Ro-vibrational states of triplet H2D+

We present rotational term values for J < or = 3 of the vibrational states with up to twofold excitation of H2D+ in the lowest electronic triplet state (a3sigma(u)+). The calculations were performed using the method of hyperspherical harmonics and our recent accurate double many-body expansion potential energy surface.     

A realistic double many-body expansion potential energy surface for SO2(X1A') from a multiproperty fit to accurate ab initio energies and vibrational levels

A single-valued double many-body expansion potential energy surface (DMBE I) recently obtained for the ground electronic state of the sulfur dioxide molecule by fitting correlated ab initio energies suitably corrected by scaling the dynamical correlation energy is now refined by fitting simultaneously available spectroscopic levels up to 6886 cm(-1) above the minimum. The topographical features of the novel potential energy surface (DMBE II) are examined in detail, and the method is emphasized as a robust route to fit together state-of-the-art theoretical calculations and spectroscopic measurements using a single fully dimensional potential form.     

A comparison of different many-body perturbation theory calculations of the ground state of SiS

A comparison of different many-body perturbation theory (MBPT ) calculations of the ground state rotational and vibrational constants of SiS is made. The calculations are performed up to the complete fourth-order MBPT level, and in all cases two basis sets are utilized. The results of the third-order and some incomplete fourth-order calculations are in good agreement, but the complete fourth-order is among the worst as compared with the experimental data. Analysis of the different contributions to the calculated correlation eneriges points towards the necessity of including even higher-order terms of the(MBPT ) expansion.     

A New Many-Body Expansion Scheme for Atomic Clusters: Application to Nitrogen Clusters

Although the many-body expansion (MBE) approach is widely applied to estimate the energy of large systems containing weak interactions, it is inapplicable to calculating the energies of covalent or metal clusters. In this work, we propose an interaction many-body expansion (IMBE) to calculate the energy of atomic clusters containing covalent bonds. In this approach, the energy of a system is expressed as the sum of the energy of atoms and the interaction energy between the atom and its surrounding atoms. The IMBE method is first applied to calculate the energies of nitrogen clusters, in which the interatomic interactions are truncated to four-body terms. The results show that the IMBE approach could significantly reduce the energy error for nitrogen clusters compared with the traditional MBE method. The weak size and structure dependence of the IMBE error with respect to DFT calculations indicates the IMBE method has good potential application in estimating energy of large covalent systems.     

A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory

Fragment-based quantum chemistry methods are a promising route towards massively parallel electronic structure calculations in large systems. Unfortunately, the literature on this topic consists of a bewildering array of different methods, with no clear guiding principles to choose amongst them. Here, we introduce a conceptual framework that unifies many of these ostensibly disparate approaches. The common framework is based upon an approximate supersystem energy formula for a collection of intersecting (i.e., overlapping) fragments. This formula generalizes the traditional many-body expansion to cases where the "bodies" (fragments) share some nuclei in common, and reduces to the traditional many-body expansion for non-overlapping fragments. We illustrate how numerous fragment-based methods fit within this framework. Preliminary applications to molecular and ionic clusters suggest that two-body methods in which dimers are constructed from intersecting fragments may be a route to achieve very high accuracy in fragment-based calculations.     

Accurate double many-body expansion potential energy surface for ground-state HS2 based on ab initio data extrapolated to the complete basis set limit

A double many-body expansion potential energy surface is reported for the electronic ground state of HS(2) by fitting accurate multireference configuration interaction energies calculated with aug-cc-pVTdZ and aug-cc-pVQdZ basis sets upon separate extrapolation of the complete-active-space self-consistent field and dynamical correlation components of the total energy to the complete basis set limit. The major topographical features of the potential energy surface are examined in detail, and the model function is used for thermalized calculations of the rate constants for the S + SH → H + S(2) reaction at 298 and 400 K. A value of (1.44 ± 0.06) × 10(-11) cm(3) s(-1) is obtained at 298 K, providing perhaps the most reliable estimate of the rate constant known thus far for such a reaction.     

Time-dependent Wave Packet Quantum Scattering Study of Reaction S(3P)+H2→HS+H on a New ab initio Potential Energy Surface 3A'

A new potential energy surface is presented for the triplet state ³A' of the chemical reaction S(³P)+H₂ from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference config-uration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8～2.2 eV. Both the centrifugal-sudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H₂ initially in the vibrational states v=0～3 (j=0). It is found that initial vibrational excitation enhances the title reaction.     

Frozen-density embedding-based many-body expansions

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.     

