Block-localized Wave Function Research Articles

The generalized block-localized wavefunction method: A case study on the conformational preference and C–O rotational barrier of formic acid

A Lewis structure corresponding to the most stable electron-localized state is often used as a reference for the measure of electron delocalization effect in the valence bond (VB) theory. As the simplest variant of ab initio VB theory, the generalized block-localized wavefunction (BLW) method defines the wavefunction for an electron-localized state with block-localized orbitals without the orthogonalization constraint on different blocks. The validity of the method can be critically examined with experimental evidences. Here the BLW method has been applied to the investigation of the roles of both the π conjugation and σ hyperconjugation effects in the conformational preference of formic acid for the trans (Z) conformer over the cis (E) conformer. On one hand, our computations showed that the deactivation of the π conjugation or σ hyperconjugation has little impact on the Z-E energy gap, thus neither is decisive and instead the local dipole-dipole electrostatic interaction between the carbonyl and hydroxyl groups is the key factor determining the Z-E energy gap. On the other hand, the present study supported the conventional view that π conjugation is largely responsible for the C-O rotation barrier in formic acid, though the existence of hyperconjugative interactions in the perpendicular structure lowers the barrier considerably.

Conjugation, Resonance, and Stability in N-Heterocyclic Silylenes and in Phosphorus Ylide Substituted Silylenes

The role of π conjugation in the thermodynamic stabilization of N-heterocyclic silylenes and phosphorus ylide substituted silylenes is analyzed using the block localized wave function (BLW) method. This method enables the direct calculation of the resonance stabilization energies caused by π-electron delocalization and/or by cyclic 6-π-electron delocalization (aromaticity). The major advantage of the BLW method is that there is no need for reference compounds, as the fully conjugated molecule itself serves as the reference compound. The observed high stability of the C═C unsaturated N-heterocyclic silylenes 1(E = Si; silaimidazol-2-ylidene) and the C–C saturated 2 (E = Si; silaimidazolin-2-ylidene) is rationalized by their high resonance energies (REs) of 79.4 and 53.4 kcal/mol, respectively. The nuclear independent chemical shift (NICSzz(1.0)) value of −22.0 for 1 (E = Si) indicates significant diatropic ring current, implying the existence of aromaticity. The additional stabilization of 1 due to aromaticity (6-π-electron delocalization) is 14 kcal/mol, which is only 18% of the total RE of 1 but is 55% of the aromatic stabilization of benzene. Thus, aromaticity contributes to the stability of 1, but it is not a prerequisite for the isolation of N-heterocyclic silylenes. Cyclic unsaturated silylenes substituted by exocyclic phosphorus ylide substituents, i.e., 12, have calculated cyclic resonance energies and thermodynamic stabilization energies similar to those of 1 (E = Si), and they are significantly larger than those of saturated 2 (E = Si); i.e., the REs of 12 (R″ = CH3, SiH3) are 73.4 and 75.6 kcal/mol, respectively. These data suggest that 12 is sufficiently stable to be isolated, as indeed was recently reported. The energy of the lone pair orbital on Si in 12 (R″ = Ph) is higher by 1.9 eV than that of 1 (E = Si, R = t-Bu), suggesting that 12 are better σ donors and thus may exhibit higher activity in transition-metal catalysis.

Block-Localized Wavefunction (BLW) Based Two-State Approach for Charge Transfers between Phenyl Rings.

The block-localized wave function (BLW) method is the simplest and most efficient variant of ab initio valence bond (VB) theory which defines electron-localized resonance states following the conventional VB concepts. Here, a BLW-based two-state approach is proposed to probe the charge/hole transfer reactions within the Marcus-Hush model. With this approach, both the electronic coupling and reorganization energies can be derived at the ab initio level. Pilot applications to the electron/hole transfers between two phenyl rings are presented. Good exponential correlation between the electronic coupling energy and the donor-acceptor distance is shown, whereas the inner-sphere reorganization shows little geometric dependency. Computations also support the assumption in Marcus theory that the thermal electron transfer barrier (ΔG*), which is a sum of the reaction barrier (ΔEa) for electron/hole transfer and the coupling energy (VAB), is a quarter of the reorganization energy (λ).

