Metal-Ligand Bonds in Rare Earth Metal-Biphenyl Complexes.

A series of theoretical methods, including density functional theory, multiconfiguration molecular orbital theory, and ab initio valence bond theory, are devoted to understanding the metal-ligand bonds in M-BP (BP = biphenyl; M = Sc, Y, or La) complexes. Different from most transition metal-BP complexes, the most stable metal-biphenyl conformers are not half-sandwich but clamshell. Energy decomposition analysis results reveal that the M-BP bonds in the clamshell conformers possess extra-large orbital relaxation. According to the wave function analysis, 2-fold donations and 2-fold back-donations exist in the clamshell M-BP bonds. The back-donations from M to BP are quite strong, while donations from BP to M are quite weak. Our work improves our understanding of the metal-ligand bonds, which can be considered as the "reversed" Dewar-Chatt-Duncanson model.

Revealing the biradicaloid nature inherited in the derivatives of thieno[3,4-c][1,2,5]thiadiazole: a computational study.

Computational studies were performed on non-classical thieno[3,4-c][1,2,5] thiadiazole and its pi donor derivatives (TT dyes) so as to delineate the factors responsible for their near-infrared (NIR) absorption. For all dyes except the unsubstituted bare dye, adiabatic singlet-triplet energy gaps (estimated through the ΔSCF procedure using the B3LYP and M062X DFT methods and SFTDDFT with the 5050 functional) were less than 1eV. Percentage calculations of the biradicaloid character suggested a moderate biradicaloid nature in all derivatives. There was a resemblance between the frontier molecular orbital (MO) picture of the TT bicyclic ring and the degenerate non-bonding molecular orbitals of Trimethyleneethane (TME, a known biradical). Inter-fragment charge transfer analysis revealed not only a considerable donation of charge to the central ring (Acceptor, TT part) but also substantial charge redistribution within the ring itself. From these results, it was inferred that NIR absorption, in these dyes, was due to: (1) a reduced HOMO-LUMO gap (HLG) as a TME biradical substructure forms its chromophoric part; and (2) charge transfer from the donor substituents. The non-bonding nature of the S atom, in the bare dye, with its neighbouring N/C atom (of the highest occupied π-MOs), led to an examination of its electronic structure using the ab initio valence bond method. The relatively large weight and energetic stability of the biradicaloid VB structures compared to those of the ylidic structures clearly disclosed the importance of biradicaloid structures in the overall resonance of the bare dye. Their utility as singlet fission materials was screened using singlet and triplet energy-based molecular structure activity criteria. The results were encouraging, demanding experiments to reaffirm the materials' usefulness.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited.

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.

Novel implementation of seniority number truncated valence bond methods with applications to H22 chain.

Both the efficiency and capability of the seniority number truncated valence bond (VB) methods are highly improved by using our recently proposed extension of Malmqvist's algorithm for the reciprocal transformation of many-electron bases constructed by nonorthogonal orbitals [Zhou, Chen, and Wu, J. Chem. Phys. 149(4), 044111 (2018)] and by the adoption of the direct technique in solving the generalized eigenvalue problem. Due to the compactness of the wave function that benefited from seniority number restriction, the memory need and computational cost for energy evaluation and orbital optimization in valence bond self-consistent field calculation are largely reduced. The last obstacle in nonorthogonal orbital based ab initio VB calculation is thus removed. Consequently, we can accomplish seniority number truncated VB calculation at the same computational scaling as that of the most general configuration selected multiconfigurational self-consistent field with a memory cost much less than the corresponding complete active space self-consistent field (CASSCF). Test on Hn string molecules shows that the seniority number truncated VB calculation maintains the majority of static correlation by using a more compact wave function than CASSCF.

Valence Bond Based Energy Decomposition Analysis Scheme and Its Application to Cation-π Interactions.

