About the calculation of exchange coupling constants in polynuclear transition metal complexes

The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H. He and CH(2). He units to compare with Hartree-Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data.     

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.     

Predicting exchange coupling constants in frustrated molecular magnets using density functional theory

We study the Heisenberg exchange couplings in polynuclear transition-metal clusters with strong spin frustration using a variety of theoretical techniques. We present results for a trinuclear Cr(III) molecule, a tetranuclear Fe(III) complex, and an octanuclear Fe(III) molecular magnet. We explore the physics of the exchange couplings in these systems using standard broken-symmetry (BS) techniques and a more recently developed constrained density functional theory (C-DFT) approach. The calculations show that the expected picture of localized spin moments on the metal centers is appropriate, and in each case C-DFT predicts coupling constant values in good agreement with experiment. Furthermore, we demonstrate that all of the C-DFT spin states for a given cluster can be reasonably described by a single Heisenberg Hamiltonian. These findings are significant in part because standard BS calculations are in conflict with the experiments on a number of key points. For example, BS-DFT predicts a doublet (rather than quartet) ground state for the Cr(III) cluster while for the Fe(III) complexes BS-DFT predicts some of the exchange couplings to be ferromagnetic whereas the experimentally derived couplings are all antiferromagnetic. Furthermore, for BS-DFT the best-fit exchange parameters can depend significantly on the set of spin configurations chosen. For example, by choosing configurations with Ms closer to Ms(max) the BS-DFT couplings can typically be made somewhat closer to the C-DFT and experimental results. Thus, in these cases, our results consistently support the experimental findings.     

Ionization potentials and electron affinities in the Perdew-Zunger self-interaction corrected density-functional theory

Using a self-consistent implementation of the Perdew-Zunger self-interaction corrected (PZ-SIC) density-functional theory, we have calculated ionization potentials (IP) and electron affinities (EA) of first- and second-row atoms and a set of small molecules. Several exchange-correlation functionals were tested. IPs and EAs were obtained by two methods: as the difference in self-consistent field (SCF) energies of neutrals and ions (deltaSCF) and as negatives of highest-occupied orbital energies. We found that, except for local spin-density approximation, PZ-SIC worsens DeltaSCF IPs and EAs. On the other hand, PZ-SIC brings orbital eigenvalues into much better agreement with electron removal energies. The Perdew-Zunger SIC seems to over-correct many-electron systems; for molecules it performs worse than for atoms. We also discuss several common approximations to PZ-SIC such as spherical averaging of orbital densities in atoms.     

The absolute sign of J coupling constants determined using the order matrix calculation

A novel methodology using the order matrix calculation to determine the absolute sign of spin-spin couplings based on the structure of organic compounds is presented. The sign of the residual dipolar coupling (RDC) depends on the sign of corresponding scalar spin-spin coupling constant and the sign of the RDC has a dramatic influence on the order matrix calculation. Therefore, the sign of the spin-spin coupling constant can be obtained by an order matrix calculation through the corresponding RDC. Six types of spin-spin coupling constants, including 2J(H,H), 1J(C,F), 2J(C,F), 3J(C,F), 2J(F,H) and 3J(F,H), were obtained simultaneously. Except for 3J(C,F) where the measured RDCs have very small magnitudes, the signs were determined unambiguously.     

An alternative self-interaction correction in the generalized exchange local-density functional theory

The local-density functional (LDF) theory does not accurately predict the total energy and the orbital energy of an atom, because of the incomplete cancellation of the self-interaction in the Coulomb integral by that in the exchange integral. Recent investigations showed that the agreement of the total energy and one-electron eigenvalue of an atom in the LDF and Hartree–Fock (HF) theories are remarkably improved by introducing a self-interaction correction in the LDF theory. An alternative self-interaction correction (ASIC) in the generalized exchange local-density functional (GX-LSD) theory is developed by equalizing the one-electron eigenvalue with the ionization potential of the corresponding orbital. The ASIC is subsequently applied to some closed-shell atoms and shown to give numerically better results than both the self-interaction corrected (SIC) exchange-only local-spin-density functional theory (SIC-XO-LSD) and the self-interaction corrected GX-LSD theory (SIC-GX-LSD).     

High magnetic exchange coupling constants: a density functional theory based study of substituted schlenk diradicals

The Schlenk diradical has been known since 1915. After a detailed experimental work by Rajca, its magnetic nature has remained more or less unexplored. We have investigated by quantum chemical calculations the nature of magnetic coupling in 11 substituted Schlenk diradicals. Substitution has been considered at the fifth carbon atom of the meta-phenylene moiety. The UB3LYP method has been used to study 12 diradicals including the original one. The 6-311G(d,p) basis set has been employed for optimization of molecular geometry in both singlet and triplet states for each species. The singlet optimization has led to the optimization of the broken-symmetry structure for 10 species including the unsubstituted one. This development makes it possible to carry out further broken symmetry calculations in two ways. The triplet calculation has been done using 6-311++G(d,p) basis set and the optimized triplet geometry in both procedures. The broken symmetry calculations have used the optimized geometries of either the triplet states or the broken symmetry solutions. The first method leads to the prediction of electron paramagnetic resonance (EPR) compatible magnetic exchange coupling constant (J) in the range 517-617 cm(-1). A direct optimization of the broken symmetry geometry gives rise to a lower estimate of J, in the range of 411-525 cm(-1) and compatible with macroscopic Curie studies. The calculated J for the unsubstituted Schlenk diradical is 512 cm(-1) that can be compared with 455 cm(-1) estimated by Rajca. In both cases, introduction of groups with +M and +I effects (Ingold's notation) decreases the J value from that for the unsubstituted Schlenk diradical while -I and -M groups at the same position increases J. These trends have been explained in terms of Hammett constants, atomic spin densities, and dihedral angles.     

