Perturbative calculation of the Hartree–Fock interaction energy using orthogonalized orbitals

A many‐body perturbation theory based on the partitioning of the dimer Hamiltonian, formulated in an orthogonalized basis set, is used for the calculation of interaction energies at the Hartree–Fock (HF) level. Numerical results for the (HF)₂ and (H₂O)₂ systems in selected geometries are presented. The interaction‐energy components are compared with the results obtained from the standard supermolecular approach and the intermolecular perturbation theory based on the biorthogonal basis set. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 81–88, 1999     

Theoretical Study on the Intermolecular Interactions between 1,1‐Diamino‐2,2‐Dinitroethylene and H2O

The density functional method was applied to the study of 1,1‐diamino‐2,2‐dinitroethylene (Fox‐7)/H₂O dimer. All the possible dimers ( 1, 2 and 3 ), as well as the monomers, were fully optimized with the DFT method at the B3LYP/6‐311++G^** level. The basis set superposition errors (BSSE) are 4.62, 4.07 and 3.45 kJ/mol, and the zero point energy (ZPE) corrections for the interaction energies are 7.94, 5.66 and 6.40 kJ/mol for 1, 2 and 3 , respectively. Dimer 1 is the most stable, judged by binding energy. After BSSE and ZPE corrections, the greatest corrected intermolecular interaction energy of dimer 1 was predicted to be ?29.36 kJ/mol. The charge redistribution mainly occurs on the adjacent N–H··· O atoms and N–O··· H atoms between submolecules. The oxygen in the nitro group acts as a moderate hydrogen acceptor as compared to water oxygen. Based on the statistical thermodynamic method, the standard thermodynamic functions, heat capacities (C⁰_P), entropies (S⁰_T) and thermal corrections to enthalpy (H⁰_T), and the changes of thermodynamic properties on going from monomer to dimer over the temperature range 200.00‐700.00 K were predicted. It is energetically or thermodynamically favorable for Fox‐7 to bind with H₂O and to form dimer 1 at room temperature.     

Methods for the calculation of Voh in OH?O hydrogen bonds

Ab initio calculations are reported for dimerization-induced changes, Δk, in the harmonic force constant k of the H-bonded OH in water dimer. Two dimer geometries are considered. Δk is obtained by considering the perturbation of a given monomer OH potential by the interaction energy in the dimer in question. The interaction energy is partitioned to identify the role of the various contributions to Δk. The sensitivity of Δk to the choice of the one-electron basis set is studied by using five different basis sets, some of which have a set of bond functions in the H? O bond. At the correlated level, correction for basis set superposition error is found to be essential. A comparison is made of the correlation contribution to Δk as given by the CEPA1, MP2, MP3, and MP4 methods. Of these, MP2 gives exaggerated results. Nevertheless, for economical and reasonably accurate calculations on large systems the MP2 approach in the ESPB basis set is advocated. The most accurate calculations yield a shift Δv_0-;1 of – 121 cm^?1 for the uncoupled donor O-H vibrational frequency in water dimer.     

Helium states II. Perturbation treatment of the ground state using the coordinates r< and r>

In an attempt to improve upon the convergence properties of the Hylleraas-Scherr-Knight-Midtdal perturbation expansion for the ground-state energies and eigenfunctions of the helium isoelectronic sequence, the term r is included in the zeroth-order Hamil-tonian. This term dominates the usual perturbation r for the ground state of these systems, and by removing it from H⁽¹⁾ we substantially reduce, in some sense, its size. In order to find the exact eigenfunction of the resulting zeroth-order Hamiltonian it was found necessary to include in H⁽⁰⁾ two additional terms involving the delta function δ(r₁ ? r₂) = δ(r_< ? r_>) and one such term in H⁽¹⁾. Approximate first- and second-order eigenfunctions are calculated variationally giving the energies to fifth order. The results are disappointing. The errors in the energies to fifth order for He, Li⁺, and Be²⁺, although quite small, are significantly larger than the corresponding errors in the more conventional perturbation treatment. Reasons for the failure to improve upon the earlier results are discussed. A “paradox” noted some time ago by Snyder and Parr is examined in an Appendix.     

