Intermolecular Perturbation Theory Research Articles

BSSE-free second-order intermolecular perturbation theory

A second-order BSSE-free intermolecular perturbation theory is developed starting from the orbitals and orbital energies obtained by solving the monomer SCF problems and treating electron correlation and intermolecular interaction simultaneously. The unperturbed Hamiltonian is defined as the sum of the monomer Fock operators by taking into account the intermolecular overlap. A second-quantized formalism is used in which the creation and annihilation operators pertaining to the non-orthogonal basis are expanded in terms of analogous ones in an auxiliary orthogonal basis. The first-order wavefunction is calculated by using the BSSE-free CHA Hamiltonian and the second-order energy contribution is determined by using the generalized Hylleraas functional recently proposed by one of us. The sample calculations on helium and water dimers show the applicability of the proposed scheme for most different types of intermolecular interaction.

The water dimer interaction energy: Convergence to the basis set limit at the correlated level

The water dimer interaction energy and its convergence to the basis set limit was investigated, with electron correlation effects treated at the level of second order Mo/ller-Plesset perturbation theory (MP2). ANO-type and large uncontracted basis sets were used, spreading over a wide range in size; the biggest set included 1046 functions with angular momentum up to (l=7). Core correlation effects were treated accurately by augmenting the original valence basis with extended sets of core polarization functions. The MP2 dimer interaction energy at the basis set limit was determined to −4.94±0.02 kcal/mol, with a contribution due to core correlation of −0.04 kcal/mol. Furthermore, based on some elementary considerations from intermolecular perturbation theory, a simple procedure was devised, which brings the counterpoise corrected interaction energies of moderate basis set calculations closer to the basis set limit. The interaction energies so obtained turned out be surprisingly stable with respect to extensions of the basis set.

First-order intermolecular diatomics-in-molecule potentials. Potential energy surfaces, spectra, and fragmentation dynamics of the Ne⋯Cl2 complex

First-order perturbative approximations to the diatomics-in-molecule (DIM) approach are implemented for studying interactions between the neon atom and chlorine molecule in the X 1Σg+(0+) and B 3Πu(0+) states. Intermolecular DIM perturbation theory (IDIM PT1) [J. Chem. Phys. 104, 9913 (1996)], which accounts for the atomic component of spin-orbit interaction, is compared to the anisotropic model by Naumkin and Knowles [J. Chem. Phys. 103, 3392 (1995)] which is proven to be a first-order approximation to the nonrelativistic DIM approach. An importance of the spin-orbit effects for the ground-state potential energy surface (PES) is demonstrated. Semiempirical PESs are used in the accurate quantum calculations on the vibrationally averaged geometry, B←X vibronic spectra, and vibrational predissociation dynamics of the Ne⋯Cl2 van der Waals complex. The IDIM PT1 model is shown to provide good agreement with available experimental data. The effects of interaction potential topology on the spectroscopic and dynamic properties of the complex and the relation of DIM-based PESs to the results of ab initio calculations are discussed.

Chemical Shifts in Liquid Water Calculated by Molecular Dynamics Simulations and Shielding Polarizabilities

The gas-to-liquid chemical shifts of water have been calculated by combining molecular dynamics simulations and quantum chemically derived shielding polarizabilities. The use of a force field based on intermolecular perturbation theory ensures that the electric fields are adequately modeled. The experimental proton shift and its temperature dependence are reproduced, but the oxygen shift lacks higher order terms such as the linear field-gradient contribution. Shifts arising from the difference in the gas phase and liquid geometries of the water molecule have been estimated and discussed.

Hydrogen bonding of carbonyl, ether, and ester oxygen atoms with alkanol hydroxyl groups

