Symmetry-adapted Perturbation Theories Research Articles

Characterizing the Interactions of Dimethyl Sulfoxide with Water: A Rotational Spectroscopy Study.

The interaction of dimethyl sulfoxide with water has been investigated by Fourier-transform microwave spectroscopy of the 1:1 complex and its isotopologues, complemented with quantum chemical calculations. The rotational spectra of 34S and 13C isotopologues in natural abundance and the H218O and deuterated water enriched isotopologues have been measured, allowing a partial structure determination and establishing the position of water in the complex. In the most stable conformation water was found to be the donor of a primary OH···OS bond to the oxygen atom of dimethyl sulfoxide and acceptor of two weak CH···OH bonds with the methyl hydrogen atoms of dimethyl sulfoxide. From the structural determination confirmed by quantum chemical calculations, the water molecule lies in the symmetry plane of dimethyl sulfoxide, and the complex has an overall Cs symmetry. The experimental findings are supported by atoms in molecules and symmetry-adapted perturbation theories, which allowed for determining the hydrogen bond and intermolecular interaction energies, respectively.

Is the Fluorine in Molecules Dispersive? Is Molecular Electrostatic Potential a Valid Property to Explore Fluorine-Centered Non-Covalent Interactions?

Can two sites of positive electrostatic potential localized on the outer surfaces of two halogen atoms (and especially fluorine) in different molecular domains attract each other to form a non-covalent engagement? The answer, perhaps counterintuitive, is yes as shown here using the electronic structures and binding energies of the interactions for a series of 22 binary complexes formed between identical or different atomic domains in similar or related halogen-substituted molecules containing fluorine. These were obtained using various computational approaches, including density functional and ab initio first-principles theories with M06-2X, RHF, MP2 and CCSD(T). The physical chemistry of non-covalent bonding interactions in these complexes was explored using both Quantum Theory of Atoms in Molecules and Symmetry Adapted Perturbation Theories. The surface reactivity of the 17 monomers was examined using the Molecular Electrostatic Surface Potential approach. We have demonstrated inter alia that the dispersion term, the significance of which is not always appreciated, which emerges either from an energy decomposition analysis, or from a correlated calculation, plays a structure-determining role, although other contributions arising from electrostatic, exchange-repulsion and polarization effects are also important. The 0.0010 a.u. isodensity envelope, often used for mapping the electrostatic potential is found to provide incorrect information about the complete nature of the surface reactive sites on some of the isolated monomers, and can lead to a misinterpretation of the results obtained.

Revealing Factors Influencing the Fluorine-Centered Non-Covalent Interactions in Some Fluorine-Substituted Molecular Complexes: Insights from First-Principles Studies.

We examine the equilibrium structure and properties of six fully or partially fluorinated hydrocarbons and several of their binary complexes using computational methods. In the monomers, the electrostatic surface of the fluorine is predicted to be either entirely negative or weakly positive. However, its lateral sites are always negative. This enables the fluorine to display an anisotropic distribution of charge density on its electrostatic surface. While this is the electrostatic surface scenario of the fluorine atom, its negative sites in some of these monomers are shown to have the potential to engage in attractive engagements with the negative site(s) on the same atom in another molecule of the same type, or a molecule of a different type, to form bimolecular complexes. This is revealed by analyzing the results of current state-of-the-art computational approaches such as DFT, together with those obtained from the quantum theory of atoms in molecules, molecular electrostatic surface potential and symmetry adapted perturbation theories. We demonstrate that the intermolecular interaction energy arising in part from the universal London dispersion, which has been underappreciated for decades, is an essential factor in explaining the attraction between the negative sites, although energy arising from polarization strengthens the extent of the intermolecular interactions in these complexes.

Electron Density Based Partitioning Scheme of Interaction Energies.

In this paper, a new partitioning of the complex interaction energy is proposed. This new partitioning is based on the decomposition of the one-electron and exchange-correlation densities into unperturbed and deformation densities. Thus, the proposed energy fragmentation can be applied at the SCF level and post-SCF levels as long as the corresponding density matrices have been evaluated previously. It provides the typical description of the complex interaction as a summation of electrostatic, exchange-repulsion, and polarization terms. However, the new method allows splitting up the exchange-repulsion into exchange and Pauli-repulsion energies. A full theoretical description of the method is presented, and some examples of its application to small complexes are discussed. A comparison with results obtained using perturbation methods is also carried out, showing that the first order terms obtained from symmetry adapted perturbation theories are perfectly reproduced with the new method. A clear bridge between qualitative deformation density plots and quantitative measures of the interaction energy components can be established within the framework of this new partitioning scheme, giving rise to a graphical and very intuitive interpretation of the complex formation.

Two new symmetry-adapted perturbation theories for the calculation of intermolecular interaction energies

We outline two new symmetry-adapted perturbation theories (SAPTs) and present some results obtained with them. The first is superior to the symmetrized Rayleigh–Schrodinger (SRS) theory in that it corrects a fundamental defect of that theory, namely, that carried to infinite order the SRS theory cannot predict even the ground-state energy for most interacting atoms and molecules. The new theory includes correction terms which have a large cumulative effect, but which, order by order, make only small contributions. When applied to interacting closed-shell systems and truncated after first order in the wave function, it is equal in accuracy to the SRS theory. Thus, it provides both an understanding of why the SRS theory gives results of useful accuracy and justification for its continued use when truncated to low order. The second new SAPT also corrects the SRS theory's flaw, but achieves significantly greater accuracy than the SRS theory when truncated after first order in the wave function. Applied to the interaction between the open-shell Li and H atoms, a critical test case, the second theory gives the ground-state dissociation energy with an error of 1%, whereas the SRS theory is in error by 38%. The LiH molecule is a critical test case because its physical ground-state energy, like that of nearly all systems, lies in a continuum of accessible states which violate the Pauli exclusion principle.

