Many-body Expansion Method Research Articles

Double many-body expansion potential energy surface for ground state HSO2

A global potential energy surface is reported for the ground electronic state of HSO2 by using the double many-body expansion (DMBE) method. It employs realistic DMBE functions previously reported from accurate ab initio calculations (in some cases, fine tuned to spectroscopic data) for the triatomic fragments, and four-body energy terms that were modelled by fitting novel ab initio FVCAS/AVTZ calculations for the tetratomic system. In some cases, FVCAS/AVDZ energies have been employed after being scaled to FVCAS/AVTZ ones. To assess the role of the dynamical correlation, exploratory single-point Rayleigh-Schrödinger perturbation calculations have also been conducted at one stationary point. All reported calculations are compared with previous ab initio results for the title system. The potential energy surface predicts HOSO to be the most stable configuration, in good agreement with other theoretical data available in the literature. In turn, the HSO2 isomer with H bonded to S is described as a local minimum, which is stable with respect to the H + SO2 dissociation asymptote.

Analytical global potential energy surface for the X2A′ state of HCS

Abstract We report a global analytical potential energy surface (PES) corresponding to the lowest adiabatic X 2 A ′ state of HCS. High quality ab initio calculations were performed at a multi-reference configuration interaction calculation (MRCI) level using a triple-zeta basis set. Energies were calculated on a grid of 1357 points for the lowest state. They were used to construct a single-valued global analytical PES with the double many-body expansion (DMBE) method for all dissociation channels. Special attention was paid to the description of an anisotropic long-range potential. Geometries and energies of the main stationary points of the X 2 A ′ surface are compared with other theoretical and experimental data. By using the potential energy surface we have carried out a detailed dynamical study of the C( 3 P) + SH(X 2 Π) → CS(X 1 Σ + ) + H( 2 S) exothermic reaction over a wide range of translational energies.

A realistic multi-sheeted potential energy surface for NO2(2A′) from the double many-body expansion method and a novel multiple energy-switching scheme

We report a new multi-sheeted double many-body expansion potential energy surface that reproduces most known topological features of the title system. Near spectroscopic accuracy is conveyed to the ground-state sheet of 2A1 (1 2A′ in Cs) symmetry in the vicinity of the minimum by merging it with a spectroscopically determined Taylor-series-expansion-type form via a novel multiple energy-switching scheme. A high energy ridge for C2v insertion of N(4S) into O2(X 3Σg−) has also been imposed to mimic the result of accurate ab initio complete active space self-consistent field and second-order perturbation theory on CAS wave function calculations carried out for such geometries. This ridge decreases for Cs geometries yielding a minimum barrier height for the N+O2 reaction of 0.273 eV at a bent N–O–O structure defined by RNO=3.107a0, ROO=2.513a0, and ∠NOO=113.5 deg. Both the location and height of this barrier are in good agreement with existing ab initio calculations and the recommended values. Another salient feature is a shallow minimum on the à 2B2 potential energy surface that is separated from the absolute X̃ 2A1 minimum by a conical intersection. Such a feature is accurately predicted by the newly reported ab initio calculations and well mimicked by the global double many-body expansion/energy-switching potential energy surface here reported. This is therefore commended both for spectroscopic and reactive dynamics studies on the title system. A final comment in relation to the conical intersection and the energy-switching scheme goes to the expected accuracy of current approaches for spectroscopically determined effective single-valued forms.

Accurate double many-body expansion potential energy surface for triplet H3+. I. The lowest adiabatic sheet (a3Σu+)

We report on a global potential energy hypersurface for the lowest triplet state of H3+ based on the double many-body expansion (DMBE) method and ab initio data points of V5Z quality. These data points are represented with a root mean square deviation of only 3.46 cm−1 in the energy region below the H2+(X2Σg+)+H(2S) dissociation threshold and with less than 15 cm−1 up to the three-particle breakup energy. As expected from a DMBE approach, all dissociation limits are represented accurately and are approached in a physically correct manner.