Effctive nonadiabatic calculations on the ground state of the HD+ molecule

The nonadiabatic methodology, which is based on an effective elimination of the center-of-mass motion rather than explicit separation achieved by a coordinate transformation, is applied to the ground state of the HD⁺ molecule. The many-body nonadiabatic wave function is generated in terms of explicitly correlated Gaussian functions. The analytical first and second derivatives of the variational functional with respect to the Gaussian exponents are applied in conjunction with the Newton–Raphson optimization method to find the nonadiabatic energy and the ground–wave function. The numerical results are compared with conventional nonadiabatic calculations. © 1995 John Wiley & Sons, Inc.     

Ab initio-based double many-body expansion potential energy surface for the first excited triplet state of the ammonia molecule

A global single-sheeted double many-body expansion potential energy surface is reported for the first excited triplet state of NH(3). It employs an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments. Four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. A new switching function formalism has been reported to approximate the true multisheeted nature of NH(3)((3)A(2) (')) potential energy surface, thus allowing the correct behavior at the NH(2)((2)A(")) + H((2)S) and NH(2)((4)A(")) + H((2)S) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under the permutation of identical atoms, and predicts the correct behavior at all dissociation channels while providing a realistic representation at all interatomic separations. The major attributes of the NH(3) double many-body expansion potential energy surface have also been characterized, and found to be in good agreement, both with the calculated ones from the raw ab initio energies and the theoretical results available in the literature.     

Generation of potential energy curves for the X1Sigma(+)g, B1Delta(+)g, and B'1Sigma(+)g states of C2 using the effective valence shell Hamiltonian method

Calculations of the ground and excited state potential energy curves of C2 using the third-order effective valence Hamiltonian (Hv3rd) method are benchmarked against full configuration interaction and other correlated single-reference perturbative and nonperturbative theories. The large nonparallelity errors (NPEs) exhibited even by state-of-art coupled cluster calculations through perturbative triples indicate a serious deficiency of these single-reference theories. The Hv method, on the other hand, produces a much reduced NPE, rendering it a viable approximate many-body method for accurately determining global ground and excited state potential energy curvessurfaces.     

Interaction energies of large clusters from many-body expansion

In the canonical supermolecular approach, calculations of interaction energies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interaction energies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lower-level methods for subsequent terms in the many-body expansion. The efficiency of such "stratified approximation" many-body approach (SAMBA) is due to the rapid convergence of the many-body expansion for typical molecular clusters. The method has been applied to water clusters (H(2)O)(n), n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the many-body expansion calculations. For (H(2)O)(24), SAMBA is particularly beneficial and we report interaction energies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basis-set superposition errors should be removed in calculations for large clusters.     

Assessing group-based cutoffs and the Ewald method for electrostatic interactions in clusters and in saturated,superheated, and supersaturated vapor phases of dipolar molecules

Monte Carlo simulations in the canonical, isobaric-isothermal, grand canonical, and Gibbs ensembles were used to assess whether the computationally expensive Ewald summation method for the computation of the first-order electrostatic energy can be replaced with a simpler truncation approach for accurate simulations of the saturated, superheated, and supersaturated vapor phases of dipolar and hydrogen-bonding molecules. Rotationally averaged hydrogen fluoride dimer and trimer energies, thermophysical properties and aggregation in the superheated vapor phase of hydrogen fluoride, nucleation free energy barriers for water, and the vapor–liquid coexistence properties of hydrogen fluoride and water were investigated over a wide range of state points. We find that for densities not too close to the critical density, results obtained from simulations using a spherical potential truncation based on neutral groups (molecules or fragments) for the Coulomb interactions are statistically identical to those obtained using the Ewald summation method. Use of the simpler spherical truncation results in a significant reduction of the computational effort for simulations employing molecular mechanics force fields and also allows for straightforward implementation of many-body expansion methods to compute the potential energy from electronic structure calculations of subsystems of the entire vapor-phase system.     

Ivar Waller 90 years on June 11, 1988

Linkage properties of the diagrammatic representation of the energies obtained in the multireference many-body perturbation calculations with respect to the incompleteness or completeness of the model space are discussed. The case of not completely degenerate model space is considered for which a comparison with the standard single-reference many-body perturbation expansion is possible. The Hose–Kaldor type of graphical representation of the perturbation expansion for the effective Hamiltonian is used in this comparison. It is shown that for an incomplete model space the perturbation expansion is not size-extensive. In this case, for a truncated expansion of the effective Hamiltonian, the energies obtained by diagonalization of the effective Hamiltonian matrix are represented by both linked and unlinked irreducible contributions. The unlinked ones do not appear when the complete model space is used.     

