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The Na2B, Na3, and H3 trimers in the lowest quartet states were studied by ab initio methods, using both the supermolecular approach and the intermolecular Møller-Plesset perturbation theory. Partitioning of the nonadditive contribution into the orientational two-body part and the genuine three-body part was proposed. The lowest quartet state of the Na3 trimer and all the three lowest quartet states of the Na2B trimer are bound, and the forms of these clusters are essentially determined by two-body forces. In the case of the Na2B trimer the orientational two-body nonadditivity proved to be crucial. In addition, in the title metal trimers, in the region of the van der Waals minima, the genuine nonadditivity is very important, and amounts to 30% in Na2B and up to 70% in Na3. The leading nonadditive term is the triple-exchange Heitler-London exchange term. For triangular arrangements it considerably enhances the total stabilization. The single-exchange term and the SCF deformation play only a secondary role. The dispersion nonadditivity is negligible. The isotropic part of the basis set superposition error (BSSE) is large and must be corrected by the counterpoise method. The anisotropic contribution to BSSE is practically negligible.

Thirty-two nucleic acid hydrogen-bonded base pairs have been examined using second-order Miller-Plesset perturbation theory (MP2) and the 6-31G*(0.25) and modified aug-cc-pVDZ basis sets. Complexes of C s symmetry have been constructed from rigid monomers which allowed us to use a compact parametrization of their geometry based on the center of mass separation and Euler angles. The dependence of the interaction energy and its components on small geometrical modifications around the minima have been examined. The electrostatic and the exchange energies have been found to be the most important components of the overall interaction energy, although the dispersion and the induction energies also play important roles. The exchange energy, while typically not the largest in magnitude at the minima, is the most anisotropic component for rotations of the monomers in the plane of the complex. The analysis of the electron-correlated components reveals that the effect of the attractive dispersion energy is to a large degree canceled out by the repulsive correlation correction to the exchange energy.

Fourth-order Moller–Plesset perturbation theory (MP4) and perturbation theory of intermolecular forces were employed to investigate the potential energy surface of the NH 3 –CO complex. Most calculations were performed using a relatively large, well-tempered basis set, though for a few selected structures an augmented basis set with bond functions was used. The global minimum of −1489 μ E h was found for a bent hydrogen-bonded configuration at the intermolecular distance of 4.3 A. The minimum energy area was discovered to be very wide and flat making the complex extremely flexible. A model potential function for the complex was developed.

The CH3F···H2O complex has been studied using both the supermolecule approach through fourth-order Moller−Plesset perturbation theory (MP4) and perturbation theory of intermolecular forces. Nine co...

A combined ab initio atoms-in-molecule approach was implemented to model the photoelectron spectra of the ArO− anion. The lowest adiabatic states of Σ and Π symmetry of ArO and ArO− were investigated using the fourth-order Moller–Plessett perturbation theory including bond functions. The total energies were dissected into electrostatic, exchange, induction, and dispersion components. The complex of Ar with atomic oxygen is only weakly bound, primarily by dispersion interaction. The Π state possesses a deeper minimum (Re=3.4 A,De=380 μEh) than the Σ state (Re=3.8 A,De=220 μEh). In contrast, the anion complex is fairly strongly bound, primarily by ion-induced dipole induction forces, and the Σ state possesses a deeper minimum at shorter interatomic distances (Re=3.02 A,De=3600 μEh) than the Π state (Re=3.35 A,De=2400 μEh). The Σ–Π splittings in both systems are mainly due to differences in the exchange repulsion terms. Atoms-in-molecule models were used to account for the spin–orbit interaction, and to gene...