An attractive way to study intermolecular hydrogen bonding is to combine analysis of experimental crystallographic data with ab initio—based energy calculations. Using the Cambridge Structural Database (CSD), a distributed multipole analysis (DMA)-based description of the electrostatic energy, and intermolecular perturbation theory (IMPT) calculations, hydrogen bonding between donor alkanol hydroxyl groups and oxygen acceptor atoms in ketone, ether, and ester functional groups is characterized. The presence and absence of lone pair directionality to carbonyl and ether or ester oxygens, respectively, can be explained in terms of favored electrostatic energies, the major attractive contribution in hydrogen bonding. A hydrogen bond in its optimum geometry is only slightly stronger when formed to a ketone group than to an ether group. Hydrogen bonds formed to carbonyl groups have similar properties in a ketone or ester, but the ester O2 differs from an ether oxygen due to various environmental effects rather than a change in its intrinsic properties. For (E)-ester oxygens, there are few hydrogen bonds found in the CSD because of the competition with the adjacent carbonyl group, but the interaction energies are similar to an ether. Hydrogen bonds to O2 of (Z)-esters are destabilized by the repulsive electrostatic interaction with the carbonyl group. The relative abundance of nonlinear hydrogen bonds found in the CSD can be explained by geometrical factors, and is also due to environmental effects producing slightly stronger intermolecular interaction energies for an off-linear geometry. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 757–774, 1997

Organic Fluorine Hardly Ever Accepts Hydrogen Bonds

AbstractStatistical analysis of structural data and detailed inspection of individual crystal structures culled from the Cambridge Structural Database and the Brookhaven Protein Data Bank show that covalently bound fluorine (in contrast to anionic fluoride) hardly ever acts as a hydrogen‐bond acceptor. The weakness of covalently bound fluorine as hydrogen‐bond acceptor is backed by results of new molecular orbital calculations on model systems using ab initio intermolecular perturbation theory (IMPT), and is in accord with results of other physicochemical studies and with the physical properties of fluorinated organic compounds. Factors influencing the strength of hydrogen bonding in extended systems are discussed.

Structure and interaction energies of the Ar…Cl 2 complex. Application of first-order intermolecular potentials

The first-order intermolecular perturbation theory developed in the frame of a diatomics-in-molecule approach is used to calculate the potential energy surfaces for the Ar…Cl 2 complex in the states which correlate with the X0 g +( 1Σ +) and B0 u + ( 3Π) states of the Cl 2 fragment. Accurate vibrational calculations performed directly with these surfaces reveal close agreement with spectroscopic data.

A perturbation theory study of adlayer CO on NaCl(100)

We have constructed a potential energy function to describe the interaction of CO molecules with each other and with the (100) surface of NaCl. It uses distributed multipoles to describe the electrostatic interactions, distributed polarizabilities to describe induction, anisotropic dispersion coefficients taken from work by Rijks and Wormer, and anisotropic atom–atom repulsion terms derived from ab initio intermolecular perturbation theory. We have also investigated the structure and charge distribution of the NaCl surface. We find that an isolated CO molecule on the NaCl(100) surface adopts a position with the CO axis perpendicular to the surface and the C atom over a surface Na+ ion, but in monolayers of CO the molecules are tilted by about 28°. There are two 1×1 and two 2×1 structures, all with very similar energies; a further 1×1 structure with the molecules perpendicular to the surface is an index-2 stationary point with energy only 32 cm−1 above the lowest-energy structure. The results are consistent with the experimental infrared spectra and with the measured enthalpy of adsorption.

Intermolecular perturbation theory: Renormalized interaction energies

For intermolecular perturbation theories in which it is assumed that the unperturbed wave function of the composite system is a product of the unperturbed wave functions of its components, and which satisfy one general constraint, we derive two renormalized interaction energy expressions which are more accurate than the perturbation expansions, when all are evaluated to comparable order. This is accomplished by focusing on the parameter λ in terms of which the perturbation expansions are derived rather than on the potential of interaction between components. In the derivation of each renormalized energy formula, we discard zeroth- through infinite-order terms which do not contribute to the interaction energy when the interaction is turned on fully, i.e., when λ = 1. The first renormalized interaction energy when λ = 1 is identical in form to the interaction energy in the symmetrized Rayleigh-Schrödinger (SRS) theory, but not in interpretation. The wave function appearing in the renormalized energy cannot generally be that assumed in the SRS theory, and the renormalized energy to zeroth order in λ is not zero. The latter is not surprising because we discarded a zeroth-order term in the derivation. The second renormalized interaction energy formula is derived from the first by using the same set of assumptions and arguments that were used in deriving the first. We expect it to be more accurate than the first, which is expected to be more accurate than the sum of the perturbation energies, all evaluated to comparable order. These expectations are supported by the results of calculations on LiH using two perturbation theories, the polarization approximation and the Amos-Musher theory. The first-order wave functions for both were calculated in the configuration interaction (CI) approximation; then the interaction energies were calculated by summing the perturbation energies through third order and by evaluating the renormalized energy expressions. The perturbation results are compared to interaction energies calculated by full CI with the same basis set. As important as the formulas is the light our analysis throws on the meaning of order in intermolecular perturbation theory. © 1996 John Wiley & Sons, Inc.