Accurate first-derivative nonadiabatic couplings for the H3 system

A conical intersection exists between the ground (1 A′2) and the first-excited (2 A′2) electronic potential energy surfaces (PESs) of the H3 system for C3v geometries. This intersection induces a geometric phase effect, an important factor in accurate quantum mechanical reactive scattering calculations, which at low energies can be performed using the ground PES only, together with appropriate nuclear motion boundary conditions. At higher energies, however, such calculations require the inclusion of both the 1 2A′ and 2 2A′ electronic PESs and the corresponding nuclear derivative couplings. Here we present ab initio first-derivative couplings for these states obtained by analytic gradient techniques and a fit to these results. We also present a fit to the corresponding 1 2A′ and 2 2A′ adiabatic electronic PESs, obtained from the ab initio electronic energies. The first-derivative couplings are compared with their approximate analytical counterparts obtained by Varandas et al. [J. Chem. Phys. 86, 6258 (1987)] using the double many-body expansion method. As expected, the latter are accurate close to conical intersection configurations but not elsewhere. We also present the contour integrals of the ab initio couplings along closed loops around the above-mentioned conical intersection, which contain information about possible interactions between the 2 2A′ and 3 2A′ states.

Test studies on the potential energy surface and rate constant for the OH+O 3 atmospheric reaction

We report a single-valued potential energy surface for HO 4( 2 A) from the double many-body expansion method. All n-body ( n=2–4) energy terms are taken from published studies on the relevant fragments, with a five-body energy term of Gaussian form added to mimic the experimental activation energy for the OH( v=0)+O 3 reaction. A detailed dynamics study of this reaction is also reported using classical trajectories. Good agreement with existing experimental data is obtained.

First principles calculation of the potential energy surface for the lowest-quartet state of H3 and modelling by the double many-body expansion method

We report a study of the potential energy surface for the lowest quartet state of H3. At the ab initio level, restricted Hartree–Fock and full configuration interaction (FCI) calculations were performed with two extended Gaussian basis sets providing a detailed coverage of the molecule configuration space. A total of 102 geometries, both linear and nonlinear, have been examined. These calculated energies have then been partitioned into two-body and three-body Hartree–Fock energy components, and combined with two-body and three-body semiempirical models of the dynamical correlation energy to obtain a realistic double many-body expansion (DMBE) representation of the title potential energy surface. In conjunction with a previously reported DMBE potential energy surface for the two lowest-doublet states of H3, this completes the set of potentials on which accurate dynamics calculations may be carried out for any collision process involving three ground-state hydrogen atoms. A number of FCI calculations have also been carried out to test the reliability of the modelled DMBE potential energy surface.

Dynamics Study of the HO(v‘=0) + O2(v‘ ‘) Branching Atmospheric Reaction. 1. Formation of Hydroperoxyl Radical

We report a theoretical study of the title four-atom atmospheric reaction for a range of translational energies 0.1 ≤ Etr/kcal mol-1 ≤ 40 and the range 13 ≤ v‘ ‘ ≤ 27 of vibrational quantum numbers of the oxygen molecule. All calculations have employed the quasiclassical trajectory method, and a realistic potential energy surface obtained by using the double many-body expansion (DMBE) method for ground-state HO3.

ANALYTICAL POTENTIAL ENERGY FUNCTION FOR THE GROUND STATE (3Σ+u) OF UO2

An analytical potential energy function for the ground state 3Σ+u of UO2 has been derived using many-body expansion method. The present paper correctly determines the dissociation limits, based on group theory and atomic and molecular reactive statics (AMRS). Using the MP2 (The HF calculation followed by a second-order Moller-Plesset correlation) of Gaussian94W and the RECP (the relativistic effective core potential) for U and basis 6-311G* for O,the present work has optimized the equilibrium geometry for the ground state 3Σ+u of UO2, which is linear O—U—O,whose equilibrium nuclear distance and dissociation energy are 0.17789nm and 14.1036eV.And the metastable structure U—O—O is discovered for the first time,to our knowledge,which is 5.7731eV higher than the stable structure.Then,the potential energy function is successfully used for describing the equilibrium geometry of UO2 and UOO,which is accurate enough in the whole region for dynamical research.

Molecular structure and analytical potential energy function for the HCl +2 ( X1A′) system

The analytical potential energy function for the ground state of HCl + 2 ( X 1 A′) is derived by a many-body expansion method using its equilibrium geometry, dissociation energy, harmonic frequencies and force constants calculated with the CISD 6–31++ G ( d, p) method. The topographical feature of the potential energy function represents the characteristics of the equilibrium geometry with an HCl +···Cl saddle, the energy of which is 1 eV compared with the channel HCl + + Cl.

