Quantum Chemical Model of a Lysozyme+Substrate Complex and a Cooperative Process in It

This paper presents an ab initio (RHF/6-31G** and MP2(full)6-31G**) and density functional (DFT) study of the structure and energetics of formation of an intermolecular complex which is the simplest model of an active center lysozyme with a substrate. The calculated energy of complex formation is 41.4 (RHF), 53.4 (MP2), and 52.7 kcal/mole (DFT). The proton transfer reaction is a concerted reaction having an energy barrier of 41.1 (RHF), 31.6 (MP2), and 25.3 (DFT) kcal/mole.     

Theoretical studies of structure,stability, and chemical bonding in oxohydride OM4H6 complexes

The results of ab initio RHF/3-21G, RHF/6-31G*, and MP2/6-31G** / / HF/6-31G* calculations for 10 possible configurations of OM₄H₆ molecules (MO · 3MH₂, M = Be, Mg) are reported. Five isomers of OBe₄H₆ and three isomers of OMg₄H₆ have been found within an energy range of ã 15 kcal mol⁻¹. The “lanternlike” C_3v structure is the most favorable one for both complexes. Both molecules OM₄H₆ are stable to decomposition through all of the studied pathways. Chemical bonding in the OM_k polyhedra containing two-, three-and four-coordinated oxygen atoms is discussed. © 1996 John Wiley & Sons, Inc.     

Pathways of the reaction of nucleophilic addition of ammonia to formaldehyde in the gas phase and in the complex with formic acid:ab initio calculations

The gradient pathways of the reaction of nucleophilic addition of ammonia to formaldehyde were calculated for free molecules and in the NH₃...H₂CO...HC(O)OH complex by theab initio RHF/6-31G^**, MP2(fc)/6-31G^**, and MP2(full)/6-311++G^** methods. Both reactions proceed concertedly. In the first case, the reaction successively passes through two transitional states with an energy barrier exceeding 35 kcal mol⁻¹. In the case of the complex with formic acid, the reaction follows a conventional pathway, although its activation barrier calculated by the RHF/6-31G^** and MP2(fc)/6-31G^** methods decreases to 12.6 and 3.8 kcal mol⁻¹, respectively. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 13–20, January, 1998.     

Internal conrotation and disrotation in H2BCH2BH2 and diborylmethane 1,3 H exchange

The paths of correlated internal disrotation (barrier less than 0.4 kcal/mol) and conrotation (barrier around 1.9 kcal/mol) of the two BH₂ groups in H₂BCH₂BH₂ have been computed employing ab initio [MP2(full)/6–31G**] and density functional theory (Becke3LYP/6–311+G**) methods. Two B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative interactions stabilize the C_s symmetric H₂BCH₂BH₂ isomer ( 1 ). The B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative stabilization, evaluated by homodesmotic reactions and using the orbital deletion procedure (which “deactivates” the “vacant” born p orbital), is less than 6 kcal/mol in diborylmethane. The B(SINGLE BOND)C(DOTTED BOND)B(p) stabilization is shown to be remarkably large in C₄B₆H₁₀ (Td). At MP2(fu)/6–31G**, disproportionation into 1 and methane is only 5.6 kcal/mol exothermic. The 1,3 H exchange in diborylmethane is an asynchronous process and proceeds via a doubly bridged cyclic intermediate with 9.3 kcal/mol barrier. Structures with “planar tetracoordinate” carbon are stabilized considerably by BH₂ substituents, but they are still high in energy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1792–1803, 1997     

