First-order Interaction Energy Research Articles

Ab Initio Extended Hartree-Fock plus Dispersion Method Applied to Dimers with Hundreds of Atoms.

The Hartree-Fock plus dispersion plus first-order correlation (HFDc(1)) method consists in augmenting the HF interaction energy by the correlation part of the first-order interaction energy and the second-order dispersion and exchange-dispersion energies. All of the augmentation terms are computed using the symmetry-adapted perturbation theory based on density functional theory description of monomers [SAPT(DFT)]; thus, HFDc(1) is a fully ab initio method. A partly empirical version of this method, HFDasc(1), uses a damped asymptotic expansion for the dispersion plus exchange-dispersion term fitted to SAPT(DFT) ab initio values. The HFDc(1) interaction energies for dimers in the S22, S66, S66x8, NCCE31, IonHB, and UD-ARL benchmark data sets are more accurate than those given by most ab initio methods with comparable costs. HFDc(1) can be used routinely for dimers with nearly 200 atoms, such as included in the S12L benchmark set, giving results comparable to those obtained by the most expensive methods applicable.

Physical nature of intermolecular interactions inside Sir2 homolog active site: molecular dynamics and ab initio study.

In the present study, we analyze the interactions of NAD+-dependent deacetylase (Sir2 homolog yeast Hst2) with carba-nicotinamide-adenine-dinucleotide (ADP-HPD). For the Sir2 homolog, a yeast Hst2 docking procedure was applied. The structure of the protein–ADP-HPD complex obtained during the docking procedure was used as a starting point for molecular dynamics simulation. The intermolecular interaction energy partitioning was performed for protein–ADP-HPD complex resulting from molecular dynamics simulation. The analysis was performed for ADP-HPD and 15 amino acids forming a deacetylase binding pocket. Although the results indicate that the first-order electrostatic interaction energy is substantial, the presence of multiple hydrogen bonds in investigated complexes can lead to significant value of induction component.

Long-range interaction of anisotropic systems

The first-order electrostatic interaction energy between two far-apart anisotropic atoms depends not only on the distance between them but also on their relative orientation, according to Rayleigh-Schrödinger perturbation theory. Using the first-order interaction energy and the continuum model, we study the long-range interaction between a pair of parallel pristine graphene sheets at zero temperature. The asymptotic form of the obtained potential density, , is consistent with the random phase approximation and Lifshitz theory. Accordingly, neglectance of the anisotropy, especially the nonzero first-order interaction energy, is the reason why the widely used Lennard-Jones potential approach and dispersion corrections in density functional theory give a wrong asymptotic form .

Coupled-oscillator theory of dispersion and Casimir-Polder interactions.

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r(-4), a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called "remarkable formula" for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.

Extension of the Hartree−Fock Plus Dispersion Method by First-Order Correlation Effects

The Hartree−Fock plus dispersion (HFD) method for calculations of intermolecular interaction energies has been extended by the addition of the correlation part of the first-order interaction energy computed from Kohn−Sham determinants of monomers. This extension increases the computational requirements of the HFD approach only insignificantly and at the same time reduces the uncertainties of the interaction energies several times for most of the investigated systems. Thus, the proposed method becomes an attractive computational tool for investigating interactions of very large molecules at the HF-level costs.

Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data

Symmetry-adapted perturbation theory (SAPT) was applied to the helium dimer for interatomic separations R from 3 to 12 bohrs. The first-order interaction energy and the bulk of the second-order contribution were obtained using Gaussian geminal basis sets and are converged to about 0.1 mK near the minimum and for larger R. The remaining second-order contributions available in the SAPT suite of codes were computed using very large orbital basis sets, up to septuple-zeta quality, augmented by diffuse and midbond functions. The accuracy reached at this level was better than 1 mK in the same region. All the remaining components of the interaction energy were computed using the full configuration interaction method in bases up to sextuple-zeta quality. The latter components, although contributing only 1% near the minimum, have the largest uncertainty of about 10 mK in this region. The total interaction energy at R=5.6 bohrs is -11.000+/-0.011 K. For R< or =6.5 bohrs, the supermolecular (SM) interaction energies computed by us recently turned out to be slightly more accurate. Therefore, we have combined the SM results for R< or =6.5 bohrs with the SAPT results from 7.0 to 12 bohrs to fit analytic functions for the potential and for its error bars. The potential fit uses the best available van der Waals constants C(6) through C(16), including C(11), C(13), and C(15), and is believed to be the best current representation of the Born-Oppenheimer (BO) potential for helium. Using these fits, we found that the BO potential for the helium dimer exhibits the well depth D(e)=11.006+/-0.004 K, the equilibrium distance R(e)=5.608+/-0.012 bohrs, and supports one bound state for (4)He(2) with the dissociation energy D(0)=1.73+/-0.04 mK, and the average interatomic separation R=45.6+/-0.5 A.