Nonempirical calculations on diatomic transition metals. II. RHF investigation of lowest closed-shell states of homonuclear 3d transition-metal dimers

Potential-energy curves of the 3d dimer series Sc₂ through Cu₂ are calculated for the lowest closed-shell states within the nonempirical RHF formalism using limited basis sets of minimal to near-double-zeta–plus-polarization size. Calculated spectroscopic constants are compared to semiempirical results as well as to experimental estimates. The possibility for closed- or open-shell ground states is discussed for each dimer. For diatomic Sc and Cu a detailed study of basis set effects on calculated molecular constants is carried out.     

Computed Relative Populations of D2(22)‐C84 Endohedrals with Encapsulated Monomeric and Dimeric Water

Water monomer and dimer encapsulations into D₂(22)‐C₈₄ fullerene are evaluated. The encapsulation energy is computed at the M06‐2X/6‐31++G** level, and it is found that the monomer and dimer storage in C₈₄ yields an energy gain of 10.7 and 17.4 kcal mol^?1, respectively. Encapsulation equilibrium constants are computed by using partition functions based on the M06‐2X/6‐31G** and M06‐2X/6‐31++G** molecular data. Under high‐temperature/high‐pressure conditions, similar to that for the encapsulation of rare gases in fullerenes, the computed (H₂O)₂@C₈₄‐to‐H₂O@C₈₄ ratio is close to 1:2.     

Charge transfer and dispersion interaction stabilization of the D2h isomer of O4

The results of some minimal basis set valence bond calculations, with an antibonding midbond molecular orbital (π_m*) included, are reported for the D_2h isomer of O₄. The in-plane π_m*←π* excitations describe the charge transfer from each monomer, while the π*←π excitations on each monomer partially describe the intermolecular dispersive attractions. It is found that the charge-transfer interactions by themselves are insufficient to stabilize the S=0 spin D_2h dimer of O₄ relative to two O₂ monomers when a correction is included for basis set superposition error. The inclusion of both the charge transfer and dispersion terms yields an estimate of 14 cm⁻¹ for the binding energy (D_e) at an equilibrium separation (R_e) of 3.29 Å. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 129–134, 1998     

Valence bond studies of the D2h isomer of O4: An interim report

Single-zeta and π-electron double-zeta basis sets are used to examine some theories of the origin of the stability of the D_2h isomer of O₄, using ab initio valence-bond procedures. With these basis sets, resonance between covalent-type (i.e., O₂ ·· O₂) valence-bond structures does not lead to a stabilization of the dimer relative to the separated monomers. When basis sets of the same size are used to construct wave functions for covalent and ionic structures, covalent-ionic resonance (i.e., O₂ ·· O₂ ↔ O₂⁺ ·· O₂⁻ ↔ O₂⁻ ·· O₂⁺) is also unable to stabilize the dimer. Without consideration of the basis-set superposition error, stability is obtained when the size of the AO basis is increased for the dimer relative to the monomer, either via the basis for the ionic structures or by the inclusion of midbond functions. Brief consideration is given to an increased-valence structure for the dimer. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 547–555, 1997     

Study of the hydrogen bond and of the proton transfer between two H2S molecules

The potential energy surface for the H₂S dimer is calculated as the sum of the SCF-MO-LCGO energy with a new, modified, basis set and the estimated dispersion energy. Proton affinities for SH^– and H₂S, and, as their difference, the energy of the proton transfer between two H₂S molecules, are also calculated. Despite the limited basis set used, the results are consistent with experimental data.This work was partly supported by the Polish Academy of Sciences within the project PAN-3.     

