should be most strongly coupled to a given reaction coordinate. Normalized, mass-weighted intrinsic and direct reaction coordinates similar in form to the normal coordinates are devised by projecting atomic displacements from the reactant structure toward a transition state (intrinsic) or product (direct) structure. These serve as limiting cases for the initial projections of the multidimensional reaction trajectories. The intrinsic and direct reaction coordinates are then expanded in the basis set of normal coordinates to obtain coefficients of expansion of the reaction coordinates in this basis set. This simple scheme highlights the subset of normal coordinates which are important in promoting reaction by H-atom tunneling or O–H torsion. In 5-HOTrOH, an in-plane mode calculated at 348 cm-1 has a large coefficient of expansion along both intrinsic and direct reaction coordinates. This mode is assigned as the ‘‘promoter mode’’ W observed in the experimental study of paper I. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we present a method for locating transition states and higher-order saddles on potential energy surfaces using double-ended classical trajectories. We then apply this method to 7- and 8-atom Lennard-Jones clusters, finding one previously unreported transition state for the 7-atom cluster and two for the 8-atom cluster. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The unstable mode density of states 〈ρu(ω;T)〉 is obtained from computer simulation and is analyzed, theoretically and empirically, over a broad range of supercooled and normal liquid temperatures in the unit density Lennard-Jones liquid. The functional form of 〈ρu(ω;T)〉 is determined and the ω, T dependence is seen to be consistent with a theory given by us previously. The parameters in the theory are determined and are related to the topological features of the potential energy surface in the configuration space; it appears that diffusion involves a low degree of cooperativity at all but the lowest temperatures. It is shown that analysis of 〈ρu(ω;T)〉 yields considerable information about the energy barriers to diffusion, namely, a characteristic ω-dependent energy and the distribution of barrier heights, gν(E). The improved description of 〈ρu(ω;T)〉 obtained in the paper is used to implement normal mode theory of the self-diffusion constant D(T) with no undetermined constants; agreement with simulation in the supercooled liquid is excellent. Use of a lower frequency cutoff on the contribution of unstable modes to diffusion, in an attempt to remove spurious contributions from anharmonicities unrelated to barrier crossing, yields the Zwanzig–Bassler temperature dependence for D(T). It is argued that the distribution of barriers plays a crucial role in determining the T dependence of the self-diffusion constant. [ABSTRACT FROM AUTHOR]