Improved generator coordinate Hartree–Fock method for molecular systems: application to H2, Li2 and LiH

The improved generator coordinate Hartree–Fock (GCHF) method is extended to molecular systems. The Griffin–Hill–Wheeler–HF equations were solved by an integral discretization technique. The method is then implemented with the use of the GAMESS program and applied to the H₂, Li₂, and LiH molecules. For these molecules, sequences of basis sets of atom-centred Gaussian-type functions are employed to explore the accuracy achieved with our approach. For all systems studied, our ground-state HF total energies are better than those obtained with basis sets generated with the original GCHF method for molecules and larger even-tempered basis sets. For H₂, Li₂, and LiH, the differences between our best energies and the corresponding numerical HF results are about 2 × 10⁻², 1, and 4 × 10⁻¹ μhartree, respectively. The dipole, quadrupole, and octupole moments at the center of mass and electric field, the electric field gradient, the electrostatic potential, and the electron density at the nuclei were evaluated and compared with results reported in the literature. Received: 4 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

Ab initio structure and vibrational frequencies of lithium aromatic sulfonyl imide salts

The structure and vibrational frequencies of an aromatic lithium sulfonyl imide, i.e., lithium bis(4-nitrophenylsulfonyl)imide (LiNPSI) has been studied using self-consistent ab initio Hartree–Fock and hybrid density functional methods. These calculations engender two linkage isomers, which correspond to the local minima on the potential-energy surface. In the lowest-energy isomer, the ligand binds to the metal ion through two oxygens, one from each of the different SO₂ groups on the central nitrogen and forms a six-membered ring. Another LiNPSI isomer, wherein the anion coordinates through oxygen and nitrogen atoms and which is 55.9 kJmol⁻¹ higher in energy, has also been obtained. The S–N–S bond angle in the free anion as well as in the LiNPSI complex turns out to be nearly 121°. A comparison of the vibrational spectra of the free NPSI anion and that of the LiNPSI complex reveals that the SO₂ stretching vibrations at 1,239 and 1,205 cm⁻¹ can be used to differentiate between the two linkage isomers of the complex. The stronger complexation ability of the NPSI anion, compared to that for (CF₃SO₂)₂N⁻ has been explained in terms of the charge density within the molecular electrostatic potential isosurface encompassing both SO₂ groups of the anion. Received: 20 February 2002 / Accepted: 25 March 2002 / Published online: 3 June 2002     

Theoretical study of the structural character of weakly bonding silicon carbonyl complexes

The structures, properties and the bonding character for sub-carbonyl Si, SiCO and Si(CO)₂, in singlet and triplet states have been investigated using complete-active-space self-consistent field (CASSCF), density functional theory and second-order M?ller–Plesset methods with a 6-311+G* basis set. The results indicate that the SiCO species possesses a ³∑⁻ ground state, and the singlet ¹Δ excited state is higher in energy than the ³∑⁻ state by 17.3 kcalmol⁻¹ at the CASSCF–MP2/6-311+G* level and by 16.4 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The SiCO ground state may be classified as silene (carbonylsilene), and its CO^δ− moiety possesses CO⁻ property. The formation of SiCO causes the weakening of CO bonds. The Si–C bond consists of a weak σ bond and two weak π bonds. Although the Si–C bond length is similar to that of typical Si–C bonds, the bond strength is weaker than the Si–C bonds in Si-containing alkanes; the calculated dissociation energy is 26.2 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The corresponding bending potential-energy surface is flat; therefore, the SiCO molecule is facile. For the bicarbonyl Si systems, Si(CO)₂, there exist two V-type structures for both states. The stablest state is the singlet state (¹A₁), and may be referred to the ground state. The triplet state (³B₁) is energetically higher in energy than the ¹A₁ state by about 40 kcalmol⁻¹ at the CCSD(T)/6-311 + G* level. The bond lengths in the ¹A₁ state are very close to those of the SiCO species, but the SiCO moieties are bent by about 10°, and the CSiC angles are only about 78°. The corresponding ³B₁ state has a CSiC angle of about 54° and a SiCO angle of about 165°, but its Si–C and C–O bonds are longer than those in the ¹A₁ state by about 0.07 and 0.03 ?, respectively. This Si(CO)₂ (¹A₁) has essentially silene character and should be referred to as a bicarbonyl silene. Comparison of the CO dissociation energies of SiCO and Si(CO)₂ in their ground states indicates that the first CO dissociation energy of Si(CO)₂ is smaller by about 7 kcalmol⁻¹ than that of SiCO; the average one over both CO groups is also smaller than that of SiCO. A detailed bonding analysis shows that the possibility is small for the existence of polycarbonyl Si with more than three CO. This prediction may also be true for similar carbonyl complexes containing other nonmetal and non-transition-metal atoms or clusters. Received: 17 April 2002 / Accepted: 11 August 2002 / Published online: 4 November 2002 Acknowledgements. This work was supported by the National Natural Science Foundation of China (29973022) and the Foundation for Key Teachers in University of the State Ministry of Education of China. Correspondence to: Y. Bu e-mail: byx@sdu.edu.ch     