Is cyclobutadiene really highly destabilized by antiaromaticity?

The high energy of cyclobutadiene (CBD) is not due primarily to "anti-aromaticity," but rather to angle strain, torsional strain, and Pauli repulsion between the parallel CC bonds. Estimations including block-localized wavefunction (BLW) computations conclude that the enormous ring strain (ca. 60 kcal mol(-1)) far exceeds its antiaromatic destabilization (only 16.5 kcal mol(-1)).

Dispersion-Corrected Energy Decomposition Analysis for Intermolecular Interactions Based on the BLW and dDXDM Methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.

A study of aromatic three membered rings

AbstractThe resonance energies (REs) of neutral three membered ring analogs of the cyclopropenyl cation, computed using block localized wave function (BLW) methods, reveal considerable variations. The RE's of cyclopropenes substituted with exocyclic double bonded groups CX, (X = O, NH, CH2, S, PH, SiH2) increase with the electronegativity of X in the same row (SiH2 < PH < S and CH2 < NH < O). The extra cyclic resonance energies (ECREs) (an energetic measure of aromaticity based on comparisons with the RE's of acyclic models) of these derivatives range from +10.5 kcal/mol for cyclopropenone (X = O) (somewhat aromatic; the benzene ECRE is 29.3 kcal/mol) to −2.4 kcal/mol (slightly antiaromatic) for X = SiH2. Additional disubstitution of the CC double bond by X′ groups (X′ = CH3, NH2, OH, SiH3, PH2, SH) increases the REs considerably, but has only small effects on the ECREs. Even the ECRE of deltic acid (X = O, X′ = OH) is only increased to +13.3 kcal/mol. The conclusion based on ECRE's, that all 12 of the three membered rings are only marginally aromatic/antiaromatic, is supported by the satisfactorily plot (R2 = 0.92) of ECRE against values of NICS(0)πzz (a superior nucleus chemical independent shift magnetic index of aromaticity), which range only from −6.1 ppm (diatropic) for deltic acid (cf., −35.5 ppm for benzene and −14.2 ppm for the parent cyclopropenium ion) to +8.9 ppm (paratropic) for the silicon derivative, X = SiH2, X′ = SiH3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Aromaticity in Group 14 Homologues of the Cyclopropenylium Cation

The nature of the bonding and the aromaticity of the heavy Group 14 homologues of cyclopropenylium cations E3H3+ and E2H2E'H+ (E, E' = C-Pb) have been investigated systematically at the BP86/TZ2P DFT level by using several methods. Aromatic stabilization energies (ASE) were evaluated from the values obtained from energy decomposition analysis (EDA) of charged acyclic reference molecules. The EDA-ASE results compare well with the extra cyclic resonance energy (ECRE) values given by the block localized wavefunction (BLW) method. Although all compounds investigated are Hückel 4n+2 π electron species, their ASEs indicate that the inclusion of Group 14 elements heavier than carbon reduces the aromaticity; the parent C3H3+ ion and Si2H2CH+ are the most aromatic, and Pb3H3+ is the least so. The higher energies for the cyclopropenium analogues reported in 1995 employed an isodesmic scheme, and are reinterpreted by using the BLW method. The decrease in the strength of both the π cyclic conjugation and the aromaticity in the order C ≫ Si>Ge>Sn>Pb agrees reasonably well with the trends given by the refined nucleus-independent chemical shift NICS(0)πzz index.

Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory.

An interaction energy decomposition analysis method based on the block-localized wavefunction (BLW-ED) approach is described. The first main feature of the BLW-ED method is that it combines concepts of valence bond and molecular orbital theories such that the intermediate and physically intuitive electron-localized states are variationally optimized by self-consistent field calculations. Furthermore, the block-localization scheme can be used both in wave function theory and in density functional theory, providing a useful tool to gain insights on intermolecular interactions that would otherwise be difficult to obtain using the delocalized Kohn-Sham DFT. These features allow broad applications of the BLW method to energy decomposition (BLW-ED) analysis for intermolecular interactions. In this perspective, we outline theoretical aspects of the BLW-ED method, and illustrate its applications in hydrogen-bonding and π-cation intermolecular interactions as well as metal-carbonyl complexes. Future prospects on the development of a multistate density functional theory (MSDFT) are presented, making use of block-localized electronic states as the basis configurations.