The Nature and Geometry of Intermolecular Interactions between Halogens and Oxygen or Nitrogen

The nature of intermolecular interactions between carbon-bonded halogens (C−X, X = F, Cl, Br, or I) and electronegative atoms (El = N, O and S) has been analysed, focusing on the role of specific attractive forces and the anisotropic repulsive wall around halogen atoms. Searches of the Cambridge Structural Database show that electronegative atoms in various hybridization states clearly prefer to form contacts to Cl, Br, and I (but not F) in the direction of the extended C−X bond axis, at interatomic distances less than the sum of the van der Waals radii. Ab initio intermolecular perturbation theory calculations show that the attractive nature of the X···El interaction is mainly due to electrostatic effects, but polarization, charge-transfer, and dispersion contributions all play an important role. The magnitude of the interaction for the chloro-cyanoacetylene dimer is about 10 kJ/mol, demonstrating the potential importance of these kinds of nonbonded interactions. The directionality of the interaction is ...

Three-body effects on molecular properties in the water trimer

We report an application of diffusion Monte Carlo to investigate the importance of three-body forces on the properties of the water trimer. The potential energy surface used is due to Millot and Stone and is based on intermolecular perturbation theory to which three-body induction and dispersion energies are added. The effects of the three-body forces are considered by comparison with the same potential containing only pairwise water interactions. We have calculated minimum energy structures, vibrationally averaged structures, zero-point energies, rotational constants, cluster dissociation energies, and tunneling splittings, with and without the three-body forces. The values obtained for the vibrationally averaged rotational constants with the three-body potential are fairly close to the experimental values. Whereas the rotational constants are shown to have a significant dependence, the tunneling splittings are changed little by the three-body forces. Based on the calculated difference in anharmonic zero-point energies in water dimer and trimer, we predict that vibrational excitation of a stretching mode will cause predissociation in (H2O)3 but probably not in (D2O)3.

The polarization approximation and the Amos-Musher intermolecular perturbation theories compared to infinite order at finite separations

We argue that the most common form of intermolecular perturbation theory, the polarization approximation (PA), gives at finite separations, for nearly all systems, no usable, exact relationship between the lowest unperturbed energy and the physical ground state energy. This would be true even if the PA energy expansion converged. In contrast, the Amos-Musher (AM) theory does give an exact relationship between the lowest unperturbed energy and the physical ground state energy. We find no theoretical justification for using the PA theory beyond second order in the energy, but the AM theory may be extended to arbitrarily high order.

Nonempirical intermolecular potentials for urea–water systems

In this work, we present ab initio derived intermolecular potentials for the urea–water system. Our method of calculation, which is termed NEMO, is based on intermolecular perturbation theory. Dipole moment fluctuations as well as many-body effects in an assembly of molecules are described by including atomic polarizabilities in the potential. For the urea dimer we found a cyclic minimum with an energy of −21.9 kcal/mol and two equivalent hydrogen bonds of length 1.77 Å. Noteworthy is that this interaction energy is more than four times larger than the water dimer minimum energy. To be able to satisfactorily model the interaction between two urea molecules we have improved the NEMO approach in the description of the repulsion energy and we have also included a more accurate damping on the dispersion energy. With this improved model we reinvestigated the water dimer and urea–water potentials and found good agreement with earlier potentials derived with similar approaches. From simulations of liquid water we investigated the sensitivity of structural properties resulting from small changes in repulsion parameters. Qualitative changes of the tetrahedral hydrogen bonding may occur for inappropriate parameter choices of the same potential surface.

Stereoselectivity and regioselectivity in Diels–Alder reactions studied by intermolecular perturbation theory

Diels–Alder reactions of ethene, acrolein and acrylonitrile with butadiene and its 1-methyl, 2-methyl and 2-cyano derivatives have been studied by self-consistent field intermolecular perturbation theory. The procedure is successful in reproducing the stereochemical predictions of other theoretical techniques, and provides a way to analyse the contributions to the interaction energy and to gain theoretical insight into the effects responsible for stereoselectivity. It is less successful, however, in predicting regiochemical preferences for these reactions. Possible reasons for this are discussed.