The Attractive Gauche Effect of Ethylene Oxides

Conformational energies of monomeric (1,2-dimethoxyethane, DME) and trimeric (triglyme) model compounds of poly(ethylene oxide) have been evaluated by accurate ab initio molecular orbital (MO) calculations at the MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. The first-order interaction energies (E σ 's) for gauche states around the C-C bonds of DME and the terminal repeating unit of triglyme are ca. +0.1 kcal mol -1 , whereas the central unit of triglyme has a slightly negative E σ value of ca. -0.1 kcal mol -1 . For the C-C bond conformations of triglyme, the MO calculations exactly agree with NMR observations using a nonpolar solvent of cyclohexane-d 22 . The attractive gauche effect of the ethylene oxides has been shown to exist independently of intramolecular (C-H)···O hydrogen bonds.

Conformational Characteristics of Poly(trimethylene sulfide) and Structure−Property Relationships of Representative Polysulfides and Polyethers

Conformational characteristics of poly(trimethylene sulfide) (PTMS) have been investigated by a rotational isomeric state analysis of ab initio molecular orbital calculations and 1H and 13C NMR experiments for a monomeric model compound, 1,3-bis(methylthio)propane, and the characteristic ratio and dipole moment ratio of the unperturbed PTMS chain. Both C−S (the first-order interaction energy, −0.30 kcal mol-1) and C−C (−0.58 kcal mol-1) bonds prefer the gauche conformation. For comparison, conformational analysis of the corresponding polyether, poly(trimethylene oxide), has also been carried out. The C−O (+0.97 kcal mol-1) and C−C (−0.47 kcal mol-1) bonds show trans and gauche preferences, respectively. These results are consistent with the conformational stabilities predicted by the natural bond orbital analysis on model compounds of poly(ethylene sulfide) (PES) and poly(ethylene oxide). Without the strong S···S repulsion, therefore, the C−C bond adjacent to the C−S bond exhibits its inherent gauche preference. Without the (C−H)···O attraction, the ethereal C−C bond is subject to the attractive gauche effect. For representative polysulfides and polyethers, relationships between conformations in the ϑ and crystalline states and thermal properties have been investigated. Even in the ϑ and crystalline states, the polymers mostly keep the conformational preferences found for their small model compounds; as an exception, poly(propylene sulfide) and poly(propylene oxide), having a methyl side chain, crystallize to adopt the metastable all-trans conformation. On average, the configurational entropy of the polymers amounts to 80−90% of entropy of fusion, and the configurational energy change between crystalline and molten states accounts for ca. 30% of enthalpy of fusion. Of the polymers investigated here, PES has an exceptionally high melting point; the dipole−dipole interaction in the PES crystal was evaluated to be −1.0 kcal mol-1 (ca. 30% of the enthalpy of fusion), thus being the source of the thermostability.

Conformational Analysis of Poly(propylene sulfide)

Conformational characteristics of poly(propylene sulfide) (PPS, [CH2C*H(CH3)S]x) have been investigated. Proton and carbon-13 NMR vicinal coupling constants observed from its monomeric model compound, 1,2-bis(methylthio)propane (BMTP, CH3S−CH2−C*H(CH3)−SCH3), were analyzed to yield bond conformations of the S−C, C−C*, and C*−S bonds. Ab initio molecular orbital (MO) calculations at the MP2/6-311+G(3df,2p)//HF/6-31G(d) and B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) levels were carried out for BMTP to evaluate free energies and dipole moments of all the possible conformers. Conformational energies and bond dipole moments of BMTP were estimated therefrom. Conformational energies of BMTP and PPS were also determined by simulations based on the rotational isomeric state scheme for experimental observations of bond conformations of BMTP, characteristic ratio of atactic PPS, and dipole moment ratios of isotactic and atactic PPS. The first-order interaction energies for the S−C (Eσ) and the C−C* (Eα and Eβ) bonds were obtained as follows: Eσ = −1.0 to −0.60 kcal mol-1, Eα = 0.5−0.6 kcal mol-1, and Eβ = 1.1−1.2 kcal mol-1. The second-order ω1 and ω2 interactions, representing intramolecular C−H···S interactions, are repulsive: Eω1 = 0.6−0.9 kcal mol-1 and Eω2 = 1.0−1.2 kcal mol-1. The S−C, C−C*, and C*−S bonds were found to prefer the gauche, trans, and trans states, respectively. The conformational characteristics of unperturbed PPS are similar to those of poly(ethylene sulfide) but significantly different from those of its corresponding polyether, poly(propylene oxide) (PPO), although isotactic PPS and PPO are isomorphous. The conformational characteristics of PPS are discussed in terms of solvent effect, crystal structure, and thermal properties.