Adiabatic potential energy surfaces for the 2A′ and 2A″ states of the Ar(1S)–OH(X2Π) complex were calculated using supermolecular unrestricted fourth-order Moller–Plesset perturbation theory and a large correlation consistent basis set supplemented with bond functions. The potential energy surface (PES) of the A′ state has two minima. The global minimum from the unrestricted coupled-cluster calculations with single, double, and noniterative triple excitations occurs for the collinear geometry Ar–H–O at R=7.08a0 with a well depth of De=141.2 cm−1. There is also a local minimum for the skewed T-shaped form, whereas the Ar–O–H arrangement corresponds to a saddle point. The PES of the A″ state also has two minima, which occur for the two collinear isomers. A variational calculation of the bound rovibrational states was performed. The calculated binding energy, D0=93.8 cm−1, and the energies of the bound vibrational states are in good agreement with experiment [see Berry et al., Chem. Phys. Lett. 178, 301 (199...

A new ab initio two-dimensional potential energy surface for the Ne–CO interaction is described. The surface was obtained by the supermolecule method at the CCSD(T) level of theory. It is compared with several experimental data sets and with the symmetry-adapted perturbation theory (SAPT) surface of Moszynski et al. [J. Phys. Chem. A 101, 4690 (1997)]. The new surface gives modestly better predictions of experimental results that depend on close approach of Ne to CO, but does not describe the ground state geometry as well as the SAPT surface.

The potential energy surfaces for the ground state of the Ar–HCN complex have been calculated at several levels of theory, including the single and double excitation coupled-cluster method with noniterative perturbational treatment of triple excitation CCSD(T). Calculations have been performed using the augmented correlation-consistent polarized triple zeta basis set supplemented with bond functions (aug-cc-pVTZ+bf). The global minimum with a well depth of approximately 141 cm−1 has been found for the linear Ar–H–C–N geometry (Θ=0.0°) with the distance R between the Ar atom and the center of mass of the HCN molecule equal to 8.52a0. In addition, the potential energy surface has been found to contain a long channel that extended from the bent configuration at R=7.39a0 and Θ=59.7° (a well depth of 126 cm−1) toward the T-shaped configuration with R=7.16a0 and Θ=107.5° (a well depth of 121 cm−1). The interaction energies have been analyzed using perturbation theory of intermolecular forces. The location of th...

The potential energy surface for the Ar(1S)+NH(X 3Σ−) interaction is calculated using the supermolecular unrestricted Mo/ller–Plesset (UMP) perturbation theory approach and analyzed via the perturbation theory of intermolecular forces. The global minimum occurs for the approximate T-shaped geometry with Ar skewed toward the H atom at about Θ=67° and R=6.75 a0. Our UMP4 estimate of the well depth of the global minimum is De=100.3 cm−1 and the related ground state dissociation energy obtained by rigid-body diffusion quantum Monte Carlo calculations (RBDQMC) is D0=71.5±0.1 cm−1. These values are expected to be accurate to within a few percent. The potential energy surface also features a wide plateau in the proximity of Ar-N-H collinear geometry, at ca. 7.0 a0. RBDQMC calculations reveal nearly a free rotation of the NH subunit in the complex.

The ArHCCH interaction is investigated by the supermolecular Moller-Plesset perturbation theory and coupled-cluster theory in conjunction with the perturbation theory of intermolecular forces. The interaction energy in this cluster is dissected into the fundamental components such as exchange, induction, and dispersion, and the anisotropy of the overall surface is analysed in terms of the angular behaviors of these components. The shape of the PES of ArHCCH is very sensitive to the level of ab initio theory. The coupled-cluster approach which included the single, double, and approximate triple excitations combined with the aug-cc-pvtz basis set supplemented by bond functions was necessary to obtain the best estimates of D e (within ± 5% error) for two minima: the global one for a skew T-configuration (118 cm −1 ), and a secondary one for the collinear arrangement (115 cm −1 ). The PES generated at a lower level of calculation was used in diffusion quantum Monte Carlo (DMC) calculations of the ground and first excited bending vibrational state of the cluster. The expectation values of the coordinates and rotational constants are provided for the ground state. DMC calculations are relatively unsensitive to the details of the PES. The nature and decomposition of three-body interactions in the related cluster Ar 2 HCCH were also investigated.