Dual-level direct dynamics calculations of deuterium kinetic isotope effects for the Cl(2P)+C2H6 abstraction reaction

 Kinetic isotope effects, KIEs, for hydrogen abstraction from C₂H₆ and C₂D₆ by chlorine atom have been studied by the dual-level direct dynamics approach. A low-level potential energy surface is obtained with the MNDO-SRP method. High-level structural properties of the reactants, transition state, and products were obtained at the MP2 level with the cc-pVDZ, aug-cc-pVDZ, and the cc-pVTZ basis sets. Using the variational transition state theory with microcanonical optimized multidimensional tunneling, the values of deuterium KIE, at 300 K, range from 2.28 to 3.27, in good agreement with the experimental values (2.69–5.88). Received: 6 June 2001 / Accepted: 12 July 2001 / Published online: 19 November 2001     

Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000     

Infrared spectra of CO in absorption and evaluation of radial functions for potential energy and electric dipolar moment

From quantum-chemical calculations of rotational g factor and new experimental measurements of strengths of lines in infrared spectra of vibration–rotational bands v′–0 in absorption, with 1≤v′≤4, of ¹²C¹⁶O, and from analysis of 16,947 frequencies and wave numbers assigned to pure rotational and vibration–rotational transitions within electronic ground state X ¹Σ⁺, including new measurements of band 4–0 of ¹²C¹⁶O, we evaluate radial functions for potential energy and electric dipolar moment, the latter both in polynomial form and as a rational function that has qualitatively correct behaviour under limiting conditions. Received: 8 November 2001 / Accepted: 5 February 2002 / Published online: 14 August 2002     

Diabatic and adiabatic potential-energy surfaces for azomethane photochemistry

We propose an analytic form to represent the intersecting potential energy surfaces (PES) of the first two singlet states of azomethane. The aim is to run semiclassical simulations of photochemical events such as fragmentation and isomerization. The PES are based on ab initio calculations and corrected on the basis of available experimental data. We resort to a quasi-diabatic representation, suitable to deal with the S₀-S₁ conical intersection and to include the essential information about electronic couplings in a 2 × 2 effective hamiltonian matrix. Received: 18 February 1999 / Accepted: 12 April 1999 / Published online: 14 July 1999     

A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I)

 A relativistic pseudopotential of the energy-consistent variety simulating the Tl²¹⁺ (1s– 4f) core has been generated by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. Valence ab initio calculations using this pseudopotential have been performed for atomic excitation energies and for spectroscopic constants of the X0⁺ and A0⁺ states of TlX (X = F, Cl, Br, I). Comparison is made to experiment and to four-component density functional results. Received: 22 June 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Conformational profile of 1-aminocyclopropanecarboxylic acid

1-Aminocyclopropanecarboxylic acid (Ac₃c) is a constrained α amino acid residue that exhibits peculiar conformational characteristics. The aim of the present study is to provide a deeper understanding of these features to be used as guidance to decide when to choose Ac₃c as a building block for the design of peptide and protein surrogates. The whole Ramachandran plot of the Ace-Ac₃c-NCH₃ dipeptide was investigated at the Hartree–Fock level using a 6-31G(d) basis set and the most favorable structures were assessed on this surface by energy minimization. These results were subsequently used as a reference to generate specific molecular mechanics parameters for Ac₃c compatible with the parm94 set of the AMBER force field. The effect of water as a solvent on the conformational profile of the dipeptide was also assessed using the Miertus–Scrocco–Tomasi self-consistent reaction-field model at the Hartree–Fock level using a 6-31G(d) basis set and using the AM1 semiempirical method. The conformational profile of the Ac₃c dipeptide can be characterized by two symmetric low-energy regions for values of φ around ±80° with a wide range of values for ψ ranging from −40 to 180°, with the lower areas located at low values of ψ. Solvent effects do not alter the features of the conformational map, but a shift of the two absolute minima to (φ, ψ) values near (±90°, 0°) can be observed. These results are in accord with all experimental evidence and with the known tendency of Ac₃c to induce β-turn conformations in peptides. Received: 19 March 1999 / Accepted: 10 June 1999 / Published online: 9 September 1999     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Pseudopotential study of lanthanum and lutetium dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart–Bonn variety and extended valence basis sets have been used for the investigation of the dimers La₂ and Lu₂. It was found that the ground states for La₂ and Lu₂ are most likely ¹∑ _g ⁺ (σ _g ²π _u ⁴) and ³∑ _g ⁻ (4f ¹⁴4f ¹⁴σ _g ²σ _u ²π_u ²), respectively. The molecular constants including error bars were derived from multireference configuration interaction as well as coupled-cluster calculations, taking into account corrections for atomic spin–orbit splitting as well as possible basis set superposition errors. The theoretical values for La₂ (R _e=2.70±0.03 ?, D _e=2.31±0.13 eV, ω_e=186±13 cm⁻¹) show good agreement with the experimental binding energy (D _e=2.52±0.22 eV), but the experimental vibrational constant in an Ar matrix (ω_e=236±0.8 cm⁻¹) is significantly higher. For Lu₂ the theoretical values (R _e=3.07±0.03 ?, D _e=1.40±0.12 eV, ω_e=123±1 cm⁻¹) are in overall excellent agreement with experimental data (D _e=1.43±0.34 eV, ω_e=122± 1 cm⁻¹). The electronic structures of La₂ and Lu₂ are compared to those other lanthanide dimers and trends in the series are discussed. Received: 25 March 2002 / Accepted: 2 June 2002 / Published online: 21 August 2002     