Spin-free quantum theory. XXV. The unitary-group formulation of fermion many-body theory

The fermion unitary group formulation (UGF ) of many-body theory is based on the unitary group U(2n) where n is the number of freeon orbitals. This formulation, which conserves particle-number but not spin, is isomorphic to the particle-number-conserving, second-quantized formulation (SQF ). In UGF we derive the familiar diagrammatic algorithm for matrix elements, M(Y) = (?1)^H+L where H and L denote the numbers of hole lines and loops in the diagram D(Y) of M(Y). The unitary group derivation is considerably simpler than is the conventional, second-quantized derivation that employs time-dependence, Wick's theorem, normal-order, and contractions. In neither fermion UGF nor SQF is spin conserved. We carry out in UGF the spin-projection (symmetry adaptation to SU (2)) of the fermion vectors and obtain with a spin-free Hamiltonian the same matrix elements as with the freeon UGF (part 24 of this series). The fermion unitary group formulation for a spin-free Hamiltonian should be regarded as an alternate path to spin-free quantum chemistry.     

Studies of the hydrated oxonium radical H3O·(H2O)n and the ammoniated ammonium radical NH4·(NH3)n by neutralized ion beam techniques

Neutralized ion beam studies of the clusters NH₄·(NH₃)_n and H₃O·(H₂O)_n,n = 0–3, and their fully deuterated analogs are presented. Stabilization of the hypervalent monomer radicals is found to accompany solvation. Cluster stability is found to decrease with increasing size. Reasons for this observation are discussed. Internally excited clusters are found to stabilize efficiently through the sequential loss of structural units (NH₃ or H₂O). The mixed isotopic dimer clusters (D₂¹⁸O)·D·(D₂¹⁶O) and (HDO)·D·(D₂O) are also investigated. Presence of the D₃¹⁶O radical structural unit is found to be crucial to dimer stability. This is consistent with the results of earlier investigations involving the monomer which showed the surprising lifetime progression τ(D₃¹⁶O) ≫; τ(D₃¹⁸O) ⩾ τ(H₃¹⁶O).     

Computational studies of the intermolecular interactions in dimers of the bowl-shaped sumanene molecule

Sumanene, C₂₁H₁₂, the second smallest “buckybowl,” is a bowl-shaped fragment of buckminsterfullerene, C₆₀. It can be described as a slice of buckminsterfullerene with 21 carbon atoms with all vacant valences terminated by hydrogens. A computational study of dimers of the sumanene molecule has been carried out. The concave–convex surface arrangement is the most favorable arrangement, and the binding energy and the equilibrium distance for the most stable conformation of the sumanene dimer are predicted to be 19.3 kcal/mol and 3.7 Å, respectively. The most stable geometry was the staggered stacked concave–convex motif, where one monomer was rotated by 60° from the eclipsed conformation. The binding energy of the eclipsed concave–convex dimer is predicted to be 16.7 kcal/mol with an equilibrium distance between the monomer units of 3.8 Å. At the MP2 level, the basis set superposition errors are quite large, 3–5 kcal/mol at the equilibrium distance depending on the basis set. The basis set superposition errors are smaller for dispersion-corrected density functional methods.     

Ytterbium tris(hexafluoroacetylacetonate) Yb(C<Subscript>5</Subscript>O<Subscript>2</Subscript>HF<Subscript>6</Subscript>)<Subscript>3</Subscript>: The composition of overheated vapor and sublimation thermodynamics

A mass spectrometric study of the saturated vapor over ytterbium tris(hexafluoroacetylacetonate) Yb(hfa)₃ (hfa = CF₃-C(O)-CH-C(O)-CF₃) and of the vapor overheated up to the thermal decomposition temperature of the complex is presented. The vapor composition changes markedly with increasing temperature. At T ≈ 370 K, the mass spectrum of the vapor over Yb(hfa)₃ indicates the presence of ions containing one to three metal atoms. As the temperature is raised, the ion currents due to oligomer ions decrease. The oligomers are not detected at T > 440 K. The total decomposition temperature of Yb(hfa)₃ is 663(9) K. The second-law enthalpy of sublimation (ΔH _s^o (380 K)) is 134 ± 7 kJ/mol for the monomer and 138 ± 10 kJ/mol for the dimer. The enthalpy of dissociation of the dimer into monomer molecules is nearly equal to the enthalpy of sublimation of the monomer and dimer: ΔH _dis(380 K) = 130 ± 15 kJ/mol.     