HCN exchange on [Cu(HCN)4]+: a quantum chemical investigation

Density functional (B3LYP, B3PW91, X3LYP, BP86, PBEPBE, PW91PW91, and M06) and ab initio (MP2, MP4sdq, CCSD, and CCSD(T)) calculations with extended basis sets (6-311+G**, TZVP, LANL2DZ+p, and SDD+p, the latter including extra polarization and diffuse functions) indicate that HCN exchange on [Cu(HCN)₄]⁺ proceeds via an associative interchange (I_a) mechanism and a D_3h transition structure {[Cu(HCN)₅]⁺}^?. The activation barrier, relative to the model complex [Cu(HCN)₄]⁺·HCN, varies modestly, depending on the computational level. Typical values are 8.0?kcal?M^?1 (B3LYP/6-311+G**), 6.0?kcal?M^?1 (M06/6-311+G**), and 4.8?kcal?M^?1 (CCSD(T)/6-311+G**//MP2(full)/6-311+G**). Inclusion of an implicit solvent model (B3LYP(CPCM)/6-311+G**) leads to an activation barrier of 5.8?kcal?mol^?1. Comparison of the HCN exchange mechanisms on [Li(HCN)₄]⁺ (limiting associative, A) and [Cu(HCN)₄]⁺ (associative interchange, I_a) reveals that π back donation in the equatorial Cu–N bonds in the transition state determines the mechanism.     

Structure and isomerization of heterapentalene compounds containing hypervalent bonds with central nitrogen,phosphorus, or arsenic atom

The possibility for a specific type of isomerization (electromorphism) to occur in conjugated bicyclic organic compounds containing Group V elements was studied by the ab initio (RHF/6-31G**, MP2(full)/6-31G**), and DFT (B3LYP/6-31G**) methods. Compounds 2 (X = N, P, As) were found to exist in a monocyclic planar form with intramolecular donor-acceptor N...O coordination (X = N) and as aromatic heterapentalene structures with hypervalent O--X--O bonds (X = P, As). According to calculations, no isomerization of planar heteroaromatic structures into pyramidal ones occurs. The strength of the O--X--O hypervalent bond and the aromaticity of heterapentalene structures 2 with ten -electrons increase on going from X = N to X = P. Correct estimation of these effects requires the inclusion of electron correlation.     

Pathways of the reactions of nucleophilic addition of H2O and HF molecules to formaldehyde in the gas phase and in the complex with formic acid:ab initio calculations

The gradient pathways of the reactions of nucleophilic addition of H₂O and HF molecules to formaldehyde in the gas phase and in the XH…H₂CO…HC(O)OH complex (X=OH, F) were calculated by theab initio RHF/6-31G^**, MP2(fc)/6-31G^**, and MP2(full)/6-311++G^** methods. Both reactions proceed concertedly. The formation of H-bonded bimolecular pre-reaction complexes is the initial stage of the gas-phase reactions; at the same time, no indications of the formation of stable π-complexes were found on the potential energy surfaces of systems under study. The calculated energy barriers to the gasphase reactions exceed 40 kcal mol⁻¹, while those to reactions in the complex XH…H₂CO…HC(O)OH (X=OH, F) become more than halved. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2146–2154, November, 1998.     

The N4 molecule has an open-chain triplet C2h structure

The lowest-energy N₄ is computed ab initio to be the planar C_2h(³B_u) open-chain structure 13 . The open-chain N₄ singlet-state structures dissociate on geometry optimization. The tetraazatetrahedrane T_d structure 1 and the tetrazete D_2h structure 2 are minima at MP 2/6-31G *. However, both are higher in energy than 13 (24.1 and 21.2 Kcal/mol [UQCISD ) (T )(full)/6-311+G *//MP 2/6-31G * + ZPE (MP 2/6-31G )*, respectively]. The energy of 13 is 157.5 kcal/mol higher than that of two N₂(¹∑ molecules [UQCISD (T )(Full)/6-311+G *//MP 2/6-31G *] © 1993 John Wiley & Sons, Inc.     

