MP2 Corrections Research Articles

Treating dispersion effects in extended systems by hybrid MP2:DFT calculations—protonation of isobutene in zeolite ferrierite

We propose use of a hybrid method to study problems that involve both bond rearrangements and van-der-Waals interactions. The method combines second-order Møller-Plesset perturbation theory (MP2) calculations for the reaction site with density functional theory (DFT) calculations for a large system under periodic boundary conditions. Hybrid MP2:DFT structure optimisation for a cluster embedded in the periodic model is the first of three steps in a multi-level approach. The second step is extrapolation of the MP2 energy to the complete basis set limit. The third step is extrapolating the high-level (MP2) correction to the limiting case of the full periodic structure. This is done by calculating the MP2 correction for a series of cluster models of increasing size, fitting an analytic expression to these energy corrections, and applying the fitted expression to the full periodic structure. We assume that, up to a constant, the high-level correction is described by a damped dispersion expression. Combining the results of all three steps yields an estimate of the MP2 reaction energy for the full periodic system at the complete basis set level. The method is designed for a reaction between a small or medium sized substrate molecule and a very large chemical system. For adsorption of isobutene in zeolite H-ferrierite, the energies obtained for the formation of different structures, the pi-complex, the isobutoxide, the tert-butoxide, and the tert-butyl carbenium ion, are -78, -73, -48, and -21 kJ mol(-1), respectively. This corresponds to corrections of the pure DFT (PBE functional) results by -62, -70, -67, and -29 kJ mol(-1), respectively. Hence, the MP2 corrections are substantial and, perhaps more importantly, not the same for the different hydrocarbon species in the zeolite. Coupled-cluster (CCSD(T)) calculations change the MP2 energies by -4 kJ mol(-1) (tert-butyl cation) or less (below +/-1 kJ mol(-1) for the other species).

The adsorption of benzene on industrially important nanostructured catalysts (H-BEA, H-ZSM-5, and H-FAU): confinement effects

The structure of industrially important zeolitic catalysts (H-BEA, H-ZSM-5, and H-FAU) and their interactions with benzene have been investigated within the framework of our-own-N-layered integrated molecular orbital+molecular mechanics (ONIOM) approach utilizing the three-layer ONIOM scheme (B3LYP/6-31G(d,p):HF/3-21G:UFF). Inclusion of the extended zeolitic framework covering the nanocavity has an effect on adsorption properties and leads to differentiation of different types of zeolite, unlike the small cluster models which are not able to make this differentiation. The ONIOM adsorption energies of benzene on ZSM-5, BEA, and FAU zeolites are −19.23, −16.11, and −15.22 kcal/mol, respectively, which agrees well with the known adsorption trend of these three zeolites. On the other hand, the small cluster models underestimate the adsorption energies and even yield an unreasonable trend of adsorption energies (−8.09, −8.48, and −8.93 kcal/mol for ZSM-5, BEA, and FAU, respectively). With the inclusion of basis set superposition error (BSSE) and the MP2 corrections, the ONIOM3(MP2/6-31G(d,p):HF/3-21G:UFF) adsorption energies are predicted to be −18.96, −16.34, and −15.18 kcal/mol, for ZSM-5, BEA, and FAU, respectively. The last value can be compared well with the experimental data (−15.31 kcal/mol) for benzene adsorption on a FAU zeolite. The results derived in this study suggest that the ONIOM3(MP2/6-31G(d,p):HF/3-21G:UFF) scheme provides a more accurate method for investigating the adsorption of aromatic hydrocarbons on these zeolites.

Vibrational frequencies of (H2O) n and (D2O) n clusters for n = 2 and 8: possible relevance to inelastic neutron scattering of ice

Hartree-Fock plus MP2 corrections are reported for the vibrational frequencies in (H2O)2 and (D2O)2 and in the cubic octamers (H2O)8 and (D2O)8. The motivation was the inelastic incoherent neutron scattering of ice as studied experimentally by Li et al. (J.-C. Li, D. Londono, D.K. Ross, J.L. Finney, S.M. Bennington and A.D. Taylor (1992). J. Phys. Cond. Matter, 4, 2109). Some contact is made between our results and these experiments, and also with earlier infrared and Raman studies of Bertie and coworkers.