A potential energy surface for the Ar(1S)+O2(X 3Σg−) interaction is calculated using the supermolecular unrestricted Mo/ller–Plesset (UMP) perturbation theory and analyzed via the perturbation theory of intermolecular forces. The global minimum occurs for the T-shaped geometry, around 6.7 a0. Our UMP4 estimate of the well depth of the global minimum is De=117 cm−1 and the related ground state dissociation energy obtained by diffusion Monte Carlo calculations is 88 cm−1. These values are expected to be accurate to within a few percent. The potential energy surface also reveals a local minimum for the collinear geometry at ca∼7.6 a0. The well depth for the secondary minimum at the UMP4 level is estimated at De=104 cm−1. The minima are separated by a barrier of 23 cm−1. The global minimum is determined by the minimum in the exchange repulsion in the direction perpendicular to the O–O bond. The secondary, linear minimum is enhanced by a slight flattening of the electron density near the ends of the interoxyge...

We analyze the many-body exchange interactions in atomic and molecular clusters as they arise in the supermolecular SCF and MP2 approaches. A rigorous formal setting is provided by the symmetry-adapted perturbation theory. Particular emphasis is put on the decomposition into the single exchange (SE) and triple exchange (TE) terms, at the SCF and correlated levels. We also propose a novel approach, whereby selected SE nonadditive exchange terms are evaluated indirectly, as differences of the two-body SAPT corrections arising between the components of the trimer treated as a complex of a dimer and a monomer (pseudodimer approach). This provides additional insights into the nature of various nonadditive effects, an interpretation of supermolecular interaction energies, and may serve as a viable alternative for the calculation of some SE terms.

Ab initio calculations using unrestricted Mo/ller–Plesset perturbation theory to fourth order (UMP-4) were carried out for the interaction of He with the B 3Π0u+ state of Cl2. Also, more reliable unrestricted coupled cluster singles, doubles, and noniterative triples (UCCSD(t)) calculations were performed for several points on the B electronic state surface and were used to scale the UMP-4 points. Exp-6 type two center potential energy functions were fitted to the modified UMP-4 points (B state) to construct an analytical three-dimensional potential energy surface. An r (Cl–Cl separation) dependence was incorporated in the B state potential energy surface to allow the calculation of HeCl2 properties in different vibrational states so that vibrational predissociation rates could be calculated. Excitation spectra, predissociation lifetimes, and rotational product distributions were calculated and compared to the available experimental data. It was found that the calculated B←X, 8←0 spectrum is in good agree...

Potential energy surfaces for the 2A′ and 2A″ states of the He(1S)–CH(X 2Π) complex were calculated using supermolecular unrestricted Mo/ller–Plesset perturbation theory and analyzed via the relevant perturbation theory of intermolecular forces. It has been found that the two states are distinctly different. The potential energy surface (PES) of the A″ state has only a single and relatively deep minimum of De≊335 μEh for the T‐shaped geometry, at R=5.0 a0 and Θ=100°. The position of this minimum is determined by the exchange repulsion which is substantially reduced at this geometry. The minimum is unusually deep for a complex of He, and it can be viewed as an example of an incipient chemical bond. In contrast, the A′ state’s PES represents a typical van der Waals interaction which is characterized by two similarly deep minima. The shape and location of these minima are determined primarily by the anisotropy of the dispersion component. The first minimum occurs for the collinear He–C–H arrangement, at R≊7....

Potential energy surface for the He(1S)+O2(X 3Σ−g) interaction is calculated using the supermolecular unrestricted Mo/ller‐Plesset perturbation theory approach and is analyzed via the perturbation theory of intermolecular forces. The latter has been generalized to provide a decomposition of the interaction energies into electrostatic, exchange, induction, and dispersion constituents for monomers described by unrestricted Hartree–Fock determinants. The global minimum occurs for the T‐shaped geometry, around 6.0a0. Our UMP4 estimate of the well depth of the global minimum is De=27.7 cm−1. This value is expected to be accurate to within a few percent. The potential energy surface reveals also a local minimum for the collinear geometry at about 7.0a0. The well depth for the secondary minimum is estimated at De=25.5 cm−1(UMP4) and is expected to be accurate within a few percent. The minima are separated by a barrier of 7.5 cm−1. The energy partitioning reveals that the origin of interaction in this complex is ...