Experimental and Quantum Chemical Studies of 5-Fluoroisatin-3-(N-Cyclohexylthiosemicarbazone) and Its Metal Complexes

Abstract

Zn(II) and Ni(II) complexes of 5-fluoroisatin-3-[-(N-cyclohexylthiosemicarbazone)] (H₂FIC) have been prepared and characterized structurally by means of elemental analyses, FTIR, electronic, and ¹H NMR spectra. The theoretical wavenumbers, IR intensities, and molecular parameters have been calculated by the ab-initio Hartree–Fock (HF) method with the LanL2DZ basis set. The theoretical wavenumbers show a good agreement with experimental data. The bond lengths, bond angles, the highest occupied molecular orbital energy (E_HOMO), the lowest unoccupied molecular orbital energy (E_LUMO), the energy gap between E_HOMO and E_LUMO (ΔE_HOMO-LUMO), dipole moment, and charges on the atoms of H₂FIC as monomer form were studied by the density functional theory/Becke-3-Lee-Yang-Parr (DFT/B3LYP) and ab-initio HF methods using 6-31G(d,p) basis set. The trimeric possible structure of H₂FIC was also investigated using HF method. The observed IR wavenumbers of the H₂FIC were analyzed in the light of the computed vibrational spectra of its monomer and trimer forms.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Kinetics and mechanism of the first aquation stage for the [Cr(pic)3]0 and [Cr(pic)2(OH)]2 0 complexes in HClO4 solutions

Aquation of [Cr(pic)₃]⁰ and [Cr(pic)₂(OH)]₂ ⁰ in aqueous HClO₄ solutions leads to formation of the common product – [Cr(pic)₂(H₂O)₂]⁺. The first, reversible stage, the ring opening via Cr—N bond breaking in [Cr(pic)₃]⁰ is followed by the second, rate-determining step – one-end bonded pic ligand liberation. In the case of the [Cr(pic)₂(OH)]₂ ⁰ complex, the first faster stage produces the singly bridged dimer, which undergoes cleavage into the parent monomers in the second, much slower step. The subsequent aquation of [Cr(pic)₂(H₂O)₂]⁺ is extremely slow and leads to [Cr(pic)(H₂O)₄]²⁺ formation, which practically does not undergo further ligand substitution under the conditions applied. Kinetics of the first aquation stage for [Cr(pic)₃]⁰ and of the second step for [Cr(pic)₂(OH)]₂ ⁰ were studied spectrophotometrically in the 0.1–1.0 M HClO₄ range at I = 1.0 M. The observed pseudo-first order rate constant for [Cr(pic)₃]⁰ decreases with [H⁺] increase according to the rate law: k _obs = k ₁ + k _–1 Q ₁/[H⁺], where k ₁ and k _–1 are the rate constants of the forward and the reverse processes in the unprotonated substrate and Q ₁ is the protonation constant of the pyridine nitrogen atom. In the case of the [Cr(pic)₂(OH)]₂ ⁰ complex, the rate for the singly bridged dimer cleavage does not depend on [H⁺]. The activation parameters for the chelate-ring opening in [Cr(pic)₃]⁰ and for the singly bridged dimer cleavage have been determined and discussed. Some kinetic data of the slow, second aquation stage for the [Cr(pic)₃]⁰ complex and of the fast, first aquation stage for the doubly bridged dimer have been studied; for both reactions the rate increases linearly with the increase in [H⁺].     

Six-dimensional tunneling dynamics of internal rotation in hydrogen peroxide molecule and its isotopomers

The six-dimensional torsion-vibration Hamiltonian of the H₂O₂ molecule and its H/D- and ¹⁸O/¹⁶O-isotopomers is derived. The Hamiltonian includes the kinetic energy operator, which depends on the tunneling coordinate, and the potential energy surface represented as a quartic polynomial with respect to the small-amplitude transverse coordinates. Parameters of the Hamiltonian were obtained from DFT calculations of the equilibrium geometries, eigenvectors, and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and both the cis- and trans-transition states, carried out with the B3LYP density functional and 6-311+G(2d,p) basis set. The quantum dynamics problem is solved using the perturbative instanton approach generalized for the excited states situated above the barrier top. Vibration-tunneling spectra are calculated for the ground state and low-lying excited states with energies below 2000 cm^–1. Strong kinematic and squeezed potential couplings between the large-amplitude torsional motion and bending modes are shown to be responsible for the vibration-assisted tunneling and for the dependence of tunneling splittings on the quantum numbers of small-amplitude transverse vibrations. Mode-specific isotope effects are predicted.     