Energetics, structures, bonding, and kinetics of the HSCl–HClS system

The [H,S,Cl] potential-energy surface has been investigated at the self-consistent field (SCF), complete active space self-consistent field (CASSCF), second-order M?ller–Plesset, coupled-cluster single-double and perturbative triple excitation, [CCSD(T)]/6-31G(d,p), 6-31G(2df,2pd), and correlation-consistent polarized valence triple zeta (cc-pVTZ) levels of theory. CCSD(T)/ cc-pVTZ results predict a very stable HSCl species, an isomer HClS, 51.84 kcal/mol higher in energy, and a transition state 57.68 kcal/mol above HSCl. Independent of the level of theory, results with the smaller 6-31G(d,p) basis set turned out to be poor, especially for HClS. Vibrational analysis indicates that both species can be easily differentiated if isolated. Bonding differences between these molecules are illustrated by contour plots of valence orbitals. Viewed classically, bonding in HClS involves a dative bond. Transition-state rate constants, and equilibrium constants for the HSCl ↔ HClS isomerization have been estimated for various temperatures (200–1000 K). At 298.15 K, the forward rate is predicted to be 7.95 × 10⁻²⁹ s⁻¹, and the equilibrium constant to be 2.31 × 10⁻³⁸. Tunneling corrections vary from 1.57 at 298.15 K to 1.05 at 1000 K. Activation energies have been obtained by a two-points linear fit to the Arrhenius equation. Received: 7 May 1999 / Accepted: 22 July 1999 / Published online: 4 October 1999     

Structure and stability of hypervalent NLi n Na2 (n = 1–4) and related species at density functional theory level

A number of configurations of NLi _n Na₂ (n = 1–4) species were optimized using the B3LYP–density functional theory method; the 6-31G^* basis set was used in this calculation. In order to study all possible dissociation energies, some related species such as NLi₂Na, NLi _n (n = 1–4), Li _n (n = 1, 2) and Na _n (n = 1, 2) were also considered. Optimizations of these species were followed by fundamental frequency calculations at the same level. Global minima of these species were shown to adopt C _{2 v} (NLi₄Na₂, NLi₂Na₂), D _{3 h} (NLi₃Na₂) and C _s (NLiNa₂ and NLi₂Na) configurations. All possible dissociation energies were obtained. Received: 30 November 1998 / Accepted: 15 October 1999 / Published online: 14 March 2000     

Theoretical study of the potential-energy surface of C2NP

 The B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the singlet potential energy surface of C₂NP, in which seven stationary isomers and seventeen interconversion transition states are involved. At the final CCSD(T)/6-311G(2df)//B3LYP6-311G(d) level with zero-point vibrational energy correction the lowest-lying isomer is a linear NCCP followed by two linear CNCP isomers at 23.9  and CCNP at 65.8 kcal mol⁻¹, respectively. The three isomers are kinetically very stable towards both isomerization and dissociation, and CCNP is even more kinetically stable than CNCP – by 14.3 kcal mol⁻¹ despite its high energy. Further comparative calculations were performed at the QCISD and QCISD(T) levels with the 6-311G(d) and 6-311G(2d) basis sets to obtain more reliable structures and spectroscopy for the three isomers. The calculated bond lengths, rotational constant, and dipole moment for NCCP were in close agreement with the experimentally determined values. Finally, similarities and discrepancies between the potential energy surface of C₂NP and those of the analogous species C₂N₂ and C₂P₂ were compared. The results presented in this paper might be helpful for future identification of the two still unknown yet kinetically very stable isomers CNCP and CCNP, both in the laboratory and in interstellar space. Received: 3 January 2001 / Accepted: 6 June 2001 / Published online: 30 October 2001     