The nonadditive interactions in the Ar2Cl− cluster are studied using the supermolecular Mo/ller–Plesset perturbation theory in conjunction with the perturbation theory of intermolecular forces. The three‐body effect is rigorously dissected into fundamental nonadditive components; the exchange, the induction, and the dispersion. All three terms are important in describing nonadditivity in this cluster. The exchange nonadditivity is further divided into two terms; ES3, the electrostatic interaction between the Cl− and Ar2 subunits due to the appearance of an ‘‘exchange‐quadrupole’’ moment on Ar2 [Cooper and Hutson, J. Chem. Phys. 98, 5337 (1993)], and the exchange counterpart of ES3, the X3 term. ES3 term is modeled analytically using the charge‐quadrupole electrostatic term. The induction nonadditivity is approximated as an interaction of induced dipoles on two Ar atoms. The three‐body dispersion term is fitted to the dipole–dipole–dipole plus dipole–dipole–quadrupole expressions. The sum of all three anal...

The nonadditive effects are studied in Ar2HX (X=F, Cl) clusters using the supermolecular Mo/ller–Plesset perturbation theory in conjunction with the perturbation theory of intermolecular forces. The range of geometrical variations include the rotation of HX within the plane of the cluster and perpendicular to it. The three‐body effect is rigorously dissected into the three fundamental nonadditive components: exchange, induction, and dispersion. The exchange nonadditivity is further divided into two terms: ES3, the electrostatic interaction between the HX and Ar2 subunits due to the appearance of exchange‐induced quadrupole moment on Ar2 [Cooper and Hutson, J. Chem. Phys. 98, 5337 (1993)], and its exchange counterpart X3. ES3 is physically interpreted as originating from the interatomic electron exchanges within the Ar2 part. The X3 term originates from triple exchanges among all three monomers. The induction nonadditivity is dominated by the third‐order effect describing the interaction of moments induced on the Ar atoms by the field of HX. This effect is faithfully represented by the multipole approximation.

Calculations of the hypermagnetizabilities (η) at the self‐consistent‐field (SCF) and second‐order Mo/ller–Plesset perturbation theory (MP2) levels of theory are reported for H2, N2, HF, and CO. Electron correlation is found to be unimportant for H2, but very important for the other three molecules. The individual components of η are more affected by correlation effects than the hypermagnetizability anisotropy (Δη) which mediates the birefringence of a material in the presence of a magnetic field (the Cotton–Mouton effect). The zero‐point‐vibrational averaging, pure vibrational corrections, and frequency dependence are important for the individual components, but are less important for Δη due to cancellation between the various contributions. Excellent agreement is found with the previous theoretical results for H2, but only fair agreement with the experimental results for N2 and CO.

Electric field gradients, generalized Sternheimer shielding constants, and electric‐field‐gradient polarizabilities are calculated for H2, N2, F2, HF, HCl, CO, HCN, HNC, H2O, and NH3. The calculations are performed at both the Hartree–Fock and second order Mo/ller–Plesset levels of approximation using large basis sets. For most of these molecules this is the first time that the shielding constants and electric field gradient polarizabilities have been determined. Electron correlation is generally found to be a significant factor.

The evaluation of second derivatives of the electronic energy for nonvariational wave functions using an energy functional is discussed. It is shown that, in certain cases, the formation of the first-order relaxed density matrix leads to an efficient algorithm for the calculation of second-order response properties. Detailed formulas are given for second-order Moller–Plesset perturbation theory. © 1994 John Wiley & Sons, Inc.