Acid-catalyzed degradation of poly(2-butyl-1, 3, 6-trioxocane)

Acid-catalyzed degradation of poly(2-butyl-1,3,6-trioxocane) (1) has been studied. With ethyl tosylate as the catalyst, the cyclic monomer 2 was the major product. The minor products are cis and trans isomers of C₃H₇CH?CH? OCH₂CH₂OCH₂CH₂OH, and three stereoisomers of C₃H₇CH?CH? OCH₂CH₂OCH₂CH₂O? CH?CH? C₃H₇ elucidated by ¹H and ¹³C NMR, IR, electron impact and chemical ionization MS, and in the case of 2 also by comparison with an authentic sample. With 98% H₂SO₄ as the catalyst 2 is only a minor product. The major products are diethylene glycol, valeraldehyde, and 1,4-dioxane with some 2-butyl-1,3-dioxolane. Capillary GC/mass spectrometry led to identification of the following less abundant products: tri-n-propylbenzene, α,β-unsaturated aldehydes, and cyclic dimer. The products of H₂SO₄-catalyzed decomposition of polymer were also obtained by heating monomer 2 with H₂SO₄. A detailed mechanism for the formation of the eight-member ring 2 in the decomposition is proposed which involves unzipping proceeds via open carbocation intermediates. According to the principle of microscopic reversibility, the same open carbocation is the propagating species in the polymerization of 2 under similar conditions.     

Spin-independent three-body effective valence-shell operators: Application to molecular oxygen

A mathematical construction is presented that uniquely defines a set of spin-independent effective valence-shell Hamiltonian (H^v) three-body matrix elements. These spin-independent H^v matrix elements separate direct and exchange portions of the three-body H^v matrix elements and therefore provide the most natural form for comparisons with parameterization schemes of semiempirical electronic structure methods in which the three-body matrix elements are incorporated into semiempirical one- and two-body Hamiltonian matrix elements in an averaged manner. Ab initio H^v three-body matrix elements of O₂ are computed through third order of quasidegenerate perturbation theory and are analyzed as a function of internuclear distance and atomic orbital overlap to aid in understanding how these three-body matrix elements may be averaged into semiempirical one- and two-body matrix elements. © 1992 John Wiley & Sons, Inc.     

Theoretical study of the relative stabilities of H+(X)2 and H+(X)3 conformers and their clustering energies: X  CO and N2

Third-order Møller–Plesset perturbation theory (MP 3) with a 6-31G** basis set was applied to study the relative stabilities of H⁺(X)₂ conformations (X ? CO and N₂) and their clustering energies. The effect of both basis set extensions and electron correlation is not negligible on the relative stabilities of the H⁺(CO)₂ clusters. The most stable conformation of H⁺(CO)₂ is found to be a C_∞v structure in which a carbon atom of CO bonds to the proton of H⁺(CO), whereas that of H⁺(N₂)₂ is a symmetry D_∞h structure. The second lowest energy conformations of H⁺(CO)₂ and H⁺(N₂)₂ lie within 2 kcal/mol above the energies of the most stable structures. Clustering energies computed using MP 3 method with the 6-31G** basis set are in good agreement with the experimental findings of Hiraoka, Saluja, and Kebarle. The low-lying singlet conformations of H⁺(X)₃ (X ? CO and N₂) have been studied by the use of the Hartree–Fock MO method with the 6-31G** basis set and second-order Møller–Plesset perturbation theory with a 4-31G basis set. The most stable structure is a T-shaped structure in which a carbon atom of CO (or a nitrogen atom of N₂) attacks the proton of the most stable conformation of H⁺(X)₂ clusters.