A new energy decomposition analysis (EDA) scheme based on valence bond (VB) wave function, called VB-EDA, is presented. In VB-EDA, the total interaction energy is decomposed into frozen, charge transfer, polarization and dynamic correlation terms based on valence bond calculations. The frozen term is the energy variation of the unrelaxed VB wave function according to the change of an interaction distance. The charge transfer term is the contribution of the additional VB structures while the polarization term is due to the relaxation of VB orbitals. Dynamic correlation term is computed by post-VBSCF methods. Different from other existing VB based EDA schemes, which were used to analyze noncovalent interactions for some specific complexes, the newly developed VB-EDA is designed for the general use. Using VB-EDA, the bonding nature of cation-π interactions in a series of cation-π complexes (cations = Li+, Na+, K+, Mg2+, and Ca2+; π systems = ethylene and benzene) is explored. Furthermore, a new covalency index, which demonstrates the covalency of cation-π interactions, is presented based on the VB-EDA results. The VB-EDA analysis reveals that the cation-π interactions in the Li+, Na+, and K+ complexes belong to the typical ionic bonds while the Mg2+ and Ca2+ complexes have the relatively large covalent characteristics. However, only the C2H4-Mg2+ complex can be regarded as a covalent bonding complex while the other complexes belong to the typical ionic complexes. Thereupon, it must be careful in the cognition for the covalency of intermolecular interaction. Large nonelectrostatic interaction component does not always correspond to a covalent bond.

Explicit construction of diabatic state and its application to the direct evaluation of electronic coupling.

A valence bond (VB) block-diagonalization approach, named VBBDA, is proposed to construct the charge-localized diabatic state explicitly within the framework of ab initio VB theory. Since the VB structure built upon the localized orbitals represents the charge localized character of the diabatic state faithfully, we are able to obtain accurate electronic coupling between diabatic states by using a very compact VB wave function. Moreover, the potential energy curves of the diabatic states and hence the crossing points of them can be accurately evaluated. The pilot applications showed that the electronic couplings computed by the VB method are consistent with the complete active space self-consistent field method and may even be close to the results of other high-level ab initio methods such as full configuration interaction and multireference configuration interaction. In addition, the computed electronic couplings show the expected exponential attenuation for the donor-acceptor systems as the distance increases. Moreover, VBBDA has the capability for handling complicated systems based on either two-state or multi-state treatment. Finally, because of the outstanding performance of the Xiamen Valence Bond software package, which is an ab initio VB program, VBBDA is capable for systems consisting more than 1000 basis functions.

How solvent influences the anomeric effect: roles of hyperconjugative versus steric interactions on the conformational preference.

The block-localized wave function (BLW) method, which can derive optimal electron-localized state with intramolecular electron delocalization completely deactivated, has been combined with the polarizable continuum model (PCM) to probe the variation of the anomeric effect in solution. Currently both the hyperconjugation and electrostatic models have been called to interpret the anomeric effect in carbohydrate molecules. Here we employed the BLW-PCM scheme to analyze the energy differences between α and ß anomers of substituted tetrahydropyran C5OH9Y (Y = F, Cl, OH, NH2, and CH3) and tetrahydrothiopyran C5SH9Y (Y = F, Cl, OH, and CH3) in solvents including chloroform, acetone, and water. In accord with literature, our computations show that for anomeric systems the conformational preference is reduced in solution and the magnitude of reduction increases as the solvent polarity increases. Significantly, on one hand the solute-solvent interaction diminishes the intramolecular electron delocalization in ß anomers more than in α anomers, thus destabilizing ß anomers relatively. But on the other hand, it reduces the steric effect in ß anomers much more than α anomers and thus stabilizes ß anomers relatively more, leading to the overall reduction of the anomeric effect in anomeric systems in solutions.

Nonorthogonal orbital based n-body reduced density matrices and their applications to valence bond theory. III. Second-order perturbation theory using valence bond self-consistent field function as reference.

Using the formulas and techniques developed in Papers I and II of this series, the recently developed second-order perturbation theory based on a valence bond self-consistent field reference function (VBPT2) has been extended by using the internally contracted correction wave function. This ansatz strongly reduces the size of the interaction space compared to the uncontracted wave function and thus improves the capability of the VBPT2 method dramatically. Test calculations show that internally contracted VBPT2 using only a small number of reference valence bond functions, can give results as accuracy as the VBPT2 method and other more sophisticated methods such as full configuration interaction and multireference configuration interaction.

