On the basis‐set dependence of local and integrated electron density properties: Application of a new computer program for quantum‐chemical density analysis

A new computer program for post‐processing analysis of quantum‐chemical electron densities is described. The code can work with Slater‐ and Gaussian‐type basis functions of arbitrary angular momentum. It has been applied to explore the basis‐set dependence of the electron density and its Laplacian in terms of local and integrated topological properties. Our analysis, including Gaussian/Slater basis sets up to sextuple/quadruple‐zeta order, shows that these properties considerably depend on the choice of type and number of primitives utilized in the wavefunction expansion. Basis sets with high angular momentum (l = 5 or l = 6) are necessary to achieve convergence for local properties of the density and the Laplacian. In agreement with previous studies, atomic charges defined within Bader's Quantum Theory of Atoms in Molecules appear to be much more basis‐set dependent than the Hirshfeld's stockholder charges. The former ones converge only at the quadruple‐zeta/higher level with Gaussian/Slater functions. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Charge density distribution and electrostatic moments of N‐(4‐chloro‐3‐ trifluromethyl‐phenyl)‐2‐ethoxy‐benzamide molecule at the active site of p300 enzyme: A quantum chemical and theoretical charge density study

A Charge density analysis of CTB molecule in gas phase (Form I ) and the same present at the active site (Form II ) of p300 enzyme were performed for the wave functions obtained from the Density functional method (B3LYP) with the basis set 6‐311G**. This study has been carried out to understand the nature of conformational modification, charge redistribution and the change of electrostatic moments of the CTB molecule when present at the active site of p300. The difference of charge density distribution between both forms of CTB molecule explicitly indicates the effect of intermolecular interaction on CTB molecule in the active site. The dipole moment of CTB in the gas phase (9.6 D) has been significantly decreased (4.27 D) when it present at the active site of p300; this large variation is attributed to the charge redistribution in CTB, due to the intermolecular interaction between the CTB and the receptor p300 molecule. The electrostatic potential maps differentiate the difference of electrostatic potential between the two forms. A large electronegative region is found at the vicinity of oxygen and fluorine atoms. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Hydrogen bond in 3-acetyl-4-hydroxycoumarin: X-ray diffraction study and quantum-chemical calculations

The proton transfer and the character of the strong intramolecular O--H...O hydrogen bond (O...O 2.442 ) in 3-acetyl-4-hydroxycoumarin were analyzed based on the results of X-ray diffraction study in the temperature range from 100 to 353 K and quantum-chemical B3LYP/6-31G(d,p) calculations. The barrier to proton transfer along the H-bond line is low (2 kcal mol^–1). However, no proton transfer was observed in the crystal at 100 K. Bader's topological analysis of the electron density distribution both in the crystal and in the isolated molecule demonstrated that the hydrogen bond corresponds to an intermediate type of interatomic interactions (E(r) < 0, ²(r) > 0 at the critical point (3, –1)).     

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     

Blue‐shifted and red‐shifted hydrogen bonds: Theoretical study of the CH3CHO· · ·HNO complexes

The blue‐shifted and red‐shifted H‐bonds have been studied in complexes CH₃CHO…HNO. At the MP2/6‐31G(d), MP2/6‐31+G(d,p) MP2/6‐311++G(d,p), B3LYP/6‐31G(d), B3LYP/6‐31+G(d,p) and B3LYP/6‐311++G(d,p) levels, the geometric structures and vibrational frequencies of complexes CH₃CHO…HNO are calculated by both standard and CP‐corrected methods, respectively. Complex A exhibits simultaneously red‐shifted C? H…O and blue‐shifted N? H…O H‐bonds. Complex B possesses simultaneously two blue‐shifted H‐bonds: C? H…O and N? H…O. From NBO analysis, it becomes evident that the red‐shifted C? H…O H‐bond can be explained on the basis of the two opposite effects: hyperconjugation and rehybridization. The blue‐shifted C? H…O H‐bond is a result of conjunct C? H bond strengthening effects of the hyperconjugation and the rehybridization due to existence of the significant electron density redistribution effect. For the blue‐shifted N? H…O H‐bonds, the hyperconjugation is inhibited due to existence of the electron density redistribution effect. The large blue shift of the N? H stretching frequency is observed because the rehybridization dominates the hyperconjugation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The nature of the chemical bond revisited: an energy-partitioning analysis of nonpolar bonds