Statistical estimates of electron correlations

While arbitrarily accurate solutions to the many-body Schrodinger equation are possible through a brute force expansion of the wave function, the length of the expansions required renders the approach intractable except for few-electron problems. By considering the form of the energy resulting from truncation of the many-particle expansion space, it is shown that accurate determination of electron correlations may be extracted from estimates of average or effective energy contributions while maintaining a reduced dimension for the expansion space. An energy formula expressed as a rational function of the expansion vector length is determined, allowing for estimates of asymptotic limits of many-body correlations.     

Embedded,graph-theoretically defined many-body approximations for wavefunction-in-DFT and DFT-in-DFT: Applications to gas- and condensed-phase ab initio molecular dynamics,and potential surfaces for quantum nuclear effects

We present a graph-theoretic approach to adaptively compute many-body approximations in an efficient manner to perform (a) accurate post-Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium- to large-sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed-phase simulations at the cost of pure density functionals, (c) reduced-cost on-the-fly basis extrapolation for gas-phase AIMD and condensed phase studies, and (d) accurate post-HF-level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM-like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many-body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph-theoretic methods. Specifically, a region of chemical interest is coarse-grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph, which forms the basis for developing the many-body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one-dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two-dimensional periodic boundary conditions.     

Vibrational relaxation of highly vibrationally excited O3 in collisions with OH

We report a theoretical study of highly excited O3 in collisions with vibrationally cold OH. Special emphasis is placed on initial vibrational energies of O3 between 9 and 21 kcal mol(-1). All calculations have employed the quasiclassical trajectory method and the realistic double many-body expansion potential energy surface for HO 4((2)A). Many aspects of the title relaxation process are presented. The results indicate that it may not be ignorable in studying the stratospheric ozone budget.     

On the Role of Charge Transfer in Many-Body Non-Covalent Interactions**

Charge transfer is one of the mechanisms involved in non-covalent interactions. In molecular dimers, its contribution to pairwise interaction energies has been studied extensively using a variety of interaction energy decomposition schemes. In polar interactions such as hydrogen bonds, it can contribute ten or several tens of percent of the interaction energy. Less is known about its importance in higher-order interactions in many-body systems, mainly because of the lack of methods applicable to this problem. In this work, we extend our method for the quantification of the charge-transfer energy based on constrained DFT to many-body cases and apply it to model trimers extracted from molecular crystals. Our calculations show that charge transfer can account for a large fraction of the total three-body interaction energy. This also has implications for DFT calculations of many-body interactions in general as it is known that many DFT functionals struggle to describe charge-transfer effects correctly.     

Microsolvation of LiH+ in helium clusters: many-body effects and additivity models for the interaction forces

The ab initio calculation of the interaction forces between the LiH+ molecular ion, at its equilibrium geometry, and several He atoms is carried out in order to isolate and assess the importance of many-body contributions in the search for realistic energy and geometry data. The full potential energy surface (PES) with a single helium partner is obtained first by using an aug-cc-pVQZ basis set for He and higher quality ones for Li and H. The calculations were performed at the CAS-SCF plus MRCI level for the lowest potential energy surface over a total of 480 grid points of the two intermolecular Jacobi coordinates, whereas the excited state surface has also been examined in order to exclude the presence of any significant nonadiabatic interaction between the two PESs. A numerical fit of the lower surface is presented and the general physical changes of the ionic interaction when going from the lower to the upper of the two potentials are described and discussed. The fairly limited importance of many-body effects for such systems is seen from further ab initio calculations including several He atoms: our results suggest that, at least in the present case, no strong charge migration occurs after He attachment, and therefore, one could realistically model larger clusters by implementing a sum-of-potentials approach via the presently computed PES.     

[He3H]＋分子基态势能面的从头计算研究

使用CCSD(T)/aug-cc-pVTZ从头计算方法，对[He3H]＋分子的一些特殊构型的电子基态势能进行扫描，并以此为基础对三体相互作用势在惰性气体质子簇中的影响进行了讨论.结果表明即使在这样一个简单的体系中三体相互作用的影响都是不能忽略的.另一方面，在[He3H]＋分子稳定构型附近仅将势能展开至三体相互作用项便可提供较精确的相互作用信息，但在强排斥区域更高阶作用的影响变得越来越突出.本文同时讨论了[He4H]＋的稳态结构. [He3H]＋与[He4H]＋的稳态结构表明,[HenH]＋簇中存在着一个[He2H]＋核.