Ller Plesset Research Articles

Ab initio study of the π-π interactions between CO2 and benzene, pyridine, and pyrrole

The π–π interactions between CO2 and three aromatic molecules, namely benzene (C6H6), pyridine (C5H5N), and pyrrole (C4H5N), which represent common functional groups in metal-organic/zeoliticimidazolate framework materials, were characterized using high-level ab initio methods. The coupled-cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second-order M⊘ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2-QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C4H5N > C6H6 ∼ C5H5N and was roughly correlated with the aromaticity and the charge transfer between CO2 and aromatic molecule in clusters. Compared with hydrogen-bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2-QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO2 and aromatic molecules. © 2013 Wiley Periodicals, Inc.

Structural and charge‐transfer properties of indolylfulgides

The structural and electronic properties of a photochromic molecule dictate their potential photochemical activity. To gain insight into these influences, the ground‐state structure and excited state properties of six indolylgulgides were calculated using several time dependent‐density functional theory (DFT) (TD‐DFT)//DFT methods, second‐order M⊘ller–Plesset (MP2), and CIS(D). These methods simulated the charge‐transfer properties and the conformation of the ground‐state structure for each molecule. Generally, TD‐DFT accurately simulated the expected charge‐transfer state. The degree of spatial overlap of the occupied and virtual molecular orbitals involved in the S1 transition of indolylfulgides quantitatively assessed their charge‐transfer character and was qualitatively useful in assessing their photochromic activity. The M06, M06‐2X, and M11 structures were quite similar to those calculated by MP2. Structural differences, similarities, and functional trends are compared and discussed. © 2013 Wiley Periodicals, Inc.

N=3–3 transitions of Ne-like ions in the iron group, especially Ca10+ and Ti12+

The Ti XIII 2s22p53l–3l′ and 2s2p63l–3l′ transitions that have been discussed previously on the basis of beam-foil spectra and laser-produced plasmas in comparison to semi-empirically scaled computations have now been treated by accurate ab initio multireference Mø ller–Plesset calculations. While most 2s22p53l–3l′ line identifications are supported by the new calculations, the 2s2p63l–3l′ transition arrays are revised. Theoretical level positions are given for all elements from Ca through Fe. The quality of the calculation is demonstrated on beam-foil spectra of Ca.

Microscopic models for self-trapped excitons in [formula omitted]-PTCDA

The three slowest radiative recombination channels observed in photoluminescence (PL) spectra of α -PTCDA single crystals can be assigned to radiative recombination between two oppositely charged molecules in different relative positions, and to an excimer in a stack geometry. For both kinds of self-trapped excitons, we construct dimer geometries involving changes of the inter-molecular distance and internal deformations of each molecule. The Stokes shift resulting from self-trapping along the inter-molecular separation is analysed with a combination of second-order M ø ller–Plesset theory (MP2) and configuration interaction of singles (CIS), and the red shift arising from the internal deformations with time-dependent density functional theory (TD-DFT). The combination of the observed PL energies with these microscopic calculations of the Stokes shift allows an assignment of the lowest charge transfer transition in the undeformed crystal. Along the stacking direction, it occurs at 2.06 eV, far below previous estimates based on micro-electrostatic calculations.

Geometries and multipole moments of AlH 4−, SiH 4, PH 3, H 2S and HCl

Second-order M o ̷ ller–Plesset, perturbation theory geometry optimizations for AlH 4 −, SiH 4, PH 3, H 2S and HCl are performed with [11s8p2d1f] and [11s8p3d2flg] basis sets of contracted Gaussian-type functions. The electric dipole, quadrupole and octopole moments of these molecules are computed at the predicted equilibrium geometries. The calculated geometries and multipole moments are in fine agreement with previous experimental results and computations of sufficiently high quality. The calculated octopole moments are the only ones available for three of these molecules.

The effect of electron correlation on the structure and properties of the benzenium ion

Ab initio restricted Hartree—Fock (RHF) calculations which incorporate electron correlation via M∅ller—Plesset theory are presented for the isoelectronic species benzene and benzenium, (C 6H 7) +. Significant geometrical differences are found between this study and the results of previous studies at the RHF level. The proton affinity of benzene is predicted to be 184.6 kcal mol −1, in excellent agreement with experiment. A limited potential surface study predicts protonation at a single carbon atom site. Various one-electron properties are reported for the predicted equilibrium structures.