VBEFP: a valence bond approach that incorporates effective fragment potential method.

An ab initio explicit solvation valence bond (VB) method, called VBEFP, is presented. The VBEFP method is one type of QM/MM approach in which the QM part of system is treated within the ab initio valence bond scheme and the solvent water molecules are accounted by the effective fragment potential (EFP) method, which is a polarized force field approach developed by Gordon et al. (J. Chem. Phys. 1996, 105, 1968). This hybrid method enables one to take the first-solvation shell and heterogeneous solvation effects into account explicitly with VB wave function. Therefore, the nature of chemical bonding and the mechanism of chemical reactions with explicit solvent environments can be explored at the ab inito VB level. In this paper, the hydrated metal-ligand complexes [M(2+)L](H(2)O)(n) (M(2+): Mg(2+), Zn(2+); L: NH(3), CH(2)O) are studied by the VBEFP method. Resonance energy and bond order are computed, and the influence of the solvent coordination and hydrogen bonding to the metal-ligand bonding are explored in the paper.

Sensing or no sensing: can the anomeric effect be probed by a sensing molecule?

The anomeric effect plays a central role in carbohydrate chemistry, but its origin is controversial, and both the hyperconjugation model and the electrostatic model have been proposed to explain this phenomenon. Recently, Cocinero et al. designed a peptide sensor, which can bind to a sugar molecule methyl D-galactose, and claimed that the anomeric effect can be sensed by the spectral changes from the ß- to the α-complex, which are ultimately attributed to the lone pair electron density change on the endocyclic oxygen atom [Nature 2011, 469, 76; J. Am. Chem. Soc. 2011, 133, 4548]. Here, we provide strong computational evidence showing that the observed spectral changes simply come from the conformational differences between the α- and ß-anomers, as the replacement of the endocyclic oxygen atom with a methylene group, which disables both the endo- and the exo-anomeric effects in methyl D-galactose, leads to similar spectral shifts. In other words, the "sensor" cannot probe the anomeric effect as claimed. We further conducted detailed energetic and structural analyses to support our arguments.

Primary Exophytic Extraskeletal Osteosarcoma of the Liver: A Case Report and Literature Review.

INTRODUCTION: Primary hepatic extraskeletal osteosarcoma (ESOS) is a rare tumor with no specific clinical manifestations, and little is known about it. Here, we describe an elderly patient with primary hepatic osteosarcoma confirmed by pathology results to raise awareness. CASE REPORT: We report an unusual case of a 62-year-old man who presented with right upper quadrant pain. The inflammatory indicators were elevated, and alkaline phosphatase (AKP), carbohydrate antigen (CA-199 and CA-125) were slightly increased. Computed tomography images and magnetic resonance images discovered a 7.8 × 7.4 × 6.6 cm mass with irregular radiated and cotton-like tumor bone between the liver and right kidney space. Pathology revealed the mass to be primary exophytic ESOS of the liver. The patient underwent a surgical operation and standard chemotherapy and is still alive with no recurrence and metastasis to date. CONCLUSION: Owing to the rarity of the tumor and the lack of clinical characteristics and specific laboratory indexes, it is difficult to make a correct diagnosis. Medical imaging features mainly behave soft tissue entity with tumor bone composition. Surgical resection combined with adjuvant chemotherapy is the main treatment for ESOS.

Topology of electron charge density for chemical bonds from valence bond theory: a probe of bonding types.

To characterize the nature of bonding we derive the topological properties of the electron charge density of a variety of bonds based on ab initio valence bond methods. The electron density and its associated Laplacian are partitioned into covalent, ionic, and resonance components in the valence bond spirit. The analysis provides a density-based signature of bonding types and reveals, along with the classical covalent and ionic bonds, the existence of two-electron bonds in which most of the bonding arises from the covalent-ionic resonance energy, so-called charge-shift bonds. As expected, the covalent component of the Laplacian at the bond critical point is found to be largely negative for classical covalent bonds. In contrast, for charge-shift bonds, the covalent part of the Laplacian is small or positive, in agreement with the weakly attractive or repulsive character of the covalent interaction in these bonds. On the other hand, the resonance component of the Laplacian is always negative or nearly zero, and it increases in absolute value with the charge-shift character of the bond, in agreement with the decrease of kinetic energy associated with covalent-ionic mixing. A new interpretation of the topology of the total density at the bond critical point is proposed to characterize covalent, ionic, and charge-shift bonding from the density point of view.