Abinitio study of oxygen vacancies in BaTiO3

In this paper we present embedded-cluster calculations onsingly charged and neutral oxygen vacancies (or F centres) in theoxide perovskite BaTiO3. The simulations include Hartree-Focktheory with MP2 corrections and density-functional-theorycalculations for a central quantum defect cluster and apair-potential description of the embedding lattice. All importantdefect-induced lattice distortions are taken into account in thisway. We discuss the possible electronic states of charged F centresand the effects of nearby acceptor-type defects. It is shown thatisolated oxygen vacancies induce electronic deep-gap levels.Scenarios are discussed to account for shallow-gap levels observedexperimentally.

The Thermal Decomposition of 1,2-Dioxetane Revisited

The ground state (S0) and lowest energy triplet state (T1) energy surfaces of the parent dioxetane have been extensively explored using various CASSCF active spaces with MP2 corrections in several ...

Structure and vibrations of catechol in the S 1 state and ionic ground state

To determine structure and vibrations of catechol and d2-catechol (C 6H 4(OD) 2) in the ionic ground state, MATI spectra as well as ab initio and DFT calculations are presented. The comparison of the experimentally observed vibrational frequencies with the calculated values leads to a complete assignment of all vibrations. CASSCF and DFT calculations predict a planar geometry of catechol in the S 0 and D 0 states. CASSCF calculations for the S 1 state show that the free OH group of catechol is rotated out of the plane of the aromatic ring by ∼24°. This calculation supports the assumptions of earlier experimental work. The adiabatic excitation energies (S 1←S 0) and the adiabatic ionization potentials of catechol and its deuterated isotopomer can be predicted by CASSCF calculations including zero-point energies and MP2 corrections.

HNNH3, a new possible isomer of N2H4: An ab initio study

Ab initio studies applying the 3-21G, 6-31G, and 6-31G** basis sets and also including the MP2 correction were carried out on H2NNH2, HNNH3, and the transition state of the reaction H2NNH2(DOUBLE BOND)HNNH3. First, the geometries of molecules were optimized using the theoretical methods mentioned in the restricted Hartree–Fock (RHF) scheme. The energies of the molecules corresponding to RHF/6-31G** geometries were subsequently calculated including electron-correlation effects at the level of the second-order Moller–Plesset (MP2) perturbation theory. The vibrational frequencies, net charges, and dipole moments were obtained from the theoretical calculations. The results of our calculations indicate unambiguously that H2NNH2 is thermodynamically more stable than is HNNH3. On the other hand, an isolated HNNH3 molecule once created would be stable since barriers for its unimolecular isomerization and decomposition are relatively high. But HNNH3 is unlikely to be isolated in measurable amounts because of bimolecular tautomerization. Nevertheless, HNNH3 can be considered as an intermediate in chemical processes involving N2H4. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 447–452, 1997

Ab initio studies on the structure and stability of P 3H 5

Ab initio studies applying the 3-21G, 6-31G, 6-31G ∗ and 6-31G ∗∗ basis sets and also including MP2 corrections were carried out on four conformations of triphosphine. First, the geometry of the four molecules was optimized using the theoretical methods mentioned in the Hartree-Fock (HF) scheme. The energies of the molecules at stationary points corresponding to HF/ 6-31G ∗∗ geometries were subsequently calculated including electron correlation effects on the level of the second-order Moller-Plesset (MP2) perturbation theory. Other physicochemical characteristics of the hydrides, such as vibrational frequencies, dipole moments, net charges, and energies of the lowest unoccupied and highest occupied molecular orbitals were obtained from theoretical calculations. The results of our ab initio calculations indicate that the gauche conformer between adjacent lone electron pairs and between P bonds with adjacent P bonds is the most stable conformer.

Interaction of halide ions with copper: the DFT approach

The applicability of density functional theory to the adsorbate-adsorbent interaction has been tested with the final goal of defining an appropriate combination of the DFT method with basis sets for metal cluster-halide ions studies. The Cu-X − (X = F, Cl, Br, I) systems have been taken as tests cases to probe the different DFT methods (SVWN, BP86 and B3LYP) together with different combinations of basis sets for systems of this type. For comparison, the standard HF and its MP2 and MP4 corrections have also been calculated. Additionally, the results of a test for the Cu 5I − cluster are presented. The good quality of the DFT methods is recorded as they give results comparable to the MP2 and, for some cases, even to the MP4 level of standard calculations. The B3LYP method combined with a fairly inexpensive description of the metal atoms is proposed as an appropriate option for studies of the adsorption of halide ions at noble metal surfaces.