The nature of the chemical bond in nonpolar molecules has been investigated by energy-partitioning analysis (EPA) of the ADF program using DFT calculations. The EPA divides the bonding interactions into three major components, that is, the repulsive Pauli term, quasiclassical electrostatic interactions, and orbital interactions. The electrostatic and orbital terms are used to define the nature of the chemical bond. It is shown that nonpolar bonds between main-group elements of the first and higher octal rows of the periodic system, which are prototypical covalent bonds, have large attractive contributions from classical electrostatic interactions, which may even be stronger than the attractive orbital interactions. Fragments of molecules with totally symmetrical electron-density distributions, like the nitrogen atoms in N(2), may strongly attract each other through classical electrostatic forces, which constitute 30.0 % of the total attractive interactions. The electrostatic attraction can be enhanced by anisotropic charge distribution of the valence electrons of the atoms that have local areas of (negative) charge concentration. It is shown that the use of atomic partial charges in the analysis of the nature of the interatomic interactions may be misleading because they do not reveal the topography of the electronic charge distribution. Besides dinitrogen, four groups of molecules have been studied. The attractive binding interactions in H(n)E-EH(n) (E=Li to F; n=0-3) have between 20.7 (E=F) and 58.4 % (E=Be) electrostatic character. The substitution of hydrogen by fluorine does not lead to significant changes in the nature of the binding interactions in F(n)E-EF(n) (E=Be to O). The electrostatic contributions to the attractive interactions in F(n)E-EF(n) are between 29.8 (E=O) and 55.3 % (E=Be). The fluorine substituents have a significant effect on the Pauli repulsion in the nitrogen and oxygen compounds. This explains why F(2)N-NF(2) has a much weaker bond than H(2)N-NH(2), whereas the interaction energy in FO-OF is much stronger than in HO-OH. The orbital interactions make larger contributions to the double bonds in HB=BH, H(2)C=CH(2), and HN=NH (between 59.9 % in B(2)H(2) and 65.4 % in N(2)H(2)) than to the corresponding single bonds in H(n)E-EH(n). The orbital term Delta E(orb) (72.4 %) makes an even greater contribution to the HC triple bond CH triple bond. The contribution of Delta E(orb) to the H(n)E=EH(n) bond increases and the relative contribution of the pi bonding decreases as E becomes more electronegative. The pi-bonding interactions in HC triple bond CH amount to 44.4 % of the total orbital interactions. The interaction energy in H(3)E-EH(3) (E=C to Pb) decreases monotonically as the element E becomes heavier. The electrostatic contributions to the E-E bond increases from E=C (41.4 %) to E=Sn (55.1 %) but then decreases when E=Pb (51.7 %). A true understanding of the strength and trends of the chemical bonds can only be achieved when the Pauli repulsion is considered. In an absolute sense the repulsive Delta E(Pauli) term is in most cases the largest term in the EPA.     