First-order intermolecular interaction energies from Kohn–Sham orbitals

It is investigated whether similar to Brueckner orbitals also Kohn–Sham monomer orbitals from current density functional approaches reliably reproduce electron correlation effects on first-order Coulomb and exchange dimer interaction energies. While the Coulomb energy is potentially exact, i.e., exact, if the monomers exact exchange-correlation potential were known, this is not true for the exchange interaction energy. Considering He 2, Ne 2, Ar 2 , NeAr, NeHF, ArHF, ( H 2) 2, ( HF) 2 , and (H 2O) 2 it is nevertheless found that electron correlation effects on both Coulomb and exchange energies were accurately reproduced when the orbitals were determined with the newly developed asymptotically correct exchange-correlation potential PBE0AC.

Conformational Characteristics of Poly(ethylene sulfide) and Poly(ethylene oxide): Solvent Dependence of Attractive and Repulsive Gauche Effects

Conformational characteristics of poly(ethylene sulfide) (PES), poly(ethylene oxide) (PEO), and their oligomeric model compounds have been investigated by the rotational isomeric state (RIS) analysis of ab initio molecular orbital (MO) calculations, NMR vicinal coupling constants, characteristic ratios, and dipole moment ratios. Conformational energies of PES were determined from 1H and 13C NMR vicinal constants of its monomeric model compound, 1,2-bis(methylthio)ethane (BMTE), and ab initio MO calculations for BMTE at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) and MP2/6-311+G(3df,2p)//HF/6-31G(d) levels. By the NMR analysis, the firs-order interaction energies for the gauche states around the C−C and C−S bonds, designated as Eσ and Eρ respectively, were evaluated as follows: in benzene, Eσ = 0.41 kcal mol-1 and Eρ = −0.74 kcal mol-1; in chloroform, Eσ = 0.31 kcal mol-1 and Eρ = −0.41 kcal mol-1. The C−C and C−S bonds were shown to prefer the trans and gauche conformations, respectively. These tendencies are consistent with the MO calculations: B3LYP, Eσ = 1.39 kcal mol-1 and Eρ = −0.24 kcal mol-1; MP2, Eσ = 0.89 kcal mol-1 and Eρ = −0.41 kcal mol-1. Inasmuch as the MO calculations represent gaseous BMTE, the conformational energies were indicated to have large solvent dependence. Ab initio MO calculations at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) and MP2/6-311+G(3df,2p)//HF/6-31G(d) levels and by the complete basis set (CBS-Q) method were carried out for 1,2-dimethoxyethane (DME), a model compound of PEO. All of the MO calculations showed the presence of the (C−H)···O attraction in the g±g∓ conformations for the C−C/C−O bond pairs. The MP2 calculations gave the first-order interaction energies (Eσ and Eρ) for the gauche states around the C−C and C−O bonds as 0.32 and 1.22 kcal mol-1, respectively. The conformational energy Eω representing the (C−H)···O interaction was evaluated as −1.12 kcal mol-1. In the RIS scheme, bond conformations of PEO in 1,4-dioxane and dipole moment ratios of PEO in benzene were simultaneously simulated, and the conformational energies of PEO in nonpolar organic solvents were determined: Eσ = −0.25, Eρ = 1.17, and Eω = −0.79 kcal mol-1. Ours and Abe and Mark's data [Eσ = −0.5, Eρ = 0.9, and Eω = 0.4 kcal mol-1, Abe, A.; Mark, J. E. J. Am. Chem. Soc. 1976, 98, 6468] show that the Eσ and Eω values of PEO so widely vary with solvent as to change the signs. Configurational entropies of 200 mers of PES and PEO were calculated to be 5.8−6.3 and 5.0−5.1 cal mol-1 K-1, respectively. Thus, the difference in melting point between PES (216 °C) and PEO (68 °C) was indicated to come from that in enthalpy (ΔHu) of fusion: ΔHu (PES) > ΔHu (PEO). The natural bond orbital analysis for BMTE and DME revealed the following facts. For BMTE and DME, vicinal bond−antibond interactions around the C−C bond cause the gauche preference. For BMTE, however, a steric S···S repulsion considerably reduces the gauche stability, and hence the trans preference appears in the C−C bond. Bond−antibond and lone pair-antibond interactions around the C−X bond (X = S or O) stabilize the gauche conformation for BMTE but the trans state for DME. Both MO calculations and NMR experiments for BMTE showed that the most stable states are g±tg∓, in which electron delocalization in the S−C−C−S antibonds is maximized and a large antiparallel dipole−dipole interaction is formed. Thus, the g±tg∓ conformations have a smaller free energy than g±tg± by ca. 0.2 kcal mol-1, being found in BMTE and PES crystals.