Trajectory Surface Hopping Study of the Li + Li2(XΣg+) Dissociation Reaction

Trajectory surface hopping calculations are reported for the Li + Li2(X1Σg+) dissociation reaction over the range of translational energies 13 ≤ Etr/kcal mol-1 ≤ 80. Both potential energy surfaces for ground doublet Li3, which have been modeled from the double many-body expansion method (DMBE III), have been employed in the dynamics calculations. For the initial internal state (v = 0, j = 10), the behavior of the dissociative cross sections as a function of translational energy shows that nonadiabatic effects are important over the whole range of energies studied. Concerning the role of initial vibration, it has been found that, for Etr = 25 kcal mol-1 and j = 10, the adiabatic dissociative cross sections are enhanced as v increases from 0 to 20, while the nonadiabatic ones just slightly increase with the vibrational quantum number.

Validation of the activity expansion method with ultrahigh pressure shock equations of state

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}

On the O 2( ν′) + O 2( ν′) atmospheric reaction: a quasiclassical trajectory study

We report a theoretical study of the title four-atom atmospheric reaction for a wide range of initial vibrational quantum numbers (ν′, ν″). All calculations have employed the quasiclassical trajectory method, and a realistic potential energy surface obtained by using the double many-body expansion (DMBE) method. The implications of the results on a recently proposed hypothesis to explain the ‘ozone deficit’ problem are tentatively assessed.

Many-body valence-bond theory

The classical theory of chemical valence, first, is naturally formalized in mathematics in the area of graph theory and, second, finds an extension in quantum mechanics in terms of the Heitler–London–Pauling “valence-bond” (VB) theory. Thus, VB theory stands in a fairly unique position, although in quantum chemistry, there often has been a preference for the alternative (perhaps even “complementary”) molecular orbital (MO) theory, presumably in large part because of computational efficacy for general molecular structures. Indeed, as formulated by Pauling and others, VB theory was described as a configuration interaction (CI) problem when there were multiple relevant classical valence structures for the same molecular structure. Also, as now recognized, a direct assault on CI is computationally intensive, prone to size-inconsistency problems, and effectively limited to smaller systems—whereas indirect approaches, e.g., via wave-function cluster expansions or renormalization-group theory, often neatly avoid these problems. Thus, what is (and perhaps always has been) needed is “many-body” schemes for VB computations (as well as for higher-order MO-based approaches, too). Here, then, certain such many-body VB-amenable computational schemes are to be discussed, in the context of semiempirical (explicitly correlated) graphical models. The collection of models are described and interrelated in a fairly comprehensive systematic manner. A selection of many-body cluster expansion methods are then discussed with special reference to resonating VB wave functions and the fundamental graph-theoretic nature of the consequent problems (such as also are noted to arise in lattice-discretized statistical-mechanical problems, too). Some examples are described incorporating resonance among exponentially great numbers of VB structures as applied: for large icosahedral-symmetry fullerenic structures, for the (polyacetylenic) linear chain, and for ladderlike conjugated polymers. It is contended that practicable many-body VB-theoretic methods are now available, retaining clear links to classical chemical valence theory. Hopefully, too, these methods may soon find use beyond the semi-empirical framework. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 421–438, 1997

Variational transition state rate constants for the reaction [formula omitted

Rate constants for the reaction O( 3 P) + O 3( 1 A 1) → 2 O 2( X 3Σ g −) are reported using variational transition state theory. A semi-empirical potential energy surface based on a double many-body expansion method due to Varandas and Pais is used to obtain transition state information. The computed rate constants are found to be in good to satisfactory agreement with available theoretical and experimental results. Preliminary studies of the reverse reaction, with one O 2 molecule in v = 0 and the other in 27 ⩽ v ⩽ 30 using a semiclassical wavepacket method reported recently show no reactivity on the potential energy surface used, contrary to some indirect evidence of reaction observed in recent experiments.

