Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the M?ller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals.     

Comparison of theoretical approaches for computing the bond length alternation of polymethineimine

Using electron-correlated wavefunction approaches and several pure and hybrid density functionals combined with three atomic basis sets, we have optimized the ground-state geometry of increasingly long polymethineimine oligomers presenting all-trans and gliding-plane symmetries. It turns out that MP2 bond length alternations (BLA) are in good agreement with higher-order electron-correlated wavefunction approaches, whereas, for both conformers, large qualitative and quantitative discrepancies between MP2 and DFT geometries have been found. Indeed, all the selected GGA, meta-GGA and hybrid functionals tend to overestimate bond length equalization in extended polymethineimine structures. On the other hand, self-interaction corrections included in the ADSIC framework provide, in this particular case, a more efficient approach to predict the BLA for medium-size oligomers.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

Reply to the comment on MORT treatment of bond length alternation in conjugated hydrocarbons

It is shown that in treating bond distortions in the framework of the approach suggested by Nakajima, the contributions of different terms to the total energy are highly sensitive to the choice of parameters and to variations in the functional dependence of the resonance integral as a function of bond length. Hence one can not unambiguously attribute the overall effect to any particular term or terms, and sometimes one has to make a rather careful adjustment in order to avoid qualitatively erroneous results. Though the simple molecular orbital resonance theory (MORT) approach is rather naive, it correctly predicts relative bond lengths in a range of molecules with essentially no parameter adjustment. This approach is hence a rather successful first order approximation to more sophisticated models which progressively incorporate missing contributions. The variation of the resonance integral with bond length and the -bond compression energy should be in these more sophisticated models undoubtedly taken into account. However, the contribution of the charge polarisation can not be totally disregarded, especially in the case of conjugated compounds containing small rings.Theoretica Chimica Acta 65, 77–80 (1984)     

Assessment of several hybrid DFT functionals for the evaluation of bond length alternation of increasingly long oligomers

We have optimized the ground-state geometry of nine series of increasingly long oligomers, using six hybrid density functionals (O3LYP, B3LYP, B97-1, B98, PBE0, and BHHLYP) combined with three different atomic basis sets. In each case, the obtained bond length alternation (BLA) is compared to the corresponding MP2 values. Three phenomenological categories have been set up. In the first, the BLA exponentially decreases, in which case all the tested functionals give results in very good agreement with MP2. In the second category fall the symmetric oligomers that, due to the Peierls theorem, show large BLA. For these chains, BHHLYP tends to give too large and quickly converging BLA wrt chain length, while O3LYP often leads to the opposite misjudgments, and the remaining hybrids provide valuable results. In the third category, one finds asymmetric compounds presenting significantly unequal bond lengths, for which the divergence between DFT and wave function approaches can be dramatic. Indeed, all hybrids yield too small BLA values, especially for long chain lengths. We also study the effect of chain conformation on the BLA.     

Revisiting the relationship between the bond length alternation and the first hyperpolarizability with range-separated hybrid functionals

We monitor the influence of the bond length alternation (BLA) modification on the static electronic polarizability and first hyperpolarizability of two polymethineimine oligomers. Four theoretical approaches are compared: HF, PBE0, LC-omegaPBE, and MP2. For the dodecamer, both HF and PBE0 are unable to foresee even the qualitative evolution of the first hyperpolarizability when varying the BLA. On the contrary, LC-omegaPBE provides (non)linear optics properties in agreement with MP2 results, especially for the longer chains. This confirms the interest of range-separated hybrids for the computation of the (hyper)polarizabilities of extended pi-conjugated compounds.     

Application of the recursion method to the study of the end effects on the bond length alternation in polyacetylene

We describe how the local equilibrium electronic structure in a large system can be determined by using the recursion method of Haydock. By applying this method to the polyacetylene molecule, the energies of each atomic site and the forces acting on each bond are estimated and the equilibrium structure near the end of polyacetylene is determined. It is found out that the degree of localization of π electrons and the bond length alternation become stronger near the end of the polyacetylene molecule.     