Stability of Noble‐Gas‐Bound SiH3+ Clusters

The stability of noble gas (Ng)‐bound SiH₃⁺ clusters is explored by ab initio computations. Owing to a high positive charge (+1.53 e^?), the Si center of SiH₃⁺ can bind two Ng atoms. However, the Si?Ng dissociation energy for the first Ng atom is considerably larger than that for the second one. As we go down group 18, the dissociation energy gradually increases, and the largest value is observed for the case of Rn. For NgSiH₃⁺ clusters, the Ar–Rn dissociation processes are endergonic at room temperature. For He and Ne, a much lower temperature is required for it to be viable. The formation of Ng₂SiH₃⁺ clusters is also feasible, particularly for the heavier members and at low temperature. To shed light on the nature of Si?Ng bonding, natural population analysis, Wiberg bond indices computations, electron‐density analysis, and energy‐decomposition analysis were performed. Electron transfer from the Ng centers to the electropositive Si center occurs only to a small extent for the lighter Ng atoms and to a somewhat greater extent for the heavier analogues. The Si?Xe/Rn bonds can be termed covalent bonds, whereas the Si?He/Ne bonds are noncovalent. The Si?Ar/Kr bonds possess some degree of covalent character, as they are borderline cases. Contributions from polarization and charge transfer and exchange are key terms in forming Si?Ng bonds. We also studied the effect of substituting the H atoms of SiH₃⁺ by halide groups (?X) on the Ng binding ability. SiF₃⁺ showed enhanced Ng binding ability, whereas SiCl₃⁺ and SiBr₃⁺ showed a lower ability to bind Ng than SiH₃⁺. A compromise originates from the dual play of the inductive effect of the ?X groups and X→Si π backbonding (p_z–p_z interaction).     

A model of the chemical bond must be rooted in quantum mechanics, provide insight, and possess predictive power

In this response to the preceding paper by Bader, we show that the core arguments and statements presented in the latter are flawed. We argue that it is insufficient for a model of the chemical bond to be rooted in quantum mechanics. A good model must in addition provide insight and possess predictive power. Our molecular orbital (MO) model of the chemical bond, in particular, the associated energy-decomposition approach satisfies all these conditions. On the other hand, Atoms-in-Molecules (AIM) theory is only rooted in quantum mechanics as far as its mathematical framework is concerned. The physical status of its central concepts is not so clear. In particular, "bond paths" and "bond critical points" are once more confirmed not to be indicators of a stabilizing interaction. Moreover, AIM theory lacks any predictive power. We also address specific questions raised in the preceding paper. Finally, interpreting chemical bonding implies choosing a perspective on this phenomenon. That there are many perspectives is a matter of fact and this is in no way unphysical. What is unscientific is to claim uniqueness and truth for one of these choices, namely AIM, and to dismiss on this ground all other approaches.     

The competition between the intramolecular hydrogen bond and π‐electron delocalization in trifluoroacetylacetone—A theoretical study

Conformational study of trifluoroacetylacetone was carried out using the HF, B3LYP, and MP2 methods with the 6‐31G(d, p) and 6‐311++G(d, p) basis sets. All of the results show that the chelated enol structures (E11 and E31) have extra stability with respect to the other forms and one of them (E11) is global minimum. The energy gap between the chelated forms is in the range 0.7–5.9 kJ mol^?1. Theoretical calculations show that this compound has an asymmetric double minimum potential energy surface which is in contrast with the electron diffraction result. Moreover, the computational results predict that due to the withdrawing effect of CF₃ group, hydrogen bond in trifluoroacetylacetone is weaker than the acetylacetone. Because of the more stability of E11, it is expected that the hydrogen bond energy in E11 is greater than the E31, but at all of the computational levels with most extended basis set the converse results were observed. These results clearly show that the hydrogen bond is not a superior parameter in conformational preference and the contribution of resonance is probably greater than the hydrogen bond. Finally, the analysis of this system by quantum theory of atoms in molecules and natural bond orbital methods fairly support the ab initio results. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Assessment of substituent effects on the parameters of 35Cl nuclear quadrupole resonance in para‐substituted benzene‐sulphenyl chloride via quantum chemical calculations

In this research, substituent effects on the parameters of ³⁵Cl nuclear quadrupole resonance (NQR) in para‐substituted benzene‐sulphenyl chloride were studied at M062X/6‐311G(d,p) theory level. The ³⁵Cl NQR parameters of the quadrupole coupling constant (QCC) and electric‐field gradient (EFG) tensor, as well as an asymmetric parameter, were shown to be correlated with Hammett constant following their calculations. The frontier orbital energy levels, HOMO‐LUMO gaps, hardness, electrophilicity, and chemical potential values of these molecules were calculated as well. natural bond orbital (NBO) analysis was applied for calculating natural populations at chlorine atoms.     

Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

杂氮硼三环类化合物的UPS及化学键的理论研究

报道了六种杂氮硼三环类化合物的紫外光电子能谱(UPS).采用RHF/3-21G优化了各分子的优势构型,根据化合物UPS的谱带特征结合RHF/6-31G^*的计算结果对化合物的UPS进行了解析和指认,精确给出了各化合物中σN-B配键电子的电离峰位置.利用电子密度拓扑分析方法对各化合物的成键情况的研究显示:在该类化合物中B原子具有较为明显的阳离子的特征,N,B原子间均存在键鞍点.从实验和理论上证实了该类体系中σN-B的存在.各化合物的UPS,SCFMO计算和电子密度拓扑分析都表明,在该类体系中环上CH~3,CH~2的引入削弱了B,N间的成键作用;环上羰基的引入增强了B,N间的成键作用。     

A comparative study of some lithium and hydrogen‐bonded complexes: Ab initio and QTAIM studies

The nature of the interactions of cyanide with lithium and hydrogen halides was investigated using ab initio calculations and topological analysis of electron density. The computed properties of the lithium‐bonded complexes RCN···LiX (R = H, F, Cl, Br, C?CH, CH?CH₂, CH₃, C₂H₅; X = Cl, Br) were compared with those of corresponding hydrogen‐bonded complexes RCN···HX. The results show that both types of intermolecular interactions are “closed‐shell” noncovalent interactions. The effect of substitution on the interaction energy and electron density at the bond critical points of the lithium and hydrogen bonding interactions is similar. In comparison, the interaction energies of lithium‐bonded complexes are more negative than those of hydrogen‐bonded counterparts. The electrostatic interaction plays a more important role in the lithium bond than in the hydrogen bond. On complex formation, the net charge and energy of the Li atom decrease and the atomic volume increases, while the net charge and energy of the H atom increase and the atomic volume decreases. © 2013 Wiley Periodicals, Inc.     

Strength of the [Z–I···Hal]− and [Z–Hal···I]− Halogen Bonds: Electron Density Properties and Halogen Bond Length as Estimators of Interaction Energy

Bond energy is the main characteristic of chemical bonds in general and of non-covalent interactions in particular. Simple methods of express estimates of the interaction energy, E_int, using relationships between E_int and a property which is easily accessible from experiment is of great importance for the characterization of non-covalent interactions. In this work, practically important relationships between E_int and electron density, its Laplacian, curvature, potential, kinetic, and total energy densities at the bond critical point as well as bond length were derived for the structures of the [Z–I···Hal]⁻ and [Z–Hal···I]⁻ types bearing halogen bonds and involving iodine as interacting atom(s) (totally 412 structures). The mean absolute deviations for the correlations found were 2.06–4.76 kcal/mol.     

Evaluation of the origin of conformational and tautomeric preferences in N‐formylformamide – A quantum chemical study

Quantum chemical study of N‐formylformamide (NFF) was carried out at various theoretical levels and the determinate equilibrium conformations were recomputed at the high level ab initio methods such as G2MP2, G2, G3, and complete basis set (CBS)‐QB3. The computational results reveal that the amide resonance and intramolecular hydrogen bonding are two superior factors in determining the most stable conformation of diamide (DA) and amide–imidic (AI) acid tautomers, respectively. The evaluation of hydrogen bond energies predicts that the hydrogen bond (HB( strength of NFF is weaker than the malonaldehyde (MA). But the results of atoms in molecules (AIM(, natural bond orbital (NBO), and geometrical parameters are given a different order, E_HB(NFF) > E_HB(MA). Although the bond average energies of tautomerization process emphasized on more stability of AI tautomer, but our theoretical calculations reveal that the DA conformers are more stable than the AI ones. The population analyses of equilibrium conformations by NBO method also predict that the origin of tautomeric preference is mainly because of the electron delocalization of amide functional group, especially LP(N)→ π*_C?O charge transfer. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Terms representing the reorganization of bonding within charge‐bond order matrices of reacting molecules