Towards a double many-body expansion method for multivalued potential energy surfaces

Using the diatomics-in-molecules formalism to get a first-order potential matrix, an extension is proposed of the double many-body expansion (DMBE) method for multivalued potential energy surfaces. The method consists of dressing the diatomic states with many-body energy terms of the extended Hartree-Fock and dynamical correlation type, with spin-recoupling and orientational effects being treated as in the traditional diatomics-in-molecules approach. All states of the polyatomic dissociate properly. Examples are discussed for s3, s2p, and sp2 systems. Specifically, a DMBE potential energy surface is reported for NO2 which shows the correct energy and geometry at the equilibrium structure and is in fair agreement with ab initio calculations at other regions of configuration space. Thus, this NO2 potential energy surface may be useful for molecular dynamics studies.

Double many-body expansion of the two lowest potential-energy surfaces for Li3 and dynamics of the Li + Li2(v) reaction. Initial orientation and vibrational excitation effects

The semiempirical double many-body expansion method has been used to obtain consistent analytic representations of the two lowest doublet potential-energy surfaces for Li3. A recently reported semiempirical formulation of the three-body dynamical correlation energy has been used, which accounts for the proper dependence on the diatomic intramolecular coordinate of the Li–Li2 long-range dispersion energy. Besides providing an accurate description of the most recent, and reliable, ab initio energies for both sheets of the potential-energy surface of the title system at the strong interaction regions, the lowest sheet of the Li3 doublet potential-energy surface shows the correct long-range behaviour for the isotropic and leading anisotropic terms in the Legendre analysis of the Li–Li2 interaction as a function of the Li2 stretching coordinate. Based on the premise that only this lowest sheet is necessary, quasiclassical trajectories have been run to explore the effect of vibrational bond stretching in the Li + Li2(v) exchange reaction. The effect of the reagent initial orientation and rotational excitation as a function of the collision energy on the lithium atom exchange dynamics has also been investigated.

Recalibration of a single-valued double many-body expansion potential energy surface for ground-state hydroperoxy and dynamics calculations for the oxygen atom + hydroxyl .fwdarw. oxygen + hydrogen atom reaction

The authors report a new single-valued potential energy surface for the ground state of HO{sub 2} from the double many-body expansion (DMBE) method. This new surface conforms with the three-body energy of recent ab initio CAS SCF/CCI calculations semiempirically corrected by the DMBE-SEC method and reproduces the most accurate estimates of the experimental dissociation energy, equilibrium geometry, and quadratic force constants for the hydroperoxyl radical. Using this new HO{sub 2} (DMBE IV) potential energy function, exploratory dynamics calculations of the O + OH {yields} O{sub 2} + H reaction have also been carried out by the quasiclassical trajectory method. Thermal rate coefficients are reported for T = 250, 1,250, and 2,250 K that are shown to be in good agreement with the best reported measurements.

The analytical representation of electronic potential-energy surfaces

This article reviews the commonly used methods for representing electronic potential-energy surfaces for small molecules and simple chemical reactions in terms of globally defined analytical functions. Four classes of methods are discussed: spline fitting methods, semiempirical methods, many-body expansion methods, and methods that represent global surfaces based on information determined along reaction paths. The application of these methods is examined in detail for four triatomic systems and one four-atom system: $\mathrm{O}(^{3}P)+{\mathrm{H}}_{2}$, Cl+HCl, H+CO, $\mathrm{O}(^{1}D)+{\mathrm{H}}_{2}\ensuremath{\rightarrow}{\mathrm{H}}_{2}\mathrm{O}\ensuremath{\rightarrow}\mathrm{OH}+\mathrm{H}$, and H+C${\mathrm{O}}_{2}$\ensuremath{\rightarrow}OH+CO. These examples illustrate both the art and the pitfalls of representing surfaces. In addition, the consequences of different potential surface representations for the dynamics of collisions on these surfaces are discussed at length.

A semiempirical method for correcting configuration interaction potential energy surfaces

A method recently proposed by Brown and Truhlar to correct large-scale configuration interaction calculations for incomplete dynamic correlation of electrons is reformulated using the formalism of the double many-body expansion method. Rather than making the assumption that large-basis-set multireference configuration interaction calculations including all single and double excitations from a complete-active space recover an approximately constant fraction of the external correlation, it is suggested that this fraction is approximately constant for the various n-body terms which arise in a cluster expansion of the total molecular energy. A new variant of this method in which the assumption of geometry-independent fraction of the external correlation is relaxed for the diatomics is also examined. Results are reported for the ground electronic states of the H3 and HO2 systems.