On the relative strengths of amide…amide and amide…water hydrogen bonds

We have performed Hayes—Stone intermolecular perturbation theory (IMPT) calculations on amide…water and amide…amide complexes in order to estimate the change Δ W in intermolecular interaction energy associated with the hydrogen bond exchange process amide(NH)…water+water…(OC)amide⇔amide(NH)…(OC)amide+water…water. Δ W is found to be small and varies by almost 5 kJ/mol and in sign for the amides formamide, acetamide, N-methyl formamide and N-methyl acetamide. The main variations in the amide hydrogen bond energies occur in the electrostatic and exchange-repulsion contributions. This reflects the variation in the charge distributions of the hydrogen bonding groups between the different amides. Thus, we cannot quantify an isolated hydrogen bond strength with any great accuracy, and care must be used in extrapolating model potentials based on small model systems to peptides and proteins.

The calculation of intermolecular potentials

The use of intermolecular perturbation theory to rationalize intermolecular forces and to provide a framework for concepts of intermolecular interactions has been routine for many years. It has long been assumed, however, that the route to accurate calculations of intermolecular potentials lies through ab initio supermolecule calculations, and it is only in relatively recent times that this view has been challenged. It is now clear that accurate intermolecular potentials can be constructed for regions where the molecules do not overlap by assembling the components described by long-range intermolecular perturbation theory —the electrostatic, induction and dispersion terms— though perturbation theory itself does not necessarily provide the best way to calculate them. At short range, the repulsion must be added, and the long-range terms modified to account for the effects of overlap. Here too, perturbation theory provides a useful to accurate numbers.

The nature of the N  H…︁OC hydrogen bond: An intermolecular perturbation theory study of the formamide/formaldehyde complex

AbstractWe have used Hayes‐Stone Intermolecular Perturbation Theory (IMPT) to study the variation with distance and orientation of the various components of the interaction energy of the N  H…︁O = C hydrogen bonded trans‐ formamide/formaldehyde complex, a model system for hydrogen bonding in proteins. The directionality of the total interaction energy is similar to that of the electrostatic component alone. We have analysed our data in terms of two model atom‐atom intermolecular potentials, using an isotropic functional form and an anisotropic one. The anisotropic form gives an excellent representation of the IMPT potential energy surface, considerably better than the isotropic model, and is comprised entirely of theoretically justified, physically meaningful terms.

Anisotropy of correlation effects in hydrogen-bonded systems: the HF dimer

Correlation corrections to the interaction energy of the (HF) 2 complex are evaluated within a supermolecules Møller-Plesset treatment as well as by the intermolecular perturbation theory approach. The correlation correction to the electrostatic effect is the most orientation-dependent contribution. The anisotropy of the dispersion energy is less pronounced and can be easily interpreted and predicted by considering the overlap of the occupied subsystems' orbitals. The validity of the Hartree-Fock plus dispersion (HF+D) potential in modeling H-bonded systems is discussed.

Interpretation of n-donor specific solvent effect on electronic spectra of copper acetate and chloride complexes by intermolecular perturbation theory

A simple second order intermolecular perturbation theory is proposed in the Fukui approximation to account for the electronic spectral behavior of electron acceptor solutes dissolved in pure n-donor solvents. This double perturbation theory considers explicitly both the solvating and complexing effects of the solvent. Using the electronic spectral data of mono- and binuclear copper acetate and chloride complexes obtained in pure pyridine derivatives it is shown that the predicted shifts brought about by increasing n-donor ability of solvent are fully corroborated by experiment. The sensitivity of mononuclear copper complexes to steric effects is also confirmed and it is shown that binuclear ones are not sensitive to this effect. New ionization potential values have also been determined using a simple interpolation–standardization procedure.

Applicability of the supermolecule MP2 approach to intermolecular interactions: He 2 and Ne 2

Arguments are given for applying the full counterpoise correction to eliminate properly the basis set superposition error in the correlation energy. Comparison is made with the intermolecular perturbation theory and more complete treatments (MP4, CEPA). The results for the dimers studied suggest that MP2 is a poor approximation. Even if very extended basis sets are used, hardly more than 65% of the stabilization energy is recovered.