Heats of atomization of some conjugated molecules containing nitrogen or oxygen by a novel semiempirical method

Heats of atomization for a range of conjugated molecules containing nitrogen or oxygen are calculated by a semiempirical method that combines some features of both the MO and VB theories. The π ground state of each conjugated molecule is represented as a linear combination of Kekulé structures. Unlike in the VB theory, each Kekulé structure is a determinant containing bond orbitals. Here experimental heats of atomization are reproduced approximately as well as by the more sophisticated SCF –MO approach. The use of this method is, however, much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.     

The electron‐pair origin of antiaromaticity: Spectroscopic manifestations

It is shown that the antiaromatic character of certain conjugated cyclic hydrocarbons is due to the presence of an even number of distinct electron pairs in the system (such as, but not necessarily π electrons). In these systems, the ground state is constructed from an out‐of‐phase combination of two valence bond (VB) structures, and its equilibrium geometry is necessarily distorted along the coordinate that interchanges these structures. If a new symmetry element appears during the transition between the two structures, the ground electronic state at the symmetric point transforms as one of the nontotally symmetric irreducible representations of the point group. The conjugate excited state, formed from the in‐phase combination of the same two structures, transforms as the totally symmetric representation of the group and is strongly bound. Its structure is similar to that of the ground state at the symmetric point, and the energy separation between the two states is small compared to that of conjugated cyclic hydrocarbons having an odd number of distinct electron pairs. Motion along the “Kekulé‐type” vibrational mode on the excited‐state potential surface is very similar to motion along the reaction coordinate connecting the two distorted structures on the ground‐state surface. It is characterized by a significantly higher vibrational frequency compared to frequencies of similar modes in ground‐state molecules. These qualitative predictions are supported by quantum chemical calculations on cyclobutadiene, cyclooctatetraene, and pentalene. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 133–145, 1999     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

The V state of ethylene: valence bond theory takes up the challenge

The ground state and first singlet excited state of ethylene, so-called N and V states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the N state and four structures for the V state, provide an N → V transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the N → V transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the V state wave function, 19.14 a ₀ ² , is in the range of accepted values obtained by large-scale state-of-the-art molecular orbital-based methods. The σ response to the fluctuations of the π electrons in the V state, known to be a crucial feature of the V state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the N state and 14 for the V state, confirm the results of the minimal structure set, yielding an N → V transition energy of 7.97 eV and a spatial extension of 19.16 a ₀ ² for the V state. Both types of valence bond calculations show that the V state of ethylene is not fully ionic as usually assumed, but involving also a symmetry-adapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the V state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the V state, known to be ca. 50 % larger than the V state.     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.     

Generation of Kekulé valence structures and the corresponding valence bond wave function

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjugated systems including fullerenes. The application of the algorithm in generating Valence Bond (VB) wave functions, in terms of Kekulé valence structures, is discussed and illustrated in actual VB calculations. Two types of VBSCF calculations, one involving Kekulé valence structures only and the second one involving all covalent VB structures, were performed for benzene, pentalene, benzocyclobutadiene, and naphthalene. Both strictly local and delocalised p-orbitals were used in these calculations. Our results show that, when the orbitals are restricted to their own atoms, other VB structures (Dewar structures) also have a significant contribution in the VB wave function. When removing this restriction, the other VB structures (Dewar and also the ionic structures) are accommodated in the Kekulé valence structures, automatically. Therefore, at VBSCF delocal level, the ground states of these systems can be described almost quantitatively by considering Kekulé valence structures only at a considerable saving of time.     

The effects of substituents and solvents on the ground-state π-electronic structure and electronic absorption spectra of a series of model merocyanine dyes and their theoretical interpretation

Two series of new merocyanine dyes have been synthesised and the dependence of their electronic structure on substituents and solvents has been studied by NMR spectroscopy, by using both the NMR (13)C chemical shifts between adjacent C atoms in the polymethine chain and the (3)J(H,H) coupling constants for trans-vicinal protons. The widely used valence bond (VB) model based on two contributing structures cannot account theoretically for the observed alternating π-electron density in the polymethine chain. In addition, the prediction of zero-π-bond order alternation (or zero-bond length alternation) by this model is also incorrect. However, the results are consistent with the predictions of a qualitative VB model which considers the resonance of a positive charge throughout the whole polymethine chain. Based on this model and the Franck-Condon principle the effect of substituents and solvents on the fine structure of the electronic spectra of these dyes can be explained as vibronic transitions from the vibrational state v = 0 to v', where v is the vibrational quantum number of the totally symmetric C=C valence vibration of the polymethine chain in the electronic ground state and v' is that in the electronic excited state. In contrast, neither the effects of substituents or solvents on the electronic structure of merocyanines and their electronic spectra can be accounted for by the simple two state VB model.     