The norbornene mystery revealed

The long-standing mystery surrounding the peculiar electronic structure of norbornene and its derivatives is revealed by the direct comparisons of their properties with those of reference analogues with localized double bonds (i.e. Lewis structures). Our block-localized wavefunction analysis coupled with the computations of NMR parameters evidently supports the manifestation of a density redistribution toward an incipient retro-Diels-Alder reaction.

New procedure to evaluate aromaticity at the density functional theory, Hartree-Fock, and post-self-consistent field levels

The spatial exchange interaction, arising from the exchange-type two-electron integrals (i(p)j(q)/i'(p)j'(q)) between two different groups P and Q, is another driving force for the delocalization of π-electrons besides orbital charge-transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange-type two-electron integrals, ensuring that the corresponding π-electrons are completely localized within their respective groups and the π-orbitals are fully localized. The extra stabilization energy (ESE) of benzene is -36.3 kcal/mol (B3LYP/6-31G*), and the level of density functional theory, Hartree-Fock, and post-self-consistent field (Møller-Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled-cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block-localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the CC single bond lengths in the ground state with its π-localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π-delocalization on single bonds is so small as to be negligible.

Consistent Aromaticity Evaluations of Methylenecyclopropene Analogues

Quantitative evaluations of the aromaticity (antiaromaticity) of neutral exocyclic substituted cyclopropenes (HC)(2)C=X (X = BH to InH (group 13), CH(2) to SnH(2) (group 14), NH to SbH (group 15), O to Te (group 16)) by their computed extra cyclic resonance energies (ECRE, via the block-localized wave function method) and by their aromatic stabilization energies (ASEs, via energy decomposition analyses) correlate satisfactorily (R(2) = 0.974). Electronegative X-based substituents increase the aromaticity of the cyclopropene rings, whereas electropositive substituents have the opposite effect. For example, (HC)(2)C=O is the most aromatic (ECRE = 10.3 kcal/mol), and (HC)(2)C=InH is the most antiaromatic (ECRE = -15.0 kcal/mol). The most refined dissected nucleus-independent chemical shift magnetic aromaticity index, NICS(0)(πzz), also agrees with both energetic indexes (R(2) = 0.968, for ECRE; R(2) = 0.974, for ASE), as do anisotropy of the induced current density plots.

Steric and electronic effects on the heterolytic H2‐splitting by phosphine‐boranes R3B/PR′3(R = C6F5, Ph; R′ = C6H2Me3,tBu, Ph, C6F5, Me, H): A computational study

AbstractThe steric and electronic effects exerted by the substituents R/R′ on the heterolytic H2‐splitting by phosphine‐boranes R3B/PR′3[R = C6F5(1), Ph (2); R′ = C6H2Me3(a),tBu (b), Ph (c), C6F5(d), Me (e), H (f)] have been studied by performing quantum mechanical density functional theory and RI‐MP2 calculations. Energy decomposition analyses based on the block‐localized wavefunction method show that the nature of the interaction between R3B and PR′3is strongly dependent on the BP distance. With short BP distances (∼2.1 Å), the strength of Lewis pairs results from the balance among various energy terms, and both strong and weak dative bonds can be found in this group. However, at long BP distances (>4.0 Å), the correlation and dispersion energy (ΔEcorr) dominates. In other words, the van der Waals (vdW) interaction rules these weakly bound complexes. No ion‐pair structures of1fand2c–2fcan be located as they instantly converge to vdW complexes R3B···H2···PR′3. We thus propose a model, which predicts that when the sum (Ehp) of the hydride affinity (HA) of BR3and the proton affinity (PA) of PR′3is higher than 340.0 kcal/mol, the ion‐pair [R3BH−][HPR′] can be observed, whereas withEhpbelow this value, the ion pair would instantly undergo the combination of proton and hydride with the release of H2. The overall reaction energies (1a–1eand2a–2b) can be best described by a fitting equation with HA(BR3), PA(PR′3), and the binding energy ΔEb(BR3/PR′3) as predictor variables: ΔER([R3BH−][HPR′]) = −0.779HA(BR3) − 0.695PA(PR′3) − 1.331 ΔE(BR3/PR′3) + 245.3 kcal/mol. The fitting equation provides quantitative insights into the steric and electronic effects on the thermodynamic aspects of the heterolytic H2‐splitting reactions. The electronic effects are reflected by HA(BR3) and PA(PR′3), and ΔEbcan be significantly influenced by the steric overcrowding. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Aromaticity and Relative Stabilities of Azines