Conformational Analysis of Poly(methylene sulfide) and Its Oligomeric Model Compounds: Anomeric Effect and Electron Flexibility of Polythioacetal

Conformational characteristics of poly(methylene sulfide) (PMS) and its oligomeric model compounds have been investigated. Carbon-13 NMR measurements for a dimeric model compound, bis(methylthio)methane, in the gas phase as well as in solutions were carried out, and the first-order interaction energy Eσ representing the gauche stabilization of the C−S bond was determined from observed vicinal C−H coupling constants. For example, the Eσ value for the gaseous dimer was evaluated as −1.43 ± 0.01 kcal mol-1, being in good agreement with the ab initio molecular orbital calculation (−1.38 kcal mol-1) at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) level. The conformational energy Eσ showed solvent dependence; polar solvents stabilize the trans conformation, in which dipole moments are parallel to each other and hence the molecule becomes polar. The characteristic ratio, dipole moment ratio, and configurational entropy of unperturbed PMS were estimated by the rotational isomeric state scheme and compared with those of poly(methylene oxide) (PMO). The PMS chain was indicated to be more flexible than PMO. The difference in melting point between PMS (245 °C) and PMO (180 °C) was suggested to come mainly from that in enthalpy (ΔHu) of fusion: ΔHu(PMS) > ΔHu(PMO). The geometrical parameters, electron densities, and atomic charges of trimers of PMS and PMO, obtained from the MO calculations, showed that the gauche stability in the C−S bond of the PMS homologues comes partly from antiparallel dipole−dipole interaction and nS → hyperconjugation formed in the gauche state, partly from steric S···S repulsion occurring in the trans form. It was also shown that sulfur electrons have such flexibility as to reduce the S···S repulsion and unfavorable (parallel) dipole−dipole interaction.

Fast approximation of the first-order intermolecular interaction energy: ab initio calculations using biorthogonal orbitals

The first-order intermolecular interaction energy is computed from a second-quantization-based perturbation method using biorthogonal orbitals. This symmetric treatment allows fast ab initio calculations of the first-order intermolecular interaction energy. In the present stage of the work, the effects of the intramolecular correlation are neglected. The truncation of the basis set (leading to the well-known BSSE in supermolecule treatments) is corrected by using the basis set of the dimer for the monomers. The calculation of the long-range electrostatic term also allows to define an exchange term corresponding to the use of a symmetry adapted perturbation method. The meaning of the electrostatic and exchange terms in these two kinds of decomposition is discussed. The relation with semi-empirical approximations is commented.

MRCI calculations on the helium dimer employing an interaction optimized basis set

Multireference configuration interaction (MRCI) calculations are presented for the helium dimer employing a new, 301-orbital basis set consisting of a [8s]6p5d4f3g2h atom-centered set and a set of 3s3p2d2 f1g midbond functions. The basis was specifically designed to optimally describe the [self-consistent field+second-order Möller–Plesset (SCF+MP2)] He2 interaction energy (at R=4.0 bohr), using a procedure recently developed for calculations on the water dimer. The MRCI calculations employ an 78-configuration reference set, which is capable of reaching full CI quality. Using the difference between the limiting (coupled-cluster single double triple [CCSD(T)]) values of Klopper and Noga [J. Chem. Phys. 103, 6127 (1995)] and the present values in order to account for basis set incompleteness, the final He2 well depth is found to be ΔE(R=5.6)=−10.99±0.02 K while at R=4.0 bohr one finds 292.72±0.2 K. These values are in excellent agreement with the results of Komasa and Rychlewski [Mol. Phys. 91, 909 (1997)], obtained in variational calculations using explicitly correlated Gaussian-type geminal wave functions. This paper also considers the role of the Möller–Plesset polarization dispersion energy Edisp(20) as well as the correlated first-order interaction energy E(1), as arising in the symmetry-adapted perturbation theory (SAPT) theory, in determining the binding energy at different levels of correlation [MP2, MP3, CCSD(T) and 78-MRCI]. From these results it appears that the SAPT calculations of Korona et al. [J. Chem. Phys. 106, 5109 (1997)] incorrectly predicted significantly more attraction at both distances.