Improved accuracy with medium cost computational methods for the evaluation of bond length alternation of increasingly long oligoacetylenes

The difference between the length of the central carbon-carbon bond and that of the adjacent flanked double bonds in polymers such as polyacetylene is closely related to their electronic properties and plays a central role in their conductivity upon doping. Simple as it seems, this bond length alternation (BLA) is a difficult test for many theoretical methods. Accurate coupled-cluster (CC) benchmark values are difficult to obtain even for small- and medium-sized oligoacetylenes due to their intrinsic computational limitations. Here we present a computationally much cheaper alternative to obtain accurate benchmark BLA values, even for large polyacetylene oligomers, by using the so-called spin-component scaled M?ller-Plesset perturbation theory up to second order (SCS-MP2). Comparison between these new benchmark BLA with those provided by density functional theory (DFT) calculations shows a large dispersion of the results depending on the amount of exact exchange used in the exchange-correlation functional. We find that the percentage of exact exchange needed to accurately reproduce the new benchmark BLA is much larger than previously thought when comparison was made with values obtained using the MP2 method.     

Energy estimate of bond polarity

Conclusions The bond polarity, determined as the ionic component fraction of the bond energy, is related in a linear manner to the Pauling polarity value.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No, 10, pp. 2401–2402, October, 1982.The author thanks I. V. Stankevich for discussing the work.     

The ultrafast photoisomerizations of rhodopsin and bathorhodopsin are modulated by bond length alternation and HOOP driven electronic effects

Rhodopsin (Rh) and bathorhodopsin (bathoRh) quantum-mechanics/molecular-mechanics models based on ab initio multiconfigurational wave functions are employed to look at the light induced π-bond breaking and reconstitution occurring during the Rh → bathoRh and bathoRh → Rh isomerizations. More specifically, semiclassical trajectory computations are used to compare the excited (S(1)) and ground (S(0)) state dynamics characterizing the opposite steps of the Rh/bathoRh photochromic cycle during the first 200 fs following photoexcitation. We show that the information contained in these data provide an unprecedented insight into the sub-picosecond π-bond reconstitution process which is at the basis of the reactivity of the protein embedded 11-cis and all-trans retinal chromophores. More specifically, the data point to the phase and amplitude of the skeletal bond length alternation stretching mode as the key factor switching the chromophore to a bonding state. It is also confirmed/found that the phase and amplitude of the hydrogen-out-of-plane mode controls the stereochemical outcome of the forward and reverse photoisomerizations.     

Bond length alternation in infinitely long conjugated polyacenes

This paper concludes that whereas linear polyacenes are stable to distortions that preserve mirror symmetry with respect to the plane which is the perpendicular bisector of their interior bonds, they are unlikely to be stable with respect to distortions that do not preserve this symmetry.     

Bond length alternation and energy band gap of polyyne

The bond length alternation (BLA) and energy band gap of polyyne are investigated by various first-principles theories, including Hartree-Fock, MP2, hybrid, and nonhybrid density functional theories. Both solid-state calculations utilizing periodic boundary conditions on polymers and molecular quantum mechanical calculations on extra-long oligomers were performed with consistent results. By validation on similar linear conjugated polymers, polyacetylene and polydiacetylene, the combination of hybrid-DFT schemes, B3LYP//BHandHLYP or B3LYP//KMLYP, is shown to give the best predictions for both geometry and band gap of polyyne based on available experimental data. We conclude that the best estimate of the BLA of polyyne is about 0.13 A and that of the band gap is about 2.2 eV.     

The bond order—bond length relationship

The difference in length between two bond orders was reported by Pauling to be essentially the same, regardless of the atoms that make up the bond. To a first approximation these differences hold not only for bond orders 1, 2 and 3 but also for six membered aromatic rings containing all carbon, carbon-nitrogen, nitrogen-nitrogen, carbon-phosphorous, carbon-arsenic, and carbon-antimony bonds. An equation was developed (based upon these differences) that relates bond order and bond length. The output of this equation was compared with those of Gordy and Pauling. Our equation as well as the Gordy equation (with revised constants) return a bond length of 1.4 Å for bond order 1.67 which is consistent with theory. (This bond order was not used in developing either the equation or the revised Gordy constants.)     