Structure and vibrations of catechol and catechol⋅H2O(D2O) in the S and S1 state

The inter- and intramolecular vibrations in the S0 and S1 state of catechol, d2-catechol, catechol(H2O)1, and d2-catechol (D2O)1 have been investigated experimentally by resonant two photon ionization (R2PI), spectral hole burning (SHB), and dispersed fluorescence spectroscopy (DF). The experimental frequencies are compared to the vibrational frequencies obtained from ab initio normal mode calculations using the 6-31G(d,p) basis set. In order to get a complete interpretation of the S0 state spectra of d2-catechol the strong coupling of the two OD torsional motions has been taken into account. A two-dimensional calculation of the torsional eigenvalues based on an ab initio potential [6-31G(d,p) basis] obtained from single point calculations is presented. Due to these calculations all vibrations in the S0 state can be assigned. Furthermore a new assignment of the vibrations in the S1 state of d2-catechol is given. In the case of catechol (H2O)1 [d2-catechol(D2O)1] different structural isomers are discussed. Using HF ab initio calculations (including MP2, BSSE, and ZPE corrections) a trans-linear hydrogen bonding arrangement turns out to be more stable by an amount of 840 cm−1 compared to a cyclic structure which is also a minimum of the PES. Normal mode calculations have been carried out for both structures and anharmonic corrections are calculated for the τ and β2 mode of the trans-linear arrangement. The prediction of the ab initio calculations is supported by the vibrational transitions observed in the spectra of the S0 and S1 state, which can be assigned on the basis of the vibrations calculated for the trans-linear structure. The most important feature of the R2PI spectrum of catechol(H2O)1 [d2-catechol(D2O)1] is the occurrence of intermolecular vibrations of very low frequencies (14, 37 cm−1). These vibrations and the low frequency torsional modes in the spectra of the S1 state of the catechol monomer strongly support the assumption that catechol is nonplanar in the S1 state with respect to the OH groups. Due to this nonplanarity a double minimum potential for the intermolecular ρ1 mode of catechol(H2O)1 is postulated. Using this assumption the low frequency vibrations of the R2PI spectra as well as the vibrations observed in the spectra of the S0 state can be assigned.

A comparative study of the energetics, structures, and mechanisms of the HCN ↔ HNC and LiCN ↔ LiNC isomerizations

The potential energy surfaces of the HCN ↔ HNC and LiCN ↔ LiNC isomerization processes were determined by ab initio theory using fully optimized triple-zeta double polarization types of basis sets. Both the MP2 corrections and the QCISD level of calculations were performed to correct for the electron correlation. Results show that electron correlation has a considerable influence on the energetics and structures. Analysis of the intramolecular bond rearrangement processes reveals that, in both cases, H (or Li+) migrates in an almost elliptic path in the plane of the molecule. In HCN ↔ HNC, the migrating hydrogen interacts with the in-plane π,π* orbitals of CN, leading to a decrease in the C—N bond order. In LiCN ↔ LiNC, Li+ does not interact with the corresponding π,π* orbitals of CN. Key words: potential energy surfaces, intra-molecular bond rearrangement, bond orders, elliptic path, migration of Li+.

Ab Initio Molecular Orbital Calculations on Low-Energy Conformers ofN-Acetyl-N‘-methylprolineamide

The results of ab initio HF/SCF calculations on nine low-energy conformers of N-acetyl-N‘-methylprolineamide (Ac-Pro-NHMe) with trans/cis imide bonds and down/up puckerings using the STO-3G, 3-21G, and 6-31G** basis sets are reported. Single-point MP2/6-31G** calculations were performed on the HF/6-31G** optimized conformations. In ab initio calculations at all levels, the intramolecularly hydrogen-bonded C7 conformer is found to be most preferred, which is consistent with the structures deduced from IR, CD, and NMR experiments in nonpolar solvents. From HF/3-21G to HF/6-31G**, the trend for the lowering of energies of Ac-Pro-NHMe appears to be quite similar to that found for alanine dipeptides, while the variations in backbone torsion angles φ and ψ (av Δφ ≈ 2° and Δψ ≈ 9°) are different, which may be attributed to rigid constraints on the N−Cα rotation imposed by pyrrolidine ring closure. The MP2 corrections increase the HF/6-31G** energies by about 1 kcal/mol, except for the conformer tCu. The down puckering seems to be about 1.5 kcal/mol more stable than the up puckering at the HF/6-31G** and MP2/6-31G** levels. The HF/6-31G** optimized bond lengths and bond angles as well as endocyclic torsion angles χ's of the pyrrolidine ring are, in general, consistent with the corresponding values of X-ray structures of peptides, but the strong dependence of structural parameters on the conformation cannot be seen. The preference and population for down and up puckered structures with the trans and cis imide bonds calculated at the HF/6-31G** and MP2/6-31G** levels agree reasonably with the results obtained from the analysis of X-ray structures of proteins. The degree of puckering for each conformer is described by three puckering amplitudes, and the linear correlations between any two of them are discussed.