Triplet-triplet energy-transfer coupling: theory and calculation

Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.     

Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes

The application of broken symmetry density functional calculations to homobinuclear and heterobinuclear transition metal complexes produces good estimates of the exchange coupling constants as compared to experimental data. The accuracy of different hybrid density functional theory methods was tested. A discussion is presented of the different methodological approaches that apply when a broken symmetry wave function is used with either Hartree–Fock or density functional calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1391–1400, 1999     

Improving the accuracy of density-functional theory calculation: the genetic algorithm and neural network approach

The combination of genetic algorithm and neural network approach (GANN) has been developed to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation and GANN correction approach has been applied to evaluate the optical absorption energies of 150 organic molecules. The neural network approach reduces the root-mean-square (rms) deviation of the calculated absorption energies of 150 organic molecules from 0.47 to 0.22 eV for the TDDFTB3LYP6-31G(d) calculation, and the newly developed GANN correction approach reduces the rms deviation to 0.16 eV.     

Improving the calculation of magnetic coupling constants in MRPT methods

The magnetic coupling in transition metal compounds with more than one unpaired electron per magnetic center has been studied with multiconfigurational perturbation theory. The usual shortcomings of these methodologies (severe underestimation of the magnetic coupling) have been overcome by describing the Slater determinants with a set of molecular orbitals that maximally resemble the natural orbitals of a high‐level multiconfigurational reference configuration interaction calculation. These orbitals have significant delocalization tails onto the bridging ligands and largely increase the coupling strengths in the perturbative calculation. © 2014 Wiley Periodicals, Inc.     

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences for the development of standard DFT to a method that can correctly describe multi-reference electron systems by treating dynamic and non-dynamic electron correlation on an equal footing, is discussed. In this connection, the seminal work of Colle and Salvetti on wave function-based correlation functionals that do no longer suffer from a SIE is essential. It is described how the Colle–Salvetti correlation functional is an anchor point for the derivation of a functional multi-reference DFT method.     

The limitations of Slater's element-dependent exchange functional from analytic density-functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density, and the one-body effective potential of density-functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method, where variationality then refers to the error in each two-electron integral and not to the total energy. However, a Taylor-series analysis shows that all analytic ab initio energies calculated with variational fits to two-electron integrals are stationary. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gàspàr-Kohn-Sham exchange-correlation potential around each atom in the system. The scaling factors are Slater's exchange parameters alpha. Of several ways of choosing these parameters, two most obvious are the Hartree-Fock (HF) alpha(HF) values and the exact atomic alpha(EA) values. The former are obtained by equating the self-consistent Xalpha energy and the HF energies, while the latter set reproduces exact atomic energies. In this work, we examine the performance of the SR method for predicting atomization energies, bond distances, and ionization potentials using the two sets of alpha parameters. The atomization energies are calculated for the extended G2 set of 148 molecules for different basis-set combinations. The mean error (ME) and mean absolute error (MAE) in atomization energies are about 25 and 33 kcal/mol, respectively, for the exact atomic alpha(EA) values. The HF values of exchange parameters alpha(HF) give somewhat better performance for the atomization energies with ME and MAE being about 15 and 26 kcal/mol, respectively. While both sets give performance better than the local-density approximation or the HF theory, the errors in atomization energy are larger than the target chemical accuracy. To further improve the performance of the SR method for atomization energies, a new set of alpha values is determined by minimizing the MAE in atomization energies of 148 molecules. This new set gives atomization energies half as large (MAE approximately 14.5 kcal/mol) and that are slightly better than those obtained by one of the most widely used generalized-gradient approximations. Further improvements in atomization energies require going beyond Slater's functional form for exchange employed in this work to allow exchange-correlation interactions between electrons of different spins. The MAE in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 A. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.     

Charge localization in stacked radical cation DNA base pairs and the benzene dimer studied by self-interaction corrected density-functional theory

The incomplete cancellation of the electron self-interaction can be a serious shortcoming of density-functional theory especially when treating odd-electron systems. In this work, several popular and potentially viable correction schemes are applied in order to characterize the electronic structure of stacked molecular pairs, consisting of a neutral molecule and adjacent radical cation, as a function of separation distance. The unphysical sharing of the positive charge between adjacent molecules separated by 6-7 A is corrected for by applying a new empirical scheme proposed by VandeVondele and Sprik [Phys. Chem. Chem. Phys. 2005, 7, 1363] with a unique choice of parameters. This method is subsequently applied to characterize the electronic structure of two neighboring guanines excised from a canonical Arnott B-DNA structure and will be used in future investigations of certain model DNA fibers.