The generalized Heitler-London theory for interatomic interaction and surface integral method for exchange energy

Based on the theory of the permutation group and the Rayleigh-Schrodinger perturbation theory, a systematic procedure is developed for the calculation of interatomic potentials. When this method is applied to the H molecule, the triplet (t) and singlet (s) energies are given by N N E = epsilon + s 1 epsilon, t, s n n x n = n = where epsilon and s are the n th-order polarization energy and overlap integral n n respectively, and epsilon is the exchange energy defined as epsilon = ( E - E ) 2. With N = 1, x x t s this expression is shown to be identical with the usual Heitler-London energy ; therefore this method is called generalized Heitler-London (GHL) theory. When epsilon x is expanded in terms of the Coulomb integral and the exchange integral, many previous symmetry-adapted perturbation theories are shown to be subsets of this expansion. The advantage of the GHL theory is that, instead of using the approximate exchange integrals, the exchange energy calculated from the surface integral method can be used directly. After a careful examination of the surface integral method for H and H, the exchange energy in a multielectron diatomic system is shown to be equal to the exchange energy of a single electron pair times a constant which can be obtained from a simple counting procedure. According to this theory, the energy curves of van der Waals potentials depend only on the known dispersion coefficients, the amplitude of the asymptotic wavefunctions, and the ionization energy of the individual atoms. With a simple analytical expression, potentials of many different diatomic systems are predicted with a high degree of accuracy. The GHL theory is also applied to the triatomic H system. Many previous semiempirical surfaces including the well known London-EyringPolanyi-Sato surface are examined in the light of the present result. In particular, the Cashion-Herschbach surface is shown to encompass far more information than previously recognized. The new theory now contains all the terms needed for an exact calculation.

Second-order exchange effects in intermolecular interactions. The water dimer

A new method of deriving explicit formulas for the calculation of second-order exchange contributions (induction as well as dispersion) within the framework of symmetry-adapted perturbation theories is presented. It is shown how exchange contributions can be expressed as a combination of electrostatic interaction energies between suitably generalized charge distributions (overlap intermolecular charge distributions). Each of these contributions are derived within the Hartree–Fock approximation (neglect of all electron correlation effects within the noninteracting molecules) and by considering only single-electron exchange between interacting molecules. Numerical calculations for the interaction of two water molecules are presented. In the region of the equilibrium geometry, it is found that the complete second-order exchange contribution accounts for about 20% of the total intermolecular interaction energy. This contribution is essentially dominated by the exchange induction component which is found to represent approximately 1 kcal/mol (using a basis set containing 94 orbitals). To our knowledge, this is the first example of calculation of exchange induction interaction energy for a molecular system. Concerning the less important, but non-negligible, exchange dispersion component, our result is found to agree with a very recent calculation for the water dimer.

Comment on symmetry-adapted perturbation theories

In a recent paper, Suzuki and I'Haya have criticized many of the proposed symmetry-adapted perturbation theories on the grounds that they are not physically adequate. We show that these criticisms are without merit.

Comments on the symmetry-adapted perturbation treatments of molecular interaction

Symmetry-adapted perturbation theories published so far are criticised. Extra conditions imposed in most of these formalisms are found to be not always physically adequate. We conclude that the formalism proposed by Hirschfelder and Silbey is the most appropriate.

Padé approximants and symmetry-adapted perturbation theories

Exchange or symmetry-adapted perturbation theories often converge slowly or even diverge. By means of calculations based on the Epstein-Johnson model it is demonstrated that Padé approximants to the series have much better convergence properties and can converge when the associated series diverge. Similar conclusions are found for the recently introduced symmetry-adapted double perturbation theories.

On the relation between Peierls' perturbation theory for projected states and exchange perturbation theory

The derivations of a rather general class of exchange perturbation theories (or symmetry-adapted perturbation theories) and Peierls' perturbation theory for projected states are discussed. While the approaches are different, the equivalence of the resulting formalisms is established.

Symmetry Adapted Perturbation Theories: Application to a Generalized Eigenvalue Equation for the Hydrogen Molecular Ion

Analogues of the Murrell—Shaw, Musher—Amos, and van der Avoid—Hirschfelder symmetry adapted perturbation theories are devised for the case of a generalized eigenvalue equation. The new procedures are applied to the hydrogen molecule ion and perturbation energies through second order are calculated at various internuclear distances.

On the derivation of symmetry adapted perturbation theories

A general formalism is developed from which many symmetry adapted perturbation theories may be obtained. Among the special cases are the Van der Avoird-Hirschfeider, Amos-Musher, Murrell-Shaw and Musher-Amos procedures. Implicit assumptions concerning the nature of the functions calculated in these methods are discussed.