The equilibrium C-H bond length

The equilibrium C-H bond length has been determined up to now for about 40 polyatomic molecules. These data are used to demonstrate the existence of quantitative correlations betweenr _e(C-H), isolated C-H bond stretching frequency and average distancer _g. It is also shown that ab initio calculations are often reliable to calculate the absolute value ofr _e(C-H), if an empirical correction is made. Some other correlations are also discussed. Finally, accurater _e(C-H) values are predicted for simple molecules.     

Correlation between thermal conductivity and bond length alternation in carbon nanotubes: A combined reverse nonequilibrium molecular dynamics—Crystal orbital analysis

The thermal conductivity (λ) of carbon nanotubes (CNTs) with chirality indices (5,0), (10,0), (5,5), and (10,10) has been studied by reverse nonequilibrium molecular dynamics (RNEMD) simulations as a function of different bond length alternation patterns (Δr_i). The Δr_i dependence of the bond force constant (k_rx) in the molecular dynamics force field has been modeled with the help of an electronic band structure approach. These calculations show that the Δr_i dependence of k_rx in tubes with not too small a diameter can be mapped by a simple linear bond length–bond order correlation. A bond length alternation with an overall reduction in the length of the nanotube causes an enhancement of λ, whereas an alternation scheme leading to an elongation of the tube is coupled to a decrease of the thermal conductivity. This effect is more pronounced in carbon nanotubes with larger diameters. The formation of a polyene‐like structure in the direction of the longitudinal axis has a negligible influence on λ. A comparative analysis of the RNEMD and crystal orbital results indicates that Δr_i‐dependent modifications of λ and the electrical conductivity are uncorrelated. This behavior is in‐line with a heat transfer that is not carried by electrons. Modifications of λ as a function of the bond alternation in the (10,10) nanotube are explained with the help of power spectra, which provide access to the density of vibrational states. We have suggested longitudinal low‐energy modes in the spectra that might be responsible for the Δr_i dependence of λ. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Role of charge transfer interaction and conjugation length on electrical polarizability of doped trans-polyacetylene oligomers

The effects of charge transfer and molecular chain length on the electrical polarizability of doped trans-polyacetylene oligomers have been investigated using a series of quantum chemical methods ranging from Hartree-Fock to current density functional theory. Polarizability tensors of pristine and metal-doped trans-polyacetylene oligomers have been estimated. The nature of variations of polarizability tensor components are quite different for pristine and doped oligomers. For doped samples, distinct minima in the average static polarizabilities per acetylene unit have been observed. The results suggest that the competitive role of charge-transfer interaction and oligomer chain length are responsible for the observed minima. To simulate the ab initio results on polarizability variation, we propose a mathematical model that describes the minima quite satisfactorily.     

Bond length alternation in cyclic polyenes. III. Alternant molecular orbital method

The bond length alternation problem in cyclic polyene models as described by the Pariser–Parr–Pople Hamiltonian and an empirical quasiharmonic π-core potential is investigated using the one-parameter alternant molecular orbital (AMO) method. It is shown that in contrast to the unrestricted Hartree–Fock (UHF) results, which lead to symmetric equidistant structures, the one-parameter AMO results yield bond length alternating structures similar to those obtained with the restricted HF approach. The correlation energy recovered by the AMO method is examined for the symmetric polyenes in the whole range of coupling constants for both the Pariser–Parr–Pople and Hubbard Hamiltonians and compared with exact full configuration interaction (FCI) results. For the first member of the cyclic polyene series we also compared the FCI and AMO correlation energies for different nuclear framework distortions. This comparison indicates that in contrast to the UHF results the fraction of the correlation energy recovered by the AMO approach is very uniform over the range of nuclear distortions considered. The AMO results thus strongly indicate the dimerization in the polyenic chains.