The most refined nucleus-independent chemical shift index (NICS(0)(πzz)) and the extra cyclic resonance energies (ECREs), based on the block localized wave function (BLW) method, show that the aromaticity of all azines is like that of benzene. The same is true for aza-naphthalenes relative to naphthalene. The lower relative energies of isomers with vicinal N's are due to the weakness of NN bonds rather than to reduced aromaticity.

How to properly compute the resonance energy within the ab initio valence bond theory: a response to the ZHJVL paper

Valence bond (VB) theory describes a conjugated system by a set of electron-localized Lewis resonance structures. VB assumes that the magnitude of the intramolecular electron delocalization can be measured in terms of a resonance energy (RE), taken to be the energy difference between the real conjugated system (delocalized) and the corresponding most stable virtual resonance structure (localized). Proper RE estimates within VB theory require both delocalized and localized states to be defined at the same theoretical level, and the definition of the localized state to closely correspond to the intuitive picture of the corresponding VB structure. In contrast, the VB-delocal and VB-local computational approaches adopted by Zielinski, et al. [preceding paper in this issue] used definitions for either the delocalized or the localized states which, in our view, depart from the intuitive chemical picture. Consequently, their RE estimates are much lower than seemingly appropriate experimental evaluations with which they strongly disagree. Very large basis sets approaching completeness blur the boundaries among resonance structures and result in “basis set artifact” problems within any variant of VB theory. However, block-localized wavefunction (BLW) computations with mid-size basis sets not only exhibit insignificant variations with theoretical levels, but the resulting RE estimates also are justified by comparisons with those employing experimental data and MO computations. We stress that RE differs from the aromatic stabilization energy (ASE). The RE measures the total stabilization of an aromatic system, whereas ASE measures only the part of the RE that exceeds that of appropriate conjugated (but non-aromatic) reference molecules.

Computational evidence that hyperconjugative interactions are not responsible for the anomeric effect

The 'anomeric effect' is the thermodynamic preference for polar substituents to occupy the axial position in the chair conformation of various heterocycles. The most common explanation given for this effect at present is hyperconjugation from the lone pairs on the ring heteroatom to the antibonding orbital between the anomeric carbon and its linking substituent. Alternatively, the anomeric effect could be explained by intramolecular electrostatic interactions between local dipoles. Few models can provide convincing data for either theory at the quantum-mechanical level. Now, using the extended block-localized wavefunction method, which is the simplest form of valence bond theory, we have evaluated the degree of hyperconjugation in various compounds that display the anomeric effect and have interpreted their conformational preferences in terms of steric, hyperconjugation and dispersion effects. The results provide strong evidence that hyperconjugative interactions are not responsible for the anomeric effect and that it is better interpreted in terms of electrostatic interactions.

Why Are Esters and Amides Weaker Carbon Acids than Ketones and Acid Fluorides? Contributions by Resonance and Inductive Effects

Two computational methodologies-a vinylogue extrapolation methodology and a block localized wave function (BLW) methodology-were employed to determine the contributions by resonance and inductive effects toward the gas-phase deprotonation enthalpies at the alpha carbons of acetone, acetamide, acetic acid, and acetyl fluoride, which were taken to be model compounds for ketones, amides, esters, and acid fluorides, respectively. Results from the vinylogue methodology suggest that resonance serves to enhance the gas-phase deprotonation enthalpy of a ketone by 34.3 kcal/mol, an amide by 26.2 kcal/mol, an ester by 30.5 kcal/mol, and an acid fluoride by 30.8 kcal/mol. Comparably, the BLW methodology suggests those numbers to be 42.3, 31.2, 36.1, and 39.7 kcal/mol, respectively. Results from the vinylogue methodology suggest that inductive effects serve to enhance the gas-phase deprotonation enthalpy of a ketone by 11.8 kcal/mol, an amide by 12.7 kcal/mol, an ester by 15.5 kcal/mol, and an acid fluoride by 26.0 kcal/mol, and in the same order, those numbers suggested by the BLW methodology are 3.0, 6.2, 8.5, and 16.3 kcal/mol.