The usual way of obtaining charge‐bond order (CBO) matrices of molecules by summing up the MO LCAO coefficients over occupied molecular orbitals (MOs) is extended to derive terms representing the reorganization of bonding in reacting systems. The CBO matrix of a certain molecule (reactant) under influence of another one (reagent) is expressed in the form of power series with respect to intermolecular interaction. Terms of this series responsible for the internal reorganization of bonding in the reactant are also shown to be representable by sums of MO LCAO coefficients of the relevant isolated compound. As opposed to the case of a single molecule, the new sums embrace all MOs of the reactant and their pairs. This result is conditioned by the fact that the actual occupation numbers of MOs differ from either two or zero in the bimolecular system because of the intermolecular charge transfer, and bond orders arise between pairs of MOs in addition. Partial increments to the final reorganization of bonding related to individual MOs and to their pairs are then studied separately. These increments may be classified on the basis of criteria applied to MOs they originate from. In particular, symmetric and antisymmetric increments are distinguished with respect to any symmetry operation of the isolated reactant lost under influence of an approaching reagent. Increments of the same symmetry are subsequently collected into separate groups representable by specific graphical schemes. Consequently, the final pattern of charge and bond order redistribution in the reactant under influence of an approaching reagent follows from superposition of a few principal schemes. The results are illustrated by consideration of specific examples, in particular of addition of electrophile to the butadiene molecule. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Disentanglement of orthogonal hydrogen and halogen bonds via natural orbital for chemical valence: A charge displacement analysis

As known, the electron density of covalently bound halogen atoms is anisotropically distributed, making them potentially able to establish many weak interactions, acting at the same time as halogen bond donors and hydrogen bond acceptors. Indeed, there are many examples in which the halogen and hydrogen bond coexist in the same structure and, if a correct bond analysis is required, their separation is mandatory. Here, the advantages and limitations of coupling the charge displacement analysis with natural orbital for chemical valence method (NOCV-CD) to separately analyze orthogonal weak interactions are shown, for both symmetric and asymmetric adducts. The methodology gives optimal results with intermolecular adducts but, in the presence of an organometallic complex, also intramolecular interactions can be correctly analyzed. Beyond the methodological aspects, it is shown that correctly separate and quantify the interactions can give interesting chemical insights about the systems.     

取代1-氯蒽醌中分子内卤键的电子密度拓扑分析

运用量子化学密度泛函B3LYP方法,在6-311＋＋G（d,p）基组水平上对邻位和间位取代1-氯葸醌的分子内卤键进行了研究．用电子定域函数和“分子中的原子,,理论对分子内卤键的性质进行了电子密度拓扑分析．通过对计算得到的密度矩阵进行σ-π兀分离,得到了π-键的键径和分子图,并讨论了。电荷密度和兀电荷密度对卤键的影响．结果表明,键鞍点和环鞍点处的电子密度拓扑性质均可作为衡量分子内卤键强度的量度．键鞍点和环鞍点处的电荷密度P越大,键鞍点与环鞍点的距离越大,卤键强度越大．除σ电荷密度外,π电荷密度对分子内卤键的性质也有明显影响．     

Bond dissociation energies for removal of the hydroxyl group in some alcohols from quantum chemical calculations

In this theoretical work, 22 alcohols and their geometric structure properties have been investigated employing quantum chemical methods to calculate the C? OH equilibrium bond distances and bond dissociation energies (BDEs). Since DFT methods have been researched to have low basis sets sensitivity for small and medium molecules in our previous work (Zhao et al., J Mol Struct, 2006, 766, 87), 22 title compounds have been studied by employing the hybrid density functional theory (B3LYP, B3PW91, B3P86, PBE1PBE) in conjunction with the 6‐311G** basis set and the complete basis set (CBS–Q) method. Comparison with the available experimental data shows that CBS–Q and B3P86 methods calculated results agree very well with the experimental values, with the average absolute errors of 1.3 kcal/mol and 3.5 kcal/mol, respectively. So considering the expensive computational time, CBS–Q method can be chosen as a satisfactory method of predicting the accurate BDEs for removal of the OH group in small and medium size alcohols. And B3P86 method may give accurate BDEs for larger alcohols we haven't studied. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011