Second-order perturbation on a SDCI calculation

Starting from a SDCI calculation the SD eigenvector is perturbed by all triply and quadruply excited determinants. Efficiency is promoted through direct CI techniques, however, some flexibility has been kept, making possible the use of various perturbational schemes (here: Epstein—Nesbet and M∅ller—Plesset). The SDCI starting point avoids divergence problems posed by CCSD(T) and also by purely perturbative methods such as MP4. Several calculations on the potential curves of some molecules (H 2O, N 2, F 2, Ne 2) show that the present method is at least as good as the MP4 or CCSD(T) methods at comparable computational cost.

Open-shell M∅ller—Plesset perturbation theory

In a previous paper, the spin constrained unrestricted Hartree—Fock method (SUHF) was introduced, in which the UHF method was amended by a constraint that 〈 Ŝ 2〉 should have a prescribed value with λ the associated Lagrange multiplier. It was shown that the limit λ→∞ gave the high spin restricted open-shell Hartree—Fock (ROHF) wavefunction and energy, although the orbitals are rotated. Here it is shown how the λ→∞ results are achieved analytically directly from ROHF calculations. M∅ller—Plesset perturbation theory may then be set up within the amended Fock operators of SUHF theory, based upon the unrestricted formalism. Single replacement contributions enter into the first-order wavefunction. The convergence of this restricted open-shell M∅ller—Plesset perturbation theory (ROMP) is examined to high order using our full configuration interaction program. The calculations show none of the slow convergence properties associated with the UMP series. For NH 2 (C 2v, 1.5 r e) and CN ( r e). ROMP2 and ROMP4 are a substantial improvement over UMP2 and UMP4.

Highly correlated systems. Excitation energies of first row transition metals Sc–Cu

The low-lying dns2→dn+1s1 excitation energies of the first row transition metal atoms Sc–Cu are calculated using fourth-order M≂ller–Plesset perturbation theory (MP4) as well as quadratic configuration interaction (QCI) techniques with large spd and spdf basis sets. The MP4 method performs well for Sc–Mn but fails dramatically for Fe–Cu. In contrast, the QCI technique performs uniformly for all excitation energies with a mean deviation from experiment of only 0.14 eV after including relativistic corrections. f functions contribute 0.1–0.4 eV to the excitation energies for these systems. The highly correlated d10 state of the Ni atom is also considered in detail. The QCI technique obtains the d9s1→d10 splitting of the Ni atom with an error of only 0.13 eV. The results show that single-configuration Hartree–Fock based methods can be successful in calculating excitation energies of transition metal atoms.

The molecular structure and vibrational spectrum of the cyclopropenyl cation, C3H+3, and its deuterated isotopomers

The equilibrium structure, harmonic vibrational frequencies, infrared intensities, anharmonic constants, vibration–rotation interaction constants and quartic and sextic centrifugal distortion constants of C3H+3, the cyclopropenyl cation, and its deuterated isotopomers have been determined via purely ab initio quantum-mechanical methods. Two one-particle basis sets have been employed in conjunction with second-order M≂ller–Plesset perturbation theory (MP2), singles and doubles configuration interaction (CISD), and singles and doubles coupled cluster (CCSD). The best estimate of the harmonic frequencies is obtained from MP2 with a triple zeta plus double polarization (TZ2P) basis set. The anharmonic analysis has been determined via second-order perturbation theory using a double zeta plus polarization (DZP) self-consistent-field (SCF) full quartic force field. A generalization of formulas for the anharmonic analysis of D3h symmetric tops is discussed. The complete quartic force field in symmetry internal coordinates is given. Additionally, the anharmonic constants, vibration–rotation interaction constants and quartic and sextic centrifugal distortion constants for C3H+3 and C3D+3 are reported. Predictions of the fundamental vibrational frequencies for C3H+3 and all its deuterated isotopomers are reported. At the TZ2P MP2 level of theory the equilibrium structure of cyclopropenyl cation is Re(C–C)=1.3647 Å, Re(C–H)=1.0753 Å. Coupling the TZ2P MP2 harmonic frequencies with the DZP SCF anharmonic corrections, the infrared active fundamentals of C3H+3 are predicted to occur at 3136, 1289, 939, and 773 cm−1, with those of C3D+3 predicted to occur at 2346, 1243, 684, and 567 cm−1.