Action of HCl on 3-hydroxypyrazolo(iso)quinolines to give 1-chloropyrazoles: evidence for an addition–elimination mechanism by ab initio calculations in gas phase and water

 Addition–elimination reactions involving a nucleophile and a remote leaving group [S^H _N(AE)^tele] are well-known under basic conditions, especially amongst electron-poor six-membered heterocycles, but are less commonly encountered for five-membered heterocycles and are rare under acidic conditions. Concentrated HCl converts 1-hydroxy-1H-pyrazolo[3,4-c] isoquinoline and 1-hydroxy-1H-pyrazolo[3,4-c]quinoline into 3-chloro-1H-pyrazolo[3,4-c]isoquinoline and 3-chloro-1H-pyrazolo[3,4-c]quinoline, respectively. However, apparently neither the isomeric 1-hydroxy-1H-pyrazolo[4,3-c](iso)-quinolines nor the parent 1-hydroxypyrazole undergo this reaction. Additionally, all these systems are refractory under basic conditions. We present a plausible mechanism for the reaction, involving the 3-addition of Cl^- to the diprotonated heterocycle, followed by the elimination of water. Calculations of the initial transition states and intermediates, using optimisation at B3LYP/6-311+G(d,p), including thermochemistry [HF/6-31+G(d)], and single-point Poisson–Boltzmann self-consistent reaction field determination of the free energy of solvation (Jaguar Poisson–Boltzmann self-consistent reaction field), support this mechanism and reproduce the observed order of reactivity, the addition step being 2–4 kcal less favourable for the isomeric 1-hydroxy-1H-pyrazolo[4,3-c](iso)quinolines and provide a rationalisation for the role of strong acid. Received: 27 June 2002 / Accepted: 6 September 2002 / Published online: 14 February 2003     

A theoretical study of photoinduced electron transfer between tetracyanoethylene and arene

 Ab initio calculations have been performed to investigate the state transition in photoinduced electron transfer reactions between tetracyanoethylene and biphenyl as well as naphthalene. Face-to-face conformations of electron donor–acceptor (EDA) complexes were selected for this purpose. The geometries of the EDA complexes were determined by using the isolated optimized geometries of the donor and the acceptor to search for the maximum stabilization energy along the center-to-center distance. The correction of interaction energies for basis set superposition error was considered by using counterpoise methods. The ground and excited states of the EDA complexes were optimized with complete-active-space self-consistent-field calculations. The theoretical study of the ground state and excited states of the EDA complex in this work reveals that the S₁ and S₂ states of the EDA complexes are charge–transfer (CT) excited states, and CT absorption which corresponds to the S₀→S₁ and S₀→S₂ transitions arise from π−π^* excitation. On the basis of an Onsager model, CT absorption in dichloromethane was investigated by considering the solvent reorganization energy. Detailed discussions on the excited state and on the CT absorptions were made. Received: 30 April 2001 / Accepted: 18 October 2001 / Published online: 9 January 2002     

Visible light photocatalytic reduction of water using SrSnO3 sensitized by CuFeO2

SrSnO_3–δ, prepared in sealed ampoules, crystallizes in the perovskite structure. The band gap is directly allowed at 3.93 eV. The conductivity was found to change markedly and occurs by polaron hopping with activation energy of 0.22 eV. The thermal variation of the thermopower indicates an electron mobility μ_{e 300K} = 3.15∙10^–6 cm²∙V^–1∙s^–1), thermally activated. The capacitance measurement shows a linear behavior from which a flat band potential of –0.20 V_SCE and an electronic density of 5.56∙10¹⁸ cm^–3 were determined. The conduction band edge (–4.32 eV/–0.42 V_SCE) lies below the H₂O/H₂ level. Accordingly, SrSnO_3–δ can be used for water photoreduction when combined with the delafossite CuFeO₂ as sensitizer. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 45, No. 3, pp. 160-166, May-June, 2009.     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: K. Morokuma e-mail: morokuma@emory.edu     

The basis set convergence of the Hartree–Fock energy for H3 +, Li2 and N2

 By using completely optimized basis functions it is shown that the convergence of the Hartree–Fock energy for the H₃ ⁺, Li₂ and N₂ molecules is significantly better described by exponential behavior than by inverse power dependence. This is the case both with respect to the number of basis functions of a given type and with respect to the highest angular momentum function included. The Hartree–Fock limit for H₃ ⁺ is estimated to be −1.300372125 hartree. Received: 14 February 2000 / Accepted: 12 April 2000 / Published online: 18 August 2000