Calculations of the magnetizabilities and the rotational g factors at the self‐consistent‐field (SCF) and second‐order Mo/ller–Plesset perturbation theory (MP2) levels of theory are reported for H2, N2, F2, HF, CO, HCN, HNC, H2O, and NH3. The sums rules, that verify the reliability of the calculations, are shown to be well satisfied. The second‐order correlation corrections to the magnetizabilities are found to be small, thus substantiating the generally observed good agreement between the experimental and SCF results. Vibrational corrections to the properties of the diatomic molecules are given. Very good agreement is found between the experimental and vibrationally corrected MP2 rotational g factors for the diatomic molecules.

The supermolecule interaction energies at the self-consistent field and the second-order Moller—Plesset perturbation theory levels are analyzed using the polarization approximation perturbation theory of intermolecular interactions. The results for the HeH+ complex show that the perturbation expansion converges and its sum is identical with the supermolecule interaction energy. The counterpoise-corrected supermolecule interaction energies for various complexes in the region of small intermolecular overlap are in excellent agreement with the perturbation results for both the basis sets of monomers and the basis set of the entire complex. Comparison of the results obtained with large and small basis sets for the HeH+ and HeLi+ complexes is used to emphasize the need to remove the basis set superposition error and to demonstrate the correctness of the counterpoise procedure.

The perturbation theory of intermolecular forces in conjunction with the supermolecular Mo/ller–Plesset treatment is applied in the analysis of the potential energy surface of Ar–CH4. The anisotropy of the Ar–CH4 potential energy surface is chiefly due to exchange repulsion. In the equilibrium structure, Ar approaches the face of CH4 tetrahedron thus avoiding contacts with C–H bonds. The equilibrium Ar–C separation was found equal to 7.5 a0 and the De energy to 113 cm−1. We estimate that our De may be too small by up to 25% with respect to the accurate value. The properties of Ar–CH4 are also compared with other Ar‐molecule systems, such as Ar–NH3, Ar–H2O, and Ar–HCl. We find that the equilibrium structures of weak proton donors bound to Ar (CH4, NH3) are determined by the exchange repulsion, while those of efficient proton donors, such as HCl (and to a lesser extent H2O), result from the strong polarization of Ar in the field of a molecule.

Explicitly electron‐correlated wave functions have been used to calculate the hypermagnetizability anisotropy (Δη) for H2 and D2. This property is the essential feature of the birefringence of a material in the presence of a magnetic field (the Cotton–Mouton effect). The calculations were carried out in the framework of perturbation theory and both dispersion and vibrational effects were fully taken into account. A detailed analysis of our results is made and it is concluded that electron correlation and ‘‘pure’’ vibrational effects are less important than vibrational averaging and dispersion. The experimental results are only in fair agreement with our theoretical ones.

The basis set effects on the total self‐consistent field (SCF) and second‐order Mo/ller–Plesset (MP2) interaction energies in the HF dimer (in the equilibrium geometry) are investigated in relation to their components: electrostatic, exchange, induction, and dispersion, calculated within the framework of intermolecular Mo/ller–Plesset perturbation theory (IMPPT). The basis set dependence of the SCF interaction energy in the HF dimer is almost exactly determined by the electrostatic contribution. The exchange, induction, and the SCF‐deformation terms are found substantially less sensitive. The MP2 correlation contribution reflects primarily the basis set dependence of dispersion. However, an accurate image of the basis set dependence is reproduced only if the electrostatic‐correlation term is considered as well. Other correlation contributions: the deformation‐ correlation and exchange terms are found to be much less sensitive to basis set effects. All these conclusions are valid only under the condition that the supermolecular interaction energies are counterpoise‐corrected for the basis set superposition error and IMPPT interaction energies are calculated with the full basis set of the dimer.

By using the recently developed density approach to the analytic MBPT (2) gradients we derive the spin-adapted form of the correlation correction to the Hartree-Fock electrostatic energy using the relaxed MBPT (2) density matrix. This correction is shown to be essential for a perturbation theory analysis of the MBPT (2) supermolecular interaction energy at large distances. Applications are presented for various configurations of the H2 dimer and the results are compared to the full CI electrostatic energy data.