λ-Density Functional Valence Bond: A Valence Bond-Based Multiconfigurational Density Functional Theory With a Single Variable Hybrid Parameter.

A new valence bond (VB)-based multireference density functional theory (MRDFT) method, named λ-DFVB, is presented in this paper. The method follows the idea of the hybrid multireference density functional method theory proposed by Sharkas et al. (2012). λ-DFVB combines the valence bond self-consistent field (VBSCF) method with Kohn-Sham density functional theory (KS-DFT) by decomposing the electron-electron interactions with a hybrid parameter λ. Different from the Toulouse's scheme, the hybrid parameter λ in λ-DFVB is variable, defined as a function of a multireference character of a molecular system. Furthermore, the E C correlation energy of a leading determinant is introduced to ensure size consistency at the dissociation limit. Satisfactory results of test calculations, including potential energy surfaces, bond dissociation energies, reaction barriers, and singlet-triplet energy gaps, show the potential capability of λ-DFVB for molecular systems with strong correlation.

The Menshutkin reaction in the gas phase and in aqueous solution: a valence bond study.

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017-6024) valence bond method coupled to a polarized continuum model (VBPCM) is applied to the Menshutkin reaction, NH3+CH3Cl-->CH3NH3(+)+Cl-, in the gas phase and in aqueous solution. The computed barriers and reaction energies at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimental values in solution. The gas-phase reaction is endothermic and leads to an ion-pair complex via a late transition state. By contrast, the reaction in the aqueous phase is exothermic and leads to separate solvated ions as reaction products, via an early transition state. The VB calculations provide also the reactivity parameters needed to apply the valence bond state correlation diagram method, VBSCD (S. Shaik, A. Shurki, Angew. Chem. Int. Ed. 1999, 38, 586). It is shown that the reactivity parameters along with their semiempirical derivations provide together a satisfactory qualitative and quantitative account of the barriers.

Hamiltonian Matrix Correction Based Density Functional Valence Bond Method.

In this work, a valence bond type multireference density functional theory (MRDFT) method, called the Hamiltonian matrix correction based density functional valence bond method (hc-DFVB), is presented. In hc-DFVB, the static electronic correlation is considered by the valence bond self-consistent field (VBSCF) strategy, while the dynamic correlation energy is taken into account by Kohn-Sham density functional theory (KS-DFT). Different from our previous version of DFVB (J. Chem. Theory Comput. 2012, 8, 1608), hc-DFVB corrects the dynamic correlation energy with a Hamiltonian correction matrix, improving the functional adaptability and computational accuracy. The method was tested for various physical and chemical properties, including spectroscopic constants, bond dissociation energies, reaction barriers, and singlet-triplet gaps. The accuracy of hc-DFVB matches that of KS-DFT and high level molecular orbital (MO) methods quite well. Furthermore, hc-DFVB keeps the advantages of VB methods, which are able to provide clear interpretations and chemical insights with compact wave functions.

DFVB: A Density-Functional-Based Valence Bond Method.

A new ab initio valence bond method with density-functional-based correlation correction, so-called DFVB, is presented. In the DFVB method, the dynamic correlation energy is taken into account by use of density correlation functional(s), while the static correlation energy is covered by the VBSCF wave function. Owing to incorporation of DFT methods, DFVB provides an economic route to improving the accuracy of ab initio VB theory. Various tests of the method are presented, including the spectroscopic parameters of a series of diatomic molecules, the dipole moments of the NF molecule for different electronic states, and the singlet-triplet gaps of the diradical species, chemical reactions barriers, and total charge-shift resonance energies. These tests show that DFVB is capable of providing high accuracy with relatively low computational cost by comparison to the currently existing post-VBSCF methods.