6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001     

Theoretical study of the red‐ and blue‐shifted hydrogen bonds of nitroxyl and acetylene dimers

Ab initio molecular orbital and density functional theory (DFT) in conjunction with different basis sets calculations were performed to study the C? H…O red‐shifted and N? H…π blue‐shifted hydrogen bonds in HNO? C₂H₂ dimers. The geometric structures, vibrational frequencies and interaction energies were calculated by both standard and counterpoise (CP)‐corrected methods. In addition, the G3B3 method was employed to calculate the interaction energies. The topological and natural bond orbital (NBO) analysis were investigated the origin of N? H…π blue‐shifted hydrogen bond. From the NBO analysis, the electron density decrease in the σ* (N? H) is due to the significant electron density redistribution effect. The blue shifts of the N? H stretching frequency are attributed to a cooperative effect between the rehybridization and electron density redistribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Kinetic Study and NBO Analysis of the Dehydrogenation Mechanism of Five‐membered Ring Heterocyclic 2,5‐Dihydro‐[furan,thiophene, selenophene

The theoretical study of the dehydrogenation of 2,5‐dihydro‐[furan ( 1 ), thiophene ( 2 ), and selenophene ( 3 )] was carried out using ab initio molecular orbital (MO) and density functional theory (DFT) methods at the B3LYP/6‐311G**//B3LYP/6‐311G** and MP2/6‐311G**//B3LYP/6‐311G** levels of theory. Among the used methods in this study, the obtained results show that B3LYP/6‐311G** method is in good agreement with the available experimental values. Based on the optimized ground state geometries using B3LYP/6‐311G** method, the natural bond orbital (NBO) analysis of donor‐acceptor (bond‐antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from non‐bonding lone‐pair orbitals [LP(e)_X3] to δ*_{C(1)  H(2)} antibonding orbital, decrease from compounds 1 to 3 . The LP(e)_X3→δ*_{C(1)  H(2)} resonance energies for compounds 1 – 3 are 23.37, 16.05 and 12.46 kJ/mol, respectively. Also, the LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the decrease of occupancies of LP(e)_X3 non‐bonding orbitals in ring of compounds 1 – 3 ( 3 > 2 > 1 ). The electronic delocalization from LP(e)_X3 non‐bonding orbitals to δ*_{C(1)  H(2)} antibonding orbital increases the ground state structure stability, Therefore, the decrease of LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the kinetic of the dehydrogenation reactions of compounds 1 – 3 (k ₁ >k ₂ >k ₃ ). Also, the donor‐acceptor interactions, as obtained from NBO analysis, revealed that the (_C(4)C(7)→δ*_{C(1)  H(2)} resonance energies decrease from compounds 1 to 3 . Further, the results showed that the energy gaps between (_C(4)C(7) bonding and δ*_{C(1)  H(2)} antibonding orbitals decrease from compounds 1 to 3 . The results suggest also that in compounds 1 – 3 , the hydrogen eliminations are controlled by LP(e)→δ* resonance energies. Analysis of bond order, natural bond orbital charges, bond indexes, synchronicity parameters, and IRC calculations indicate that these reactions are occurring through a concerted and synchronous six‐membered cyclic transition state type of mechanism.     

Electronic structure,chemical bonding,and oxidation numbers of first‐row transition metals in [MePIm2] complexes and their cations

The qualitative structures of the upper one‐electron energy levels of imidazole‐coordinated first‐row transition metal porphyrin [MePIm₂] complexes established in the present study have shown that the second oxidation number of the first‐row transition metals in the neutral complexes do not change in their cations and double cations. It was found that occupied orbitals of the density functional theory method obtained with B3LYP functional are not correctly ordered. Therefore, they cannot be used in investigations of the orbital structure of the upper molecular orbitals. A qualitative analysis of density functional theory method wave functions in terms of Mulliken and natural charges of atoms, together with an analysis of electrostatic potentials of the neutral [MePIm₂] complex, its single and double cations, demonstrates that the highest occupied orbitals of these complexes are mainly formed by atomic orbitals of the porphyrin ring atoms. Therefore, transition metal atoms are not active in chemical reactions with these complexes unless the 3d electrons of transition metal atoms are excited, for example by light. A mechanism of an electron transfer reaction that occurs between a heme cytochrome and Fe‐oxide mineral surface is discussed in the light of the obtained results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An ab initio evaluation of the role of p,π interaction: I. Ethylene derivatives

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for XCH=CH₂ molecules (X = F, Cl, Br, CH₃, CH₂CH₃, CH₂F, CHO). The p _y electron density distribution in these molecules and the bonding molecular orbitals formed by the p _y orbitals of atoms of the planar fragment of these molecule (atomic orbitals whose symmetry axes are perpendicular to this plane) are not determined by the p,π conjugation between the lone electron pair of the heteroatom in substituent X and π electrons of the C=C bond. Changes in the population of the p _y orbitals of the halogen and carbon atoms in going from X = F to X = Cl and Br are not associated with changes in the extent of this p,π interaction. Taking into account the electon correlation in the MP2 method does not noticeably alter the features of the electron density distribution in these molecules estimated by restricted Hartree-Fock calculations.     