Ab initio quantum-chemical calculations of interactions of ions and hydrides of alkali metals with C3H6 and C4H8 molecules

Calculations of the C₃H₆ · LiH, C₄H₈ · M⁺, and C₄H₈ · MH systems and of C₂H₂ · MH complexes (M = Li or Na) were carried out by the unrestricted Hartree-Fock-Roothaan (UHF) method with partial optimization of the geometry using fixed geometric parameters of the C₃H₆ and C₄H₈ molecules. The standard 3-21G and 6-31G* basis sets were used. Unlike the C₃H₆ · LiH structure, the C₄H₈ · M⁺ and C₄H₈ · MH systems are typical complexes. It was found that the C₄H₈ · M⁺, C₄H₈ · MH, and C₂H₂ · MH complexes are similar in coordination of M⁺ ions and MH molecules by carbon atoms in spite of considerable differences in the interatomic distances (–1 A) between these atoms in the C₄H₈ and C₂H₂ molecules. The heats of formation (Q), which were calculated in the UHF/6-31G* approximation and using second- and fourth-order Möller-Plesset perturbation theory taking into account the electron correlation energy in the MP2/6-31G*. MP4(SDQ)/6-31G*, and MP4(SDTQ)/6-31G* approximations, satisfy the following relationships: Q(C₂H₃ · MH) < Q(C₄H₈ · MH) < Q(C₄H₈ · M⁺). It was observed that in going from Li to Na the corresponding values of Q tend to decrease.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 7, pp. 1636–1640, July, 1996.     

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 Møller–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     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 July 2000 / Published online: 27 September 2000     

Structure and stability of closo-hexaboranes and their heteroanalogs

The molecular and electronic structures of closo-hexaboranes B₆H₆ ^2–, B₆H₇ ^–, and B₆H₈ and closo-heterohexaboranes XYB₄H₄ (X = Y = CH, N; X = BH, Y = CH^–, N^–, NH, O) were studed by the ab initio (MP2(full)/6-311+G**) and density functional (B3LYP/6-311+G**) methods. The bridging H atoms in closo-hexaboranes B₆H₇ ^– and B₆H₈ can undergo facile low-barrier migrations around the boron cage (the barrier heights are about 10—15 kcal mol^–1). All heteroboranes having octahedron-like structures with hypercoordinated N and O atoms are rather stable and can be the subject of synthetic research efforts.     

Ligand‐Exchange Processes on Solvated Beryllium Cations. Part III

On the basis of DFT calculations (B3LYP/6‐311+G**), the possibility to include solvent effects is considered in the investigation of the H₂O‐exchange mechanism on [Be(H₂O)₄]²⁺ within the widely used cluster approach. The smallest system in the gas phase, [Be(H₂O)₄(H₂O)]²⁺, shows the highest activation barrier of +15.6 kcal/mol, whereas the explicit addition of five H‐bonded H₂O molecules in [{Be(H₂O)₄(H₂O)}(H₂O)₅]²⁺ reduces the barrier to +13.5 kcal/mol. Single‐point calculations applying CPCM (B3LYP(CPCM:H₂O)/6‐311+G**//B3LYP/6‐311+G**) on [Be(H₂O)₄(H₂O)]²⁺ lower the barrier to +9.6 kcal/mol. Optimization of the precursor and transition state of [Be(H₂O)₄(H₂O)]²⁺ within an implicit model (B3LYP(CPCM:H₂O)/6‐311+G** or B3LYP(PCM:H₂O)/6‐311+G**) reduces the activation energy further to +8.3 kcal/mol but does not lead to any local minimum for the precursor and is, therefore, unfavorable.     

Structure and stability of X4Y4H4 (XY=CC,BN)

Ab initio calculations have been carried out to study the structures and relative stabilities of the planar eight‐membered ring B₄N₄H₄ and its isoelectronic species C₈H₄ at the HF/6‐31G*, MP2/6‐31G*, MP2/6‐311G**, and MP4SDQ/6‐31G* levels. The analyses of Milliken population, vibration frequencies, π‐molecular orbital components, and orbital energy levels were used to evaluate the relative stabilities of these two similar systems. The homodesmotic reactions were also taken to be a useful index of relative stability for X₄Y₄H₄ (XY=CC, BN) and gave the resonance energies with MP4SDQ/6‐31G* of C₈H₄ (?37.2 kcal/mol) < B₄N₄H₄ (?29.2 kcal/mol). Furthermore, we calculated the thermodynamic functions of these reactions to discuss the influence of temperature. It is concluded that B₄N₄H₄ may exist in theory and could be a little more stable than C₈H₄. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 293–298, 2001     