Analytic first-order properties from explicitly correlated many-body perturbation theory and Gaussian geminal basis

Theory of analytic first-order properties is formulated in a basis set independent way using the first-quantized many-body perturbation theory. This formulation allows the correlation effects to be described with explicitly correlated basis sets. The basis of Gaussian geminals is employed to calculate the second- and third-order correlation corrections to the lowest multipole moments of the H2 and LiH molecules. The same formalism is also utilized to compute the intra-atomic correlation contribution to the first-order interaction energy for the helium dimer. The results compare favorably with the literature data obtained using the conventional, orbital basis approach.

The PMO method for analysis of structural features of polycyclic aromatic hydrocarbons relevant to asphaltenes

Use of the simple perturbation molecular orbital (PMO) method allows the first-order estimation of energies of formation ( E f) of polycyclic aromatic hydrocarbons (PAH) as well as their localization ( E L) and bislocalization ( E b) energies. These calculations give theoretical support to experimental evidence in the literature which suggests that massive systems (more than six condensed aromatic rings) are not likely to be found in significant quantities in petroleum samples. From E L and E f it is predicted that ortho- and peri-fused systems such as pyrene are more likely than ortho-fused systems such as chrysene. The PMO method is also used for the estimation of first-order interaction energies responsible for the stabilization of free radicals.

Accurate Heitler-London interaction energy for He2

A 75-term Gaussian geminal wave function for the helium atom that has a variational energy within 0.42 μhartree of the exact one is constructed. It predicts an electron density that agrees to better than 0.4% with the predictions of energetically superior Hylleraas wave functions to electron-nucleus distances as large as 6 a 0 . The first-order Heitler-London interaction energy E (1) between a pair of helium atoms was computed using an antisymmetrized product of this Gaussian geminal wave function for each of the atoms. This interaction energy is an essential component in the exchange-Coulomb model for the He 2 potential. Our E (1) is probably converged to within 0.03 μhartree for interatomic distances between 3.0 a 0 and 7.5 a 0 . The Coulombic part of the interaction energy was checked by computations using even more accurate Hylleraas wave functions for the monomers. Comparison with an E (1) value computed from self-consistent-field atomic wave functions shows that intra-atomic correlation effects range between 4% and 9%.

Accurate Heitler-London interaction energy for He 2

A 75-term Gaussian geminal wave function for the helium atom that has a variational energy within 0.42 μhartree of the exact one is constructed. It predicts an electron density that agrees to better than 0.4% with the predictions of energetically superior Hylleraas wave functions to electron-nucleus distances as large as 6 a 0. The first-order Heitler-London interaction energy E (1) between a pair of helium atoms was computed using an antisymmetrized product of this Gaussian geminal wave function for each of the atoms. This interaction energy is an essential component in the exchange-Coulomb model for the He 2 potential. Our E (1) is probably converged to within 0.03 μhartree for interatomic distances between 3.0 a 0 and 7.5 a 0. The Coulombic part of the interaction energy was checked by computations using even more accurate Hylleraas wave functions for the monomers. Comparison with an E (1) value computed from self-consistent-field atomic wave functions shows that intra-atomic correlation effects range between 4% and 9%.

First-order Coulomb interaction energies for atoms and diatomic molecules

Abstract Gaussian multipoles (differentiated Gaussian functions) are used to describe molecular charge densities. Their use simplifies considerably the calculation of the first-order Coulomb interaction energy between pairs of molecules, which is an important part of the intermolecular potential. Methods are developed for expressing the charge densities of linear molecules economically and accurately using Gaussian multipoles. Partial-wave expansions are calculated for the first-order Coulomb interaction energies of H2-He, N2-He, CO-He, H2-H2, N2-N2 and CO-H2, and their convergence is discussed as a function of molecular anisotropy and intermolecular separation. It is confirmed that the multipole approximation is very inaccurate for physically important dimer separations.

First-order Coulomb interaction energies for atoms and diatomic molecules

Abstract Gaussian multipoles (differentiated Gaussian functions) are used to describe molecular charge densities. Their use simplifies considerably the calculation of the first-order Coulomb interaction energy between pairs of molecules, which is an important part of the intermolecular potential. Methods are developed for expressing the charge densities of linear molecules economically and accurately using Gaussian multipoles. Partial-wave expansions are calculated for the first-order Coulomb interaction energies of H2-He, N2-He, CO-He, H2-H2, N2-N2 and CO-H2, and their convergence is discussed as a function of molecular anisotropy and intermolecular separation. It is confirmed that the multipole approximation is very inaccurate for physically important dimer separations.