An ab initio study of the p,π interaction: III. Interaction of an ether oxygen atom with a double bond

RHF/6-311G(d) calculations were performed for the H₂C=CHOCH₃ and H₂C=CClOCH₃ molecules with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The first molecule has one energy minimum and one transition state, and the second molecule, two minima. Changes in the populations of the p _y orbitals of the olefinic carbon and oxygen atoms (orbitals whose symmetry axes are perpendicular to the molecular plane) and in the fractional charges on these carbon atoms, occurring upon rotation of the methoxy groups about the C-O bonds, cannot be attributed to changes in the extent of the p,π conjugation between the lone electron pairs of the oxygen atoms and π electrons of the C=C bonds.     

Al8P8团簇环状结构与性质的密度泛函理论研究

用密度泛函理论(DFT)中的杂化密度泛函B3LYP方法, 在6-31G*水平上对Al8P8团簇的环状结构进行了几何结构优化, 并在同一水平上计算了Al8P8团簇的电子结构、振动特性及极化率和超极化率. 用自然键轨道(NBO)方法分析了成键性质, Al8P8团簇中离子键和共价键共存, 而且在不同轨道中原子间成键有不同的杂化方式. 计算结果表明: 优化后的Al8P8团簇为双层环状结构; 价电子态密度显示其电子结构具有半导体的性质; 最强的IR和Raman谱峰分别位于530.65 cm-1和366. 54 cm-1处.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

An ab initio study of the p,π interaction: IV. Interaction of an ether oxygen atom with a carbonyl group

RHF/6-311G(d) calculations were performed for the H₃COCOH molecule with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The molecule can exist in two stable conformations with the dihedral angle O¹C¹O²C² of 0.00° and 179.99°. The influence of the rotation angle on the population of the p _y orbital of the carbonyl oxygen atom in compounds with different types of the adjacent bond is essentially similar. The results obtained are inconsistent with the concept of the p,π conjugation involving the p _y orbitals of the planar molecular fragment (orbitals whose symmetry axes are perpendicular to this fragment).     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The Bonding Nature of the Canonical Molecular Orbitals in Simple Diatomic Molecules

The bonding nature of the canonical molecular orbitals 2σg, 2σu and 3σg in the molecules N₂,O₂, F₂ and the related analogous molecular orbitals in the molecules P₂ and CO, is analysed using Weinhold's natural bond orbital set. When the canonical molecular orbitals can be well localized into natural bond orbitals, the covalent bond can be completely attributed to the bonding type natural bond orbitals. The decomposition of canonical molecular orbitals into the natural bond orbital basis then gives the weighted bond order as the component of the bonding portion in the canonical molecular orbital. The weighted bond order results match the photoelectron spectroscopy assignment quite satisfactorily.     

Evaluation of N—H…S and N—H…π interactions in O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate: a combination of X‐ray crystallographic and theoretical studies

In the crystal structure of O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate, C₁₃H₂₂NO₂PS, two symmetrically independent thiophosphoramide molecules are linked through N—H…S and N—H…π hydrogen bonds to form a noncentrosymmetric dimer, with Z′ = 2. The strengths of the hydrogen bonds were evaluated using density functional theory (DFT) at the M06‐2X level within the 6‐311++G(d,p) basis set, and by considering the quantum theory of atoms in molecules (QTAIM). It was found that the N—H…S hydrogen bond is slightly stronger than the N—H…π hydrogen bond. This is reflected in differences between the calculated N—H stretching frequencies of the isolated molecules and the frequencies of the same N—H units involved in the different hydrogen bonds of the hydrogen‐bonded dimer. For these hydrogen bonds, the corresponding charge transfers, i.e. lp (or π)→σ*, were studied, according to the second‐order perturbation theory in natural bond orbital (NBO) methodology. Hirshfeld surface analysis was applied for a detailed investigation of all the contacts participating in the crystal packing.     

Interplay between Metal⋅⋅⋅π Interactions and Hydrogen Bonds: Some Unusual Synergetic Effects of Coinage Metals and Substituents

The ternary systems of C₂H₄ (C₂H₂ or C₆H₆)‐MCN‐HF (M=Cu, Ag, Au) and the respective binary systems were investigated to study the interplay between metal???π interactions and hydrogen bonds. The metal???π interactions in C₂H₄‐MCN become stronger with the irregular order Ag<Cu<Au, while the hydrogen bonds in MCN‐HF become weaker following the same order. The metal???π interactions are weakened as the H atoms in the π system are replaced with electron‐withdrawing groups and enhanced by electron‐donating groups. Type 1 of these ternary systems, in which MCN acts as Lewis base and acid simultaneously, is more stable than type 2, in which C₂H₄ acts as a double Lewis base. Negative cooperativity is present in type 2 ternary systems with a weakening of the metal???π interactions and the hydrogen bonds. Positive cooperativity is found in type 1 ternary systems with an enhancement of the metal???π interactions and the hydrogen bonds, except for C₂(CN)₄‐AuCN‐HF‐1. The weaker metal???π interaction in C₆H₆‐AuCN has a greater enhancing effect on the hydrogen bond in AuCN‐HF than those in C₂H₄‐AuCN and C₂H₂‐AuCN. These synergetic effects were analyzed with the natural bond orbital and energy decomposition.     