Valence bond theoretical study for chemical reactivity

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Recasting wave functions into valence bond structures: A simple projection method to describe excited states

A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap‐based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low‐lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V‐state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V‐state of ethene. © 2015 Wiley Periodicals, Inc.     

Model studies of hydrogen atom addition and abstraction processes involving ortho-, meta-, and para-benzynes.

H-atom addition and abstraction processes involving ortho-, meta-, and para-benzyne have been investigated by multiconfigurational self-consistent field methods. The H(A) + H(B)...H(C) reaction (where r(BC) is adjusted to mimic the appropriate singlet-triplet energy gap) is shown to effectively model H-atom addition to benzyne. The doublet multiconfiguration wave functions are shown to mix the "singlet" and "triplet" valence bond structures of H(B)...H(C) along the reaction coordinate; however, the extent of mixing is dependent on the singlet-triplet energy gap (DeltaE(ST)) of the H(B)...H(C) diradical. Early in the reaction, the ground-state wave function is essentially the "singlet" VB function, yet it gains significant "triplet" VB character along the reaction coordinate that allows H(A)-H(B) bond formation. Conversely, the wave function of the first excited state is predominantly the "triplet" VB configuration early in the reaction coordinate, but gains "singlet" VB character when the H-atom is close to a radical center. As a result, the potential energy surface (PES) for H-atom addition to triplet H(B)...H(C) diradical is repulsive! The H3 model predicts, in agreement with the actual calculations on benzyne, that the singlet diradical electrons are not coupled strongly enough to give rise to an activation barrier associated with C-H bond formation. Moreover, this model predicts that the PES for H-atom addition to triplet benzyne will be characterized by a repulsive curve early in the reaction coordinate, followed by a potential avoided crossing with the (pi)1(sigma*)1 state of the phenyl radical. In contrast to H-atom addition, large activation barriers characterize the abstraction process in both the singlet ground state and first triplet state. In the ground state, this barrier results from the weakly avoided crossing of the dominant VB configurations in the ground-state singlet (S0) and first excited singlet (S1) because of the large energy gap between S0 and S1 early in the reaction coordinate. Because the S1 state is best described as the combination of the triplet X-H bond and the triplet H(B)...H(C) spin couplings, the activation barrier along the S0 abstraction PES will have much less dependence on the DeltaE(ST) of H(B)...H(C) than previously speculated. For similar reasons, the T1 potential surface is quite comparable to the S0 PES.     

Density embedded VB/MM: a hybrid ab initio VB/MM with electrostatic embedding

A hybrid QM/MM method that combines ab initio valence-bond (VB) with molecular mechanics (MM) is presented. The method utilizes the ab initio VB approach to describe the reactive fragments and MM to describe the environment thus allows VB calculations of reactions in large biological systems. The method, termed density embedded VB/MM (DE-VB/MM), is an extension of the recently developed VB/MM method. It involves calculation of the electrostatic interaction between the reactive fragments and their environment using the electrostatic embedding scheme. Namely, the electrostatic interactions are represented as one-electron integrals in the ab initio VB Hamiltonian, hence taking into account the wave function polarization of the reactive fragments due to the environment. Moreover, the assumptions that were utilized in an earlier version of the method, VB/MM, to formulate the electrostatic interactions effect on the off-diagonal matrix elements are no longer required in the DE-VB/MM methodology. Using DE-VB/MM, one can calculate, in addition to the adiabatic ground state reaction profile, the energy of the diabatic VB configurations as well as the VB state correlation diagram for the reaction. The abilities of the method are exemplified on the identity SN2 reaction of a chloride anion with methyl chloride in aqueous solution. Both the VB configurations diagram and the state correlation diagram are presented. The results are shown to be in very good agreement with both experimental and other computational data, suggesting that DE-VB/MM is a proper method for application to different reactivity problems in biological systems.     

