Supermolecular Method Research Articles

A newab initiointeraction energy surface and high-resolution spectra of the H2–CO van der Waals complex

A new four-dimensional intermolecular potential-energy surface for the H(2)-CO complex is presented. The ab initio points have been computed on a five-dimensional grid including the dependence on the H-H separation (the C-O separation was fixed). The surface has then been obtained by averaging over the intramolecular vibration of H(2). The coupled-cluster supermolecular method with single, double, and noniterative triple excitations has been used to calculate the interaction energy. The correlation part of the interaction energy has been obtained from extrapolations based on calculations in a series of basis sets. An analytical fit of the ab initio potential-energy surface has the global minimum of -93.049 cm(-1) at the intermolecular separation of 7.92 bohr for the linear geometry with the C atom pointing toward the H(2) molecule. For the other linear geometry, with the O atom pointing toward H(2), the local minimum of -72.741 cm(-1) has been found for the intermolecular separation of 7.17 bohr. The potential has been used to calculate the rovibrational energy levels of the para-H(2)-CO complex. The results agree very well with those observed by McKellar [A. R. W. McKellar J. Chem. Phys. 108, 1811 (1998)]: the discrepancies are smaller than 0.1 cm(-1). The calculated dissociation energy is equal to 19.527 cm(-1) and significantly smaller than the value of 22 cm(-1) estimated from the experiment. Predictions of rovibrational energy levels for ortho-H(2)-CO have also been done and can serve as a guidance to assign recorded experimental spectra. The interaction second virial coefficient has been calculated and compared with the experimental data.

Coupled Cluster Calculation of the n → π* Electronic Transition of Acetone in Aqueous Solution

The combined linear response coupled cluster/molecular mechanics (CC/MM) scheme including mutual polarization effects in the coupling Hamiltonian is applied together with supermolecular CC methods to the study of the gas-to-aqueous solution blue shift of the n --> pi* excitation energy in acetone. The aug-cc-pVDZ basis set is found to be adequate for the calculation of this excitation energy. In the condensed phase, the shift in the excitation energy is obtained by statistical averaging over 800 solute-solvent configurations extracted from a molecular dynamics simulation. We find the shift to be around 1100-1200 cm(-1) depending on the specific model used to describe solvent polarization. The importance of including explicit polarization in both the molecular dynamics simulation as well as the CC/MM calculations is emphasized. Furthermore, the significant dependence of the excitation energy on the CO bond length of acetone is discussed.

Ab initio intermolecular potential energy surface, bound states, and microwave spectra for the van der Waals complex Ne–HCCCN

We report two ab initio intermolecular potential energy surfaces for Ne-HCCCN using a supermolecular method. The calculations were performed at the fourth-order Møller-Plesset (MP4) and the coupled cluster singles-and-doubles with noniterative inclusion of connected triples [CCSD(T)] levels with the full counterpoise correction for the basis set superposition error and a large basis set including bond functions. The complex was found to have a planar T-shaped structure minimum and a linear minimum with the Ne atom facing the H atom. The two-dimensional discrete variable representation method was employed to calculate the rovibrational bound states. In addition, the microwave spectra including intensities for the ground vibrational state were predicted. The results show that the spectrum is dominated by b-type (DeltaK(a) = +/-1) transitions with very weak a-type (DeltaK(a) = 0) transitions. The calculated results at the CCSD(T) potential are in good agreement with those at MP4 potential.

Theoretical Study of H2...I- van der Waals Anion Complex

The ab initio potential energy surface (PES) for the weak interaction of hydrogen molecule with iodine anion is presented. The surface was obtained by the supermolecular method at the MP4(SDTQ) level of theory. Our calculations indicate the van der Waals (vdW) system for the linear configuration at rH-H = 0.752 Å and R = 3.76 Å with a well depth of De = 2096 μEh. The presented PES reveals also a transition state for the perpendicular arrangement at rH-H = 0.7416 Å and R = 4.63 Å with an interaction energy of -113 μEh. The physical origin of stability of the vdW H2...I- structure with respect to the H2...X- (X = F, Cl, Br) one was analysed by the symmetry adapted perturbation theory (SAPT) based on the single determinant HF wave function. The separation of the interaction energy shows that the dispersion forces play a much more important role for the systems with Cl, Br and I than for H2...F- and their importance slightly increases in the order Cl < Br < I. The global importance of the electrostatic and the induction energies decreases in the order F > Cl > Br > I.