An ab initio evaluation of the role of p,π interaction: II. Molecules of the CH3COX series

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for CH₃COX molecules (X = F, Cl, Br, CH₃). Variations in the populations of the p _y orbitals of their halogen and carbon atoms (orbitals whose symmetry axes are perpendicular to the molecular plane) from X = F to X = Cl, Br, and CH₃ are not associated with variations in the extent of the p,π conjugation between the lone electron pair of the halogen atom and the π-electron system of the carbonyl group. The bonding molecular orbitals formed by these atomic p _y orbitals are not determined by this interaction. The RHF/6-311G(d) and MP2/6-311G(d) calculations give similar results.     

The theoretical study on anionic polymerization mechanism of maleimide: Chain propagation by p‐π conjugation process

A complete research on the mechanism of the anionic polymerization of maleimide was performed, not only including the chain initiation, but the propagation as well. The density functional theory method is employed to investigate the reaction pathway using 6‐311+G* basis set, and the Onsager model is also applied to imitate the effect of solvent on the structures and thermodynamic functions of the key steps. It is found that the initiation starts with a nucleophilic reaction, in which the key transition state shows a π‐complex structure. In contrast, the calculated chain propagation (both dimer and trimer process) employs a p‐π conjugation chain propagation mechanism (p‐π CCPM), characterized by the formation of p‐π conjugation orbital between the chain terminal C atom and monomer C?C double bond. This mechanism is in good agreement with the frontier molecular theory and the principle of conservation of molecular orbital symmetry. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

磷的d轨道在H~3PO分子中的作用

用分子片轨道在分子环境中发生极化的概念研究d轨道在H~3PO分子中的作用。H~3PO分子被分为两个分子片---H~3P和O.在RHF/6-31G^*水平上计算出分子环境中的极化了的分子片轨道(FOM)。再剔除d函数为主的FOM,用剩余的FOM为基进行构型优化,得到与RHF/6-31G^*相近的结果。这一结果说明磷原子的d函数在H~3PO分子中仅仅起一个极化函数的作用,而不是起价轨道作用。     

Density Functional Theory Study on Hydrogen Bonding Interaction of Catechin-(H2O)n

Density functional theory B3LYP method with 6‐31G* basis set has been used to optimize the geometries of the catechin, water and catechin‐(H₂O)_n complexes. The vibrational frequencies have been studied at the same level to analyze these complexes. Six and eleven stable structures for the catechin‐H₂O and catechin‐(H₂O)₂ have been found, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are from ?13.27 to ?83.56 kJ/mol. All calculations also indicate that there are strong hydrogen‐bonding interactions in catechin‐water complexes. The strong hydrogen‐bonding contributes to the interaction energies dominantly. The O–H stretching motions in all the complexes are red‐shifted relative to that of the monomer.     

The influence of CH…π interaction on hydrogen bonding ability of –CONH<Subscript>2</Subscript> functional group of benzamide

Interplay between CH…π and hydrogen bond interactions of benzamide has been investigated by quantum mechanical calculations. The effect of the substituents on geometrical parameters has also been studied at the B3LYP level with 6-311++G(d,p) basis set. The electron-withdrawing substituents enhance the total interaction energy of the complexes. The results indicated that the cooperativity of interactions leads to extra stability of the ternary complexes. The CH…π interaction and the hydrogen bond energies have been estimated using the electron densities calculated by the atoms in molecules (AIM) method at hydrogen bond critical points. The strength of hydrogen bonding increases in the presence of CH…π interaction in the ternary complexes. The effect of CH…π interaction on the hydrogen bond interaction has also been studied by the natural bond orbital, AIM and the molecular electrostatic potential analyses.     

Structure, thermochemistry, and conformational analysis of peroxides ROOR and hydroperoxides ROOH (R = Me, But, CF3)

The equilibrium structures, total energies, and harmonic frequencies of peroxides ROOR and ROOH (R = Me, Bu^t, CF₃) were calculated using the perturbation theory (MP4//MP2 method) and density functional approach (B3LYP) in the 6-31G(d,p) basis set. The conformational flexibility of peroxides under rotation about the O-O bond was investigated. It was found that the stable conformation of a peroxide molecule is determined by superposition of the destabilizing effects (repulsion between the lone electron pairs, steric hindrances) and the interaction of the nonbonding orbitals of oxygen atoms with the antibonding orbitals of the adjacent polar bonds. The latter effect stabilizes the nonplanar structure of the peroxide molecule. The role of orbital interactions in manifestation of the d-effect (distortion of the tetrahedral configuration of the X₃CO fragment of peroxide molecule) was revealed. The vibrational spectra of peroxides were calculated and compared with the experimental data. The potential energy distribution over normal vibrations was analyzed. The enthalpies of formation and the bond strengths in the molecules of compounds examined were calculated in the framework of the isodesmic reaction approach.