The Effects of Substituents and Solvents on the Ground‐State π‐Electronic Structure and Electronic Absorption Spectra of a Series of Model Merocyanine Dyes and Their Theoretical Interpretation

Two series of new merocyanine dyes have been synthesised and the dependence of their electronic structure on substituents and solvents has been studied by NMR spectroscopy, by using both the NMR ¹³C chemical shifts between adjacent C atoms in the polymethine chain and the ³J(H,H) coupling constants for trans‐vicinal protons. The widely used valence bond (VB) model based on two contributing structures cannot account theoretically for the observed alternating π‐electron density in the polymethine chain. In addition, the prediction of zero‐π‐bond order alternation (or zero‐bond length alternation) by this model is also incorrect. However, the results are consistent with the predictions of a qualitative VB model which considers the resonance of a positive charge throughout the whole polymethine chain. Based on this model and the Franck‐Condon principle the effect of substituents and solvents on the fine structure of the electronic spectra of these dyes can be explained as vibronic transitions from the vibrational state v=0 to v′, where v is the vibrational quantum number of the totally symmetric C?C valence vibration of the polymethine chain in the electronic ground state and v′ is that in the electronic excited state. In contrast, neither the effects of substituents or solvents on the electronic structure of merocyanines and their electronic spectra can be accounted for by the simple two state VB model.     

The ground and excited states of polyenyl radicals C2n-1H2n + 1 (n = 2-13): a valence bond study.

The semiempirical valence bond (VB) method, VBDFT(s), is applied to the ground states and the covalent excited states of polyenyl radicals C2n - 1H2n + 1 (n = 2-13). The method uses a single scalable parameter with a value that carries over from the study of the covalent excited states of polyenes (W. Wu, D. Danovich, A. Shurki, S. Shaik, J. Phys. Chem. A, 2000, 104, 8744). Whenever comparison is possible, the VB excitation energies are found to be in good accord with sophisticated molecular orbital (MO)-based methods like CASPT2. The symmetry-adapted Rumer structures are used to discuss the state-symmetry and VB constitution of the ground and excited states, and the expansion to VB determinants is used to gain insight on spin density patterns. The theory helps to understand in a coherent and lucid manner the properties of polyenyl radicals, such as the makeup of the various states, their geometries and energies, and the distribution of the unpaired electrons (the neutral solitons).     

Kekulé-based Valence Bond Model. II. Diels-Alder Reactivity of Polycyclic Aromatic Hydrocarbons

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Two States Are Not Enough: Quantitative Evaluation of the Valence‐Bond Intramolecular Charge‐Transfer Model and Its Use in Predicting Bond Length Alternation Effects

The structural weights of the canonical resonance contributors used in the Two‐state valence‐bond charge‐transfer model, neutral (N, R1) and ionic (VB‐CT, R2), to the ground states and excited states of a series of linear dipolar intramolecular charge‐transfer chromophores containing a buta‐1,3‐dien‐1,4‐diyl bridge have been computed by using the block‐localized wavefunction (BLW) method at the B3LYP/6‐311+G(d) level to provide the first quantitative assessment of this simple model. Ground‐ and excited‐state analysis reveals surprisingly low ground‐state structural weights for the VB‐CT resonance form using either this Two‐state model or an expanded Ten‐state model. The VB‐CT state is found to be more prominent in the excited state. Individual resonance forms were structurally optimized to understand the origins of the bond length alternation (BLA) of the bridging unit. Using a Wheland energy‐based weighting scheme, the weighted average of the optimized bond lengths with the Two‐state model was unable to reproduce the BLA features with values 0.04 to 0.02 Å too large compared to the fully delocalized (FD) structure (BLW: ca. ?0.13 to ?0.07 Å, FD: ca. ?0.09 to ?0.05 Å). Instead, an expanded Ten‐state model fit the BLA values of the FD structure to within only 0.001 Å of FD.     

Potential energy surfaces for the reaction of B+ (1S,3P) with H2 using spin-coupled VB theory: Asymptotic regions of the surfaces

We present spin-coupled VB calculations for the asymptotic regions of the potential surfaces for the (B + H₂)⁺ system. A large basis set is used and great care has been taken to ensure that all states lying within 13 eV of the BH⁺(X²Σ⁺) + H ground state are well described. A total of 592 spin-coupled structures (fully coupled configurations) was used. These calculations show a significant improvement over previous work. The present surfaces, at least in the regions studied here, appear to be of chemical accuracy. Having established the reliability of our calculations, further studies will concentrate on the inner regions of the surfaces - preferably in conjunction with dynamical studies.