On the structure and physical origin of the interaction in H(2) ... Cl(-) and H(2) ... Br(-) van der Waals anion complexes.

The ab initio three-dimensional potential energy surface (PES) for the weak interaction of hydrogen molecule with bromine anion is presented. The surface was obtained by the supermolecular method at the coupled cluster with single and double excitations and noniterative correction to triple excitations (CCSD(T)) level of theory. Our calculations indicate the van der Waals (vdW) system for the linear orientation at R=3.37 A with a well depth of D(e)=660.1 cm(-1). The presented PES reveals also transition state for the perpendicular orientation at R=4.22 A with a barrier of 607.1 cm(-1). The physical origin of the stability of vdW H(2) ... Br(-) structure with respect to the H(2) ... Cl(-) one was analyzed by the symmetry adapted perturbation theory based on the single determinant Hartree-Fock (HF) wave function. The separation of the interaction energy shows that the dispersion forces play slightly more important role in the stabilization of the vdW system with Br(-) than with Cl(-).

Solvent effects on the spin-spin coupling constants of acetylene revisited: supermolecular and polarizable continuum model calculations.

The solvent shifts of the spin-spin coupling constants of acetylene were calculated using the polarizable continuum model (PCM) for solvents ranging in polarity from cyclohexane to water, using both density functional theory (DFT) and the complete active space self-consistent field (CASSCF) method. The spin-spin coupling constants were also calculated for complexes of acetylene with water, acetonitrile, acetone and benzene using DFT/B3LYP. It is demonstrated that PCM reproduces the substantial experimental solvent shifts of the (1)J(C,C) and (1)J(C,H) couplings with great accuracy. The sign and approximate magnitude are also rendered correctly by the supermolecular method, in spite of the limitation of the models, which included only one or two solvent molecules.

Ab initio potential energy surface and rovibrational spectrum of Ar-HCCCN.

We report an ab initio intermolecular potential energy surface of the Ar-HCCCN complex using a supermolecular method. The calculations were performed using the fourth-order Møller-Plesset theory with the full counterpoise correction for the basis set superposition error and a large basis set including bond functions. The complex was found to have a planar T-shaped structure minimum and a linear minimum with the Ar atom facing the H atom. The T-shaped minimum is the global minimum with the well depth of 236.81 cm(-1). A potential barrier separating the two minima is located at R=5.57 A and theta=20.39 degrees with the height of 151.59 cm(-1). The two-dimensional discrete variable representation was employed to calculate the rovibrational energy levels for Ar-HCCCN. The rovibrational spectra including intensities for the ground state and the first excited intermolecular vibrational state are also presented. The results show that the spectra are mostly b-type (Delta K(a)=+/-1) transitions with weak a-type (Delta K(a)=0) transitions in structure, which are in good agreement with the recent experimental results [A. Huckauf, W. Jager, P. Botschwina, and R. Oswald, J. Chem. Phys. 119, 7749 (2003)].

On the structure and physical origin of the interaction between lithium and acetylene molecule

The supermolecular UHF coupled-clusters method was used to investigate the energetics of the weak interaction of rigid acetylene molecule with lithium atom. The obtained potential energy surface (PES) corrected on the basis set superposition error indicate the strong interaction for the perpendicular orientation at R =2.59 Å with a well depth of D e =1716 μ E h . The presented PES reveals also the second minimum for the linear orientation at R =5.85 Å with a well depth of D e =349 μ E h . The zero point correction is negligible. The physical origin of stability of localised structures was analysed by the intermolecular perturbation theory based on the single determinant UHF wave function. The separation of the interaction energy shows that the positions of the predicted stable structures (at R =2.59 Å) are primarily determined by the attractive components included in HF deformation and dispersion energies.