Proton transfers between first- and second-row atoms: (H2OHSH2)+ and (H3NHSH2)+

A b initio molecular orbital methods are used to study the transfer of the central proton along the hydrogen bonds in (H2OHSH2)+ and (H3NHSH2)+. Proton transfer potentials are generated using the 4-31G* basis set at the Hartree–Fock level for various values for the hydrogen bond length R(XS). Full geometry optimizations are carried out at each stage of proton transfer. The barrier to proton transfer increases as the hydrogen bond is lengthened. For a given bond length, the highest barriers are observed for transfer from N to S and the smallest for the reverse process. Intermediate between these two extremes are transfers between O and S for which the forward and reverse transfers lead to nearly identical barrier heights. Adiabatic transfers, in which the intermolecular separation is allowed to change as the transfer progresses, are studied as well. The barrier to adiabatic transfer from OH2 to SH2 is 2.6 kcal/mol; 1.9 for the reverse process. Similar relaxation of R(NS) leads to no stable (NH3)(SH3)+ structure and hence transfer from N to S is not expected. Application of larger basis sets and inclusion of correlation effects through second and third-order M≂ller–Plesset corrections support the reliability of the HF/4-31G* results.

Studies of dispersion energy in hydrogen-bonded systems. H2O–HOH, H2O–HF, H3N–HF, HF–HF

Dispersion energy is calculated in the systems H2O–HOH, H2O–HF, H3N–HF, and HF–HF as a function of the intermolecular separation using a variety of methods. M≂ller–Plesset perturbation theory to second and third orders is applied in conjunction with polarized basis sets of 6-311G** type and with an extended basis set including a second set of polarization functions (DZ+2P). These results are compared to a multipole expansion of the dispersion energy, based on the Unsöld approximation, carried out to the inverse tenth power of the intermolecular distance. Pairwise evaluation is also carried out using both atom–atom and bond–bond formulations. The MP3/6-311G** results are in generally excellent accord with the leading R−6 term of the multipole expansion. This expansion, if carried out to the R−10 term, reproduces extremely well previously reported dispersion energies calculated via variation-perturbation theory. Little damping of the expansion is required for intermolecular distances equal to or greater than the equilibrium separation. Although the asymptotic behavior of the MP2 dispersion energy is somewhat different than that of the other methods, augmentation of the basis set by a second diffuse set of d functions leads to quite good agreement in the vicinity of the minima. Both the atom–atom and bond–bond parametrization schemes are in good qualitative agreement with the other methods tested. All approaches produce similar dependence of the dispersion energy upon the angular orientation between the two molecules involved in the H bond.

Perturbation theory and electron correlation in extended systems: Cyclic polyene model

AbstractThe applicability of the finite‐order many‐body perturbation theory to the electron correlation problem in extended one‐dimensional systems is examined. The cyclic polyenes CNHN, N = 4ν + 2, ν = 1, 2, …, with the DNh geometry as described by both the Pariser–Parr–Pople and Hubbard Hamiltonians, are employed to model the metallic‐like one‐dimensional systems. The second‐order perturbation theory contributions to the correlation energy are obtained with three different partitionings of the Hamiltonian (Hückel, M⊘ller–Plesset, and Epstein–Nesbet). The third‐ and fourth‐order contributions are also calculated in special cases. A comparison with other methods is given wherever available. For the Hubbard Hamiltonian the asymptotic behavior of the perturbation theory expansion is examined numerically. It is shown that the finite‐order perturbation expansion can provide reliable results for the correlation energy of one‐dimensional systems even in the correlation region which corresponds to the spectroscopically determined physical value of the coupling constant.

Transition state for the singlet disilene—silylsilylene isomerization

The transition state for the singlet disilene—silylsilylene isomerization has been located at the Hartree-Fock level with basis sets of split valence plus polarization function quality (6–31G **). The transition state is positioned 18.2 kcal/mol above disilene and 20.6 kcal/mol above silylsilylene at the HF level. Correlation energy corrections based on M∅ller—Plesset third-order perturbation theory lower the position of the barrier to 17.3 and 12.3 kcal/mol above disilene and silylsilylene, respectively.