Temperature dependence of hydrogen transfer reactions via tunneling at low temperatures

AbstractIn this paper, we present a symmetrical and adiabatic reaction path for hydrogen transfer from methane by methyl by an ab initio method using the 6‐31G** basis set with the MP2 corrections for UHF/6–31G** optimized geometries. The theoretical barrier is fitted with the symmetric Eckart function. We, then, take thermal averages of the rate constant (k) considering the discrete nature of the C–H oscillators and the continuous character of the various low‐frequency modes of the composite system. Finally, we present a linear relation between log k and temperature. It is shown that this relation gives a good description of the kinetic results of both thermal and photochemical H‐transfer reactions in the region of low temperatures. © 1993 John Wiley & Sons, Inc.

Intramolecular electron correlation in the self-consistent reaction field model of solvation. A MP2/6-31G** ab initio study of the NH 3HCl complex

The effects of intramolecular electron correlation on the electronic and molecular properties of a solvated molecule have been considered in this paper throughout a general 6-31G** ab initio study of the ammonia—hydrogen chloride complex. Calculations have been performed both in vacuo and in a non-polar solvent, at the Hartree—Fock and at the second-order Møller—Plesset levels of approximation. In contrast with the isolated complex, the self-consistent reaction field model of solvation reveals the presence of two minima corresponding to an ionic and a molecular complex. The shape of the potential energy curve is substantially modified by the MP2 correction.

Basis set and correlation energy dependence of geometry and harmonic frequencies of difluoroethane, CHF2CH3

Optimum geometries and harmonic frequencies calcd. at the Hartree-Fock and the MP2 level are reported for the fluorohydrocarbon CHF2CH3; basis sets employed range from STO-3G to 6-311G**. The significantly shortened C-C distance of 1.50 .ANG. is reproduced already with the simplest split-valence basis set; the C-F distance of 1.36 .ANG. on the other hand needs MP2 correction at least at the double-z or 6-311G* level. Symmetry coordinates defined in terms of internal coordinates are in qual. agreement with available exptl. evidence. Even the best basis set yields frequencies that differ from exptl. (anharmonic) values by up to 200 cm-1 indicating the well-known necessity of including higher-order force consts. if quant. agreement with expt. is to be achieved.

Ab initio SCF and møller-plesset calculations on the hydrogen bond in hydrogen maleate

Energies of the hydrogen maleate anion were calculated for the proton located centrally ( C 2v symmetry) and off centre of the hydrogen bond (C 5 symmetry) using the STO-3G, 4-31G, 6-311G, 6-31++G and 6-31G ∗∗ basis sets with the Møller-Plesset (second order) (MP2) correlation correction on the 4-31G and 6-311G optimized geometries. The adiabatic proton potential barrier at the Hartree-Fock level is highest with the 6-311G calculation (2.12 kcal mol −1), but MP2 correction reduces it to 0.1 kcal mol −1. Non-adiabatic barriers are substantially higher. The solvation effect, calculated with a model reported previously, raises the barrier slightly. Geometrical parameters are discussed with respect to the possible strain imposed by the hydrogen bond.

Ab initio SCF and MP2 calculations of the frequency dependence of the polarizability of cyclohexane

The static and dynamic dipole polarizabilities of the cyclohexane molecule are calculated at the SCF level using a basis set optimized for polarizability calculations. MP2 corrections to the static polarizability components are used to obtain approximate MP2 dynamic polarizabilities, which are systematically 5% below the best experimental results. The Rayleigh depolarization ratio is predicted to be independent of frequency, in direct contradiction with experiment, raising questions about the role of the vibrational Raman contribution to the experimental measurements. Further observations at lower frequencies are recommended.