Ab initio studies of He–HCCCN interaction

Five two-dimensional potential energy surfaces for the interaction of He with cyanoacetylene (HCCCN) are presented, obtained from ab initio calculations using symmetry-adapted perturbation theory and the supermolecular method at different levels of electron correlation. HCCCN is taken to be a rigid linear molecule with the interatomic distances fixed at the experimental “r0” geometry extracted from ground-state rotational constants. The complex was found to have a global minimum at a T-shaped configuration and a secondary minimum at the linear configuration with the He atom facing the H atom. Two saddle points were also located. There is good agreement between the positions of the stationary points on each of the five surfaces though their energies differ by up to 19%. Rovibrational bound state calculations were performed for the He-HCCCN4 and He-HCCCN3 complexes. Spectra (including intensities) and wave functions of He-HCCCN4 obtained from these calculations are presented. The effective rotational constant of HCCCN solvated in a helium droplet was estimated by minimizing the energy of Hen–HCCCN for n=2–12, selecting the n=7 complex as giving the largest magnitude of interaction energy per He, and shifting the resulting ring of He atoms to the position corresponding to the average geometry of the ground state of the He–HCCCN dimer. This estimate is within 4.8% of the measured value.

Intermolecular potential energy surfaces and spectra of Ne–HCN complex from ab initio calculations

Ab initio calculations of five two-dimensional intermolecular potential energy surfaces of the Ne–HCN dimer have been performed using the symmetry-adapted perturbation theory and the supermolecular method at different levels of electron correlation. A basis set of spdf-symmetry orbitals (including midbond functions) was used. HCN was assumed linear with interatomic distances fixed at their vibrationally averaged 〈r−2〉−1/2 values. Fits to all calculated potential energy surfaces were obtained in the form of angular expansions incorporating the ab initio asymptotic coefficients. It has been found that high-order correlation effects are very important for Ne–HCN and contribute about 20% to the well depth. All of the five surfaces feature a global minimum at the linear Ne–HCN geometry and a narrow and relatively flat valley surrounding HCN. Rovibrational calculations on the surfaces yielded rotational spectra and a rotational constant whose relative differences from their experimental counterparts range from 2% to 12% depending on the method used to obtain the surface. This large sensitivity of spectral quantities to relatively modest differences between the potentials is related to the unusual shape of the potential well.

Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout.

The influence of electrostatic and dispersion interactions on the NMR parameters of acetylene

The NMR shielding constants and the spin–spin coupling constants of acetylene in C 2H 2–H + and C 2H 2–He complexes are calculated as functions of the intermolecular geometry, using the supermolecular method on CAS SCF level. For the obtained surfaces a fit resulting from the perturbation theory of weak interactions is applied. The signs of the changes induced by the presence of He and H + are opposite for all the NMR parameters of acetylene. The R −3 and R −2 radial dependence is prevalent for the shielding constants in C 2H 2–H +, while for the shielding constants in C 2H 2–He the dispersion interactions and the influence of He shielding anisotropy are of similar magnitude. The changes in the coupling constants are dominated by the FC term. BSSE is large for the 13 C shielding, smaller for the coupling constants, and negligible for the 1 H shielding.

Solvent effects on NMR spectrum of acetylene calculated by ab initio methods

The NMR spectrum of acetylene in the gas phase and in the solution was calculated on the SCF and CASSCF level. The calculated NMR parameters were studied in relation to the active space dimension and the basis set. Solvent-induced changes of acetylene coupling constants were calculated by the reaction field method; for shielding constants the supermolecular method was also used. The shielding and coupling constants calculated for the isolated molecule showed a strong electron correlation dependence as contrasted with the changes caused by the presence of a dielectric medium. Comparison with the experimental values confirmed an exceptional magnitude of the 1J CC solvent-induced changes in acetylene. The coupling constants changes calculated by the reaction field method are consistent with the experimental values; the shielding constants changes revealed a large discrepancy. On this basis we conclude that the shielding constants in solution are affected mainly by the short-range specific interactions while for the coupling constants the long-range electrostatic interactions also contribute significantly.