Nonadditive, multibody effects arising in the supermolecular Mo/ller–Plesset perturbation theory (MPPT) (IMPPT) calculations are classified and interpreted in terms of the exchange, induction, deformation, and dispersion contributions, as defined by the perturbation theory of intermolecular forces. As an example the many‐body effects in the equilateral Ar trimer and tetrahedral Ar tetramer, calculated through the MP4 level of theory with extended basis [7s4p2d], are reported and discussed. It is stressed that the ‘‘Heitler–London‐exchange plus dispersion’’ model for nonadditive effects is too attractive mainly because of the neglect of the second‐order exchange contribution.

The nuclear magnetic shielding σ in a molecule is changed by the presence of an external uniform electric field. This change may be expressed in terms of the shielding polarizabilities σ′ and σ″. Values of σ′ and σ″ have been evaluated for H2, N2, HF and CO using a combination of the second order Moller-Plesset theory (MP2) and the finite-field perturbation theory. The effects of electron correlation on the σ′ and σ″ tensors for N2, HF and CO are seen to be sufficiently large that a higher-order theory than MP2 will be necessary to account for them fully.

A density-functional-theory (DFT) based treatment for calculating the interaction energies of nucleic acid base pairs proposed recently by Elstner et al. [J. Chem. Phys. 114, 5149 (2001)] is criticized. It is shown that dispersion energy that they evaluated amounts to approximately only 30% of the value obtained in rigorous ab initio calculations. The use of the second-order Mo/ller–Plesset perturbation theory results obtained with the 6-31G*(0.25) basis set as a benchmark for validating the DFT results is also criticized. It is suggested that the method of Elstner et al. requires much more stringent testing before it can be deemed to be “very accurate.”

Calculations for the complex of thymine and adenine are used to show that the supermolecule second-order Moller-Plesset perturbation theory (MP2) approach for evaluating interaction energies fails in certain cases because of the behavior of one of its components: the uncoupled Hartree-Fock dispersion energy. A simple approach for correcting the MP2 supermolecule interaction energies is proposed. It focuses on correcting a relatively small difference between the MP2 and coupled cluster interaction energies, which is a very appealing feature of the new approach considering a benchmark role played by coupled cluster results.

The combination of supermolecular Mo/ller–Plesset treatment with the perturbation theory of intermolecular forces is applied in the analysis of the potential energy surface of Ar–NH3. Anisotropy of the self‐consistent field (SCF) potential is determined by the first‐order exchange repulsion. Second‐order dispersion energy, the dominating attractive contribution, is anisotropic in the reciprocal sense to the first‐order exchange, i.e., minima in one nearly coincide with maxima in the other. The estimated second‐order correlation correction to the exchange effect is nearly as large as a half ΔESCF in the minimum and has a ‘‘smoothing’’ effect on the anisotropy of e(20)disp. The model which combines ΔESCF with dispersion energy (SCF+D) is not accurate enough to quantitatively describe both radial and angular dependence of interaction energy. Comparison is also made between Ar–NH3 and Ar–PH3, as well as with the Ar dimer.

Nonadditive effects are calculated for (HF)3 and (HCl)3 complexes and analyzed via the combination of perturbation theory of intermolecular forces with Møller–Plesset perturbation theory (MPPT). In both systems the nonadditivity is dominated by the self‐consistent field (SCF) deformation effect, i.e., mutual polarization of the monomer wavefunctions. Heitler–London exchange and correlation effects are of secondary importance. Three‐body terms exhibit much lesser basis set dependence than the two‐body effects and even quite moderate basis sets which are not accurate enough for treatment of two‐body forces can yield three‐body effects of quantitative quality. This is due in large measure to the additivity of strongly basis set dependent components such as uncorrelated and correlated electrostatics and dispersion. Various approximate models for the three‐body potentials and total interaction in the (HF)3 cluster are analyzed from the point of view of their ability to predict the orientation dependence of interaction energy.