The Effect of Perfluorination on the Aromaticity of Benzene and Heterocyclic Six-Membered Rings

Despite having six highly electronegative F's, perfluorobenzene C(6)F(6) is as aromatic as benzene. Ab initio block-localized wave function (BLW) computations reveal that both C(6)F(6) and benzene have essentially the same extra cyclic resonance energies (ECREs). Localized molecular orbital (LMO)-nucleus-independent chemical shifts (NICS) grids demonstrates that the F's induce only local paratropic contributions that are not related to aromaticity. Thus, all of the fluorinated benzenes (C(6)F(n)H((6-n)), n = 1-6) have similar ring-LMO-NICS(pi zz) values. However, 1,3-difluorobenzene 2b and 1,3,5-trifluorobenzene 3c are slightly less aromatic than their isomers due to a greater degree of ring charge alternation. Isoelectronic C(5)H(5)Y heterocycles (Y = BH(-), N, NH(+)) are as aromatic as benzene, based on their ring-LMO-NICS(pi zz) and ECRE values, unless extremely electronegative heteroatoms (e.g., Y = O(+)) are involved.

4n π Electrons but Stable:N,N-Dihydrodiazapentacenes

Despite having 4n pi electrons, dihydrodiazapentacenes are more viable than their 4n+2 pi azapentacene counterparts. Ab inito valence bond block-localized wave function (BLW) computations reveal that despite having 4n pi electrons, dihydrodiazapentacenes are stabilized and benefit substantially from four dihydropyrazine ethenamine (enamine) conjugations. Almost all of these dihydrodiazapentacenes have large negative overall nucleus independent chemical shifts NICS(0)(pizz) values even though their dihydropyrazine rings (e.g., for 6-H(2)) are modestly antiaromatic, as their paratropic contributions are attenuated by delocalization throughout the system.

On the aromatic stabilization energy of the 4N π electron pyrene

The aromatic stabilization energy (ASE) of pyrene, evaluated with both isodesmic equation and ab initio valence bond (VB) theory-based block localized wavefunction (BLW) methods, gives consistent results (ca 74 kcal/mol). Biphenyl, phenanthrene and benzene, evaluated similarly, all have essentially the same ASEs per ring carbon. The aromaticity of pyrene is not diminished because of its 4n π electron count.

The Resonance Energy of Benzene: A Revisit

Zielinski and van Lenthe recently extended the block-localized wave function (BLW) method by introducing the resonating BLW (RBLW) method and performed test calculations on hexagonal H(6) and benzene [J. Phys. Chem. A 2008, 112, 13197]. However, the Pauling's resonance energies from their RBLW and ab initio valence bond (VB) calculations were greatly underestimated largely due to the imperfect use of either one-electron orbitals (method = delocal) or resonance structures (method = local). Whereas it has been well recognized that electronic resonance within a molecular system plays a stabilizing role, there are many indirect experimental evidences available to evaluate the resonance energy and, thus, to justify computational results. Here we used the BLW method, which can be regarded as the simplest variant of modern ab initio VB theory, to re-evaluate the resonance energy of benzene at the B3LYP level, following the original definition by Pauling and Wheland, who obtained the resonance energy "by subtracting the actual energy of the molecule in question from that of the most stable contributing structure". The computed vertical resonance energy (or quantum mechanical resonance energy) in benzene is 88.8, 92.2, or 87.9 kcal/mol with the basis sets of 6-31G(d), 6-311+G(d,p), or cc-pVTZ, respectively, while the adiabatic resonance energy (or theoretical resonance energy) is 61.4, 63.2, or 62.4 kcal/mol, exhibiting insignificant basis set dependency for moderate basis sets. In line with predictions, the geometry optimization of the elusive cyclohexatriene (i.e., the Kekule structure) with the BLW method also resulted in carbon-carbon bond lengths (e.g., 1.322 and 1.523 A with the cc-pVTZ basis set) comparable to those in ethylene or ethane.