Symmetry-adapted perturbation theory of three-body nonadditivity in the Ar2HF trimer

Symmetry-adapted perturbation theory (SAPT) has been used to analyze the radial and angular dependence of the nonadditivity of the Ar2HF trimer interaction energy through fourth order. This represents the first application of the high-order SAPT to a nonadditive interaction including a polar molecule. The magnitude and anisotropy of the Hartree-Fock nonadditivity is well reproduced (to within 20%) by the sum of the first-order exchange and exchange-quenched third-order induction nonadditivities. The second-order induction effects play a smaller role. The computed SAPT corrections which contribute to the second-order supermolecular many-body perturbation theory (MBPT2) nonadditivity, Eexch-disp(2;0)[3,3] and Eind-disp(3;0)[3,3], reproduce MBPT2 values rather poorly. Using the pseudo-dimer approach it was found that the exchange quenching of the third-order induction-dispersion energy is strong. Inclusion of this quenching led to good agreement with the MBPT2 nonadditivity. The third-order MBPT nonadditivity was very well reproduced by the third-order dispersion energy. The fourth-order MBPT nonadditivity was only moderately well reproduced by the SAPT components Edisp(3;1)[3,3] and Edisp(4;0)[3,3], indicating that these terms are most likely appreciably quenched by exchange counterparts. The total nonadditivities computed using SAPT and the supermolecular method through fourth order agree remarkably well. The total SAPT nonadditivity is expressed in terms of physically interpretable components which can be easily modeled.

State of the Art in Counterpoise Theory

This review, covering the period 1987-1993, deals with quantum chemical studies that employ the supermolecular method with some form of counterpoise to calculate the interaction energies of molecular complexes. A theorem is provided showing that the standard counterpoise approach, in which, at a given geometry, energies are evaluated using the full basis set of the complex, yields a pure (i.e. BSSEfree) interaction energy. Artifacts resulting from secondary BSSE have been found to become negligible before the basis set limit of this interaction energy is attained. Alternative methods in which counterpoise is achieved by restricting the fragment description in the calculation of the full complex to the level used for the isolated fragment are formally nearly correct but have been found to give less satisfactory results, mainly because the relevant fragment properties converge only slowly to the basis

Perturbation theory calculations of intermolecular interaction energies

Intermolecular interactions play an essential role in determining the structure and conformation of biomolecules, in particular, in aqueous solutions. With the recent development of computer capabilities, it is now possible to calculate the interactions of biologically relevant molecules using the standard self-consistent field approximation. For most systems, this approximation is not sufficient and the correlation component of the interaction energy must be included. Unfortunately, the supermolecular method, which is mostly used to calculate the intermolecular interactions at the correlated level, is plagued by the basis-set superposition error and does not provide any physical interpretation of the interaction energy. An alterative approach is to use the symmetry-adapted (exchange) perturbation theory developed by us. This theory is free from the basis-set superposition error, provides a clear physical picture of the interaction energy, and involves less computational effort than does a standard many-body perturbation theory calculation of equivalent order. We have developed a system of ab initio computer codes performing calculations for arbitrary molecules. For small systems—where the accuracy could be tested—our results are in excellent agreement with experiment. Large-scale calculations performed for systems such as (H2O)2, (HF)2, and uracil…water demonstrate the high efficiency and accuracy of our method.

The HeHe Coulomb and exchange interaction energy

The Coulomb and exchange interaction energy between two helium atoms is calculated, increasing systematically the basis set, by a supermolecular method which excludes the superposition error by using non-orthogonal orbitals. At 5.6 bohr an energy limit of 9.69 K is found at the Hartree-Fock level; for correlated wavefunctions the corresponding value is 11.86 K using only s orbitals, 10.70 K including p orbitals and 10.58 K adding d orbitals.