Octacoordinate carbon atom in tetra(metalloamino)methanes CN<Subscript>4</Subscript>M<Subscript>4</Subscript> (M = Be,Mg, Ca): Quantum-chemical investigation

Quantum-chemical methods, ab initio [MP2(full)/6-311+G**] and density functional theory (B3LYP/6-311+G**), were applied to investigation of the electronic and spatial structure of tetraaminomethane derivatives CN₄M₄ (M = Be, Mg, Ca) both in classic and nonclassic isomeric forms. For all compounds structurally stable nonclassic isomeric forms were found with an octacoordinate carbon atom. The CN₄Be₄ is energetically most stable in a classic structure with a tetracoordinate carbon atom, whereas CN₄Mg₄ and CN₄Ca₄ are more stable in nonclassic structures with an octacoordinate carbon center.     

Noble‐Gas Complexes: Theoretical Investigation of Multicenter Polynuclear Species

Ab initio calculations at the MP2 level of theory disclose the conceivable existence of neutral complexes containing four or five distinct noble gases (Ng) each bound to a distinct Be‐atom. These multicenter polynuclear Ng molecules are formally obtained by replacing the H‐atoms of CH₄ and but‐2‐yne with ? NBeNg moieties, which behave as independent monovalent ‘functional groups’. Our investigated complexes include the five homotetranuclear [C(NBeNg)₄] complexes 1 – 5 (Ng=He? Xe), the five heterotetranuclear complexes [CN₄Be₄(He)(Ne)(Ar)(Kr)] ( 6 ), [CN₄Be₄(He)(Ne)(Ar)(Xe)] ( 7 ), [CN₄Be₄(He)(Ne)(Kr)(Xe)] ( 8 ), [CN₄Be₄(He)(Ar)(Kr)(Xe)] ( 9 ), and [CN₄Be₄(Ne)(Ar)(Kr)(Xe)] ( 10 ), and the heteropentanuclear complex [HC₄N₅Be₅(He)(Ne)(Ar)(Kr)(Xe)] ( 11 ). We also investigated the five model complexes [H₃CNBeNg] (Ng=He? Xe) containing a single ? NBeNg moiety. The geometries and vibrational frequencies of all these species, invariably characterized as minimum‐energy structures, were computed at the MP2(full)/6‐31G(d,p)/SDD level of theory, and their stability with respect to the loss of the various Ng‐atoms was evaluated by single‐point calculations at the MP2(full)/6‐311G(d)/SDD level of theory. The beryllium‐Ng binding energies range from ca. 17 (Ng=He) to ca. 63 (Ng=Xe) kJ/mol, and the results of natural‐bond‐orbital (NBO) and atoms‐in‐molecules (AIM) analysis reveal that the Be? Ng interaction is essentially electrostatic for helium, neon, argon, and krypton, and has probably a small covalent contribution for xenon.     

Basis sets for molecular interactions. 1. Construction and tests on (HF)2 and (H2O)2

Basis set superposition error (BSSE) remains one of the major difficulties besetting current ab initio calculations of molecular interactions. Despite the widespread notion that lowering of the BSSE to negligible magnitude requires extremely large basis sets, we show that simple modifications of basis sets of only moderate size (e.g., 6-31G**) can accomplish the same end at much reduced computational expense. These modifications include reoptimization of the orbital exponents within the framework of the relevant molecules, plus addition of a single diffuse shell of sp orbitals on nonhydrogen centers. Subsequent addition of a second set of d-functions further lowers the SCF BSSE, bringing it below 0.1 kcal/mol for both (HF)₂ and (H₂O)₂. It is notable that addition of the latter d-functions without prior reoptimization of the valence orbitals produces the opposite effect of an increase in the BSSE. Although the MP2 BSSE is also substantially decreased by the above modifications, it appears difficult to reduce this quantity below about 0.4 kcal/mol.     

A quantum mechanical approach to the kinetics of the hydrogen abstraction reaction H2O2 + •OH → HO2 + H2O

The kinetics of the hydrogen abstraction from H₂O₂ by ^?OH has been modeled with MP2/6‐31G*//MP2/6‐31G*, MP2‐SAC//MP2/6‐31G*, MP2/6‐31+G**//MP2/6‐31+G**, MP2‐SAC// MP2/6‐31+G**, MP4(SDTQ)/6‐311G**//MP2/6‐31G*, CCSD(T)/6‐31G*//CCSD(T)/6‐31G*, CCSD(T)/6‐31G**//CCSD(T)/6‐31G**, CCSD(T)/6‐311++G**//MP2/6‐31G* in the gas phase. MD simulations have been used to generate initial geometries for the stationary points along the potential energy surface for hydrogen abstraction from H₂O₂. The effective fragment potential (EFP) has been used to optimize the relevant structures in solution. Furthermore, the IEFPCM model has been used for the supermolecules generated via MD calculations. IEFPCM/MP2/6‐31G* and IEFPCM/CCSD(T)/6‐31G* calculations have also been performed for structures without explicit water molecules. Experimentally, the rate constant for hydrogen abstraction by ^?OH drops from 1.75 × 10^?12 cm³ molecule^?1 s^?1 in the gas phase to 4.48 × 10^?14 cm³ molecule^?1 s^?1 in solution. The same trend has been reproduced best with MP4 (SDTQ)/6‐311G**//MP2/6‐31G* in the gas phase (0.415 × 10^?12 cm³ molecule^?1 s^?1) and with EFP (UHF/6‐31G*) in solution (3.23 × 10^?14 cm³ molecule^?1 s^?1). © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 502–514, 2005     

Theoretical refinements of theendo and theexo structures of tetraborane(8) carbonyl

The molecular structures of theendo (1a) andexo (1b) isomers of B₄H₈CO have been optimized at the ab initio MP2(Full)/6-31G^* level of theory. The agreement of the computed geometrical parameters with the recently published electron-diffraction (GED) data is very good, even though a number of geometrical constraints were applied in the experimental determination. The IGLO (individual gauge for localized orbitals)¹¹B NMR chemical shifts, calculated at the II//MP2/6-31G^* level, are also in accord with experiment. The formation of1a and1b by association of B₄H₈ and CO is computed to be exothermic by 22.8 and 22.2 kcal/mol, respectively, at the MP2(Full)/6-31G^*//MP2(Full)/6-31G^* + ZPE(6-31G^*) level of theory. The Lewis acid strength of B₄H₈ toward CO is comparable to that of BH₃.     

Degenerate lithium-hydrogen exchange reactions: Ab initio models for metallation mechanisms involving H2, CH4, NH3, H2O,and HF

Hydrogen exchange reactions between lithium and sodium compounds, MX (M=Li: X=H, CH₃, NH₂, OH, F; M=Na: X=CH₃), and the corresponding hydrides, HX, have been modelled by means of ab initio calculations including electron correlation and zero point energy (ZPE) corrections. Small or no activation barriers (from the initial complexes) are encountered in systems involving lone pairs (10.8, 2.4, 0.0 kcal/mol for X=NH₂, OH, F, respectively). Since the association energies of the initial complexes are much larger (21.0, 20.4, 23.5 kcal/mol, respectively; MP2/6–31+G*/6–31+G* + ZPE), such exchange reactions should occur spontaneously in the gas phase. The methyl systems (X=CH₃) have the largest barriers: 26.7 (M=Li) and 31.7 (M=Na) kcal/mol (MP2/6–31+G*/6–31G* + ZPE), and the initial complexes are only weakly bound. The significance of these systems as models for hydrogen exchange reactions in complexes of electropositive transition metals is discussed. However, the gegenion-free exchange of hydrogen between CH₃ and CH₄ has a much lower, 11.8 kcal/mol barrier (MP2/6–31+G*/6–31+G* + ZPE). All the transition structures are highly ionic (charges on the metals > +0.8). The effect of aggregation has been considered by examining the hydrogen exchange between (LiX)₂ and HX(X=H, CH₃, NH₂, OH). Although these dimer reactions formally involve six, instead of four electrons, no “aromatic” preference is observed.