Nondynamic Electron Correlation Research Articles

Assessment of density functional theory based ΔSCF (self-consistent field) and linear response methods for longest wavelength excited states of extended π-conjugated molecular systems.

Computational investigation of the longest wavelength excitations in a series of cyanines and linear n-acenes is undertaken with the use of standard spin-conserving linear response time-dependent density functional theory (TD-DFT) as well as its spin-flip variant and a ΔSCF method based on the ensemble DFT. The spin-conserving linear response TD-DFT fails to accurately reproduce the lowest excitation energy in these π-conjugated systems by strongly overestimating the excitation energies of cyanines and underestimating the excitation energies of n-acenes. The spin-flip TD-DFT is capable of correcting the underestimation of excitation energies of n-acenes by bringing in the non-dynamic electron correlation into the ground state; however, it does not fully correct for the overestimation of the excitation energies of cyanines, for which the non-dynamic correlation does not seem to play a role. The ensemble DFT method employed in this work is capable of correcting for the effect of missing non-dynamic correlation in the ground state of n-acenes and for the deficient description of differential correlation effects between the ground and excited states of cyanines and yields the excitation energies of both types of extended π-conjugated systems with the accuracy matching high-level ab initio multireference calculations.

Theoretical Studies of the Mechanism of N-Hydroxylation of Primary Aromatic Amines by Cytochrome P450 1A2: Radicaloid or Anionic?

Primary aromatic and heteroaromatic amines are notoriously known as potential mutagens and carcinogens. The major event of the mechanism of their mutagenicity is N-hydroxylation by P450 enzymes, primarily P450 1A2 (CYP1A2), which leads to the formation of nitrenium ions that covalently modify nucleobases of DNA. Energy profiles of the NH bond activation steps of two possible mechanisms of N-hydroxylation of a number of aromatic amines by CYP1A2, radicaloid and anionic, are studied by dispersion-corrected DFT calculations. The classical radicaloid mechanism is mediated by H-atom transfer to the electrophilic ferryl-oxo intermediate of the P450 catalytic cycle (called Compound I or Cpd I), whereas the alternative anionic mechanism involves proton transfer to the preceding nucleophilic ferrous-peroxo species. The key structural features of the catalytic site of human CYP1A2 revealed by X-ray crystallography are maintained in calculations. The obtained DFT reaction profiles and additional calculations that account for nondynamical electron correlation suggest that Cpd I has higher thermodynamic drive to activate aromatic amines than the ferrous-peroxo species. Nevertheless, the anionic mechanism is demonstrated to be consistent with a variety of experimental observations. Thus, energy of the proton transfer from aromatic amines to the ferrous-peroxo dianion splits aromatic amines into two classes with different mutagenicity mechanisms. Favorable or slightly unfavorable barrier-free proton transfer is inherent in compounds that undergo nitrenium ion mediated mutagenicity. Monocyclic electron-rich aromatic amines that do not follow this mutagenicity mechanism show significantly unfavorable proton transfer. Feasibility of the entire anionic mechanism is demonstrated by favorable Gibbs energy profiles of both chemical steps, NH bond activation, and NO bond formation. Taken together, results suggest that the N-hydroxylation of aromatic amines in CYP1A2 undergoes the anionic mechanism. Possible reasons for the apparent inability of Cpd I to activate aromatic amines in CYP1A2 are discussed.

Potential energy curves for Mo2: multi-component symmetry-projected Hartree–Fock and beyond

The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case for ab initio quantum chemistry methods. In particular, the complex binding pattern in the Mo2 molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree–Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in a D∞hS-UHF or a D∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-component D∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling – full configuration interaction) method for selected geometries.

Multiconfigurational Self-Consistent Field Calculations of the Magnetically Induced Current Density Using Gauge-Including Atomic Orbitals.

Nondynamical electron correlation based on a genuine multiconfigurational theory is of considerable importance for a balanced ab initio calculation of aromatic and antiaromatic molecules either with open-shell character or quasi-degeneracy in the electronic states. Among the various aromaticity indices, the calculation of magnetically induced ring current densities (MICD) has emerged as a strong contender, providing both a qualitative and a quantitative description of the effect. We report here the first implementation of MICD at the multiconfigurational self-consistent field (MCSCF) level of theory together with example calculations. This extension makes the method applicable to systems that cannot be appropriately handled with earlier implementations based on a single-reference starting function. We present the formulation of the MCSCF MICD theory along with applications to a prototypical antiaromatic (cyclobutadiene) and an aromatic (benzyne) system, both systems that require a multiconfigurational description. We compare the MCSCF results to those obtained using Hartree-Fock and Kohn-Sham density functional theory and discuss the effects of static correlation on the aromaticity.

The natural orbital functional theory of the bonding in Cr2, Mo2and W2

In this paper, we present for the first time a description based on the natural orbital functional theory (NOFT) of the group VI dimers, namely, Cr(2), Mo(2) and W(2). The PNOF5, Piris Natural Orbital Functional, has been used throughout this work, and the results are compared to multireferential perturbation theory (CASPT2) results. Both methods have been combined with effective core potentials to take into account the scalar relativistic effects. In addition, for Cr(2), an all-electron TZVP quality basis set has also been used to recover the core-valence dynamical correlation. In all cases, PNOF5 shows better behavior than CASPT2, which needs a larger basis set to recover comparable amounts of dynamical correlation. PNOF5 is able to account for the non-dynamical electron correlation, which is responsible for the multireferential nature of these dimers. However, it does not fully recover the dynamical correlation, which is crucial for the accurate description of these challenging potential energy curves. Consequently, PNOF5 predicts longer equilibrium distances and lower dissociation energies than the experimental values. Unlike CASPT2, the PNOF5 results do not significantly improve by using larger basis sets. These new findings represent a major step in the NOFT development, since PNOF5 is the first functional of the natural orbitals reported to yield a chemically balanced and accurate description of these challenging transition metal dimers.

Improved self-consistent and resolution-of-identity approximated Becke'05 density functional model of nondynamic electron correlation.

In a recent letter [E. Proynov, Y. Shao, and J. Kong, Chem. Phys. Lett. 493, 381 (2010)], Becke's B05 model of nondynamic electron correlation in density functional theory was implemented self-consistently with computational efficiency (the "SCF-RI-B05" scheme). Important modifications of the algorithm were done in order to make the self-consistency feasible. In the present work, we give a complete account of the SCF-RI-B05 algorithm, including all the formulae for the analytical representation of the B05 functional and for its self-consistent field (SCF) potential. The average performance of the SCF-RI-B05 method reported in the above letter was somewhat less accurate, compared to the original B05 implementation, mainly because the parameters of the original B05 model were optimized with post-local-spin-density calculations. In this work, we report improved atomization energies with SCF-RI-B05, based on a SCF re-optimization of its four linear parameters. The re-optimized SCF-RI-B05 scheme is validated also on reaction barriers, and on the subtle energetics of NO dimer, an exemplary system of strong nondynamic correlation. It yields both the binding energy and the singlet-triplet splitting of the NO dimer correctly, and close to the benchmarks reported in the literature.

Accurate Bond Energies of Hydrocarbons from Complete Basis Set Extrapolated Multi‐Reference Singles and Doubles Configuration Interaction

Quantum chemistry has become one of the most reliable tools for characterizing the thermochemical underpinnings of reactions, such as bond dissociation energies (BDEs). The accurate prediction of these particular properties (BDEs) are challenging for ab initio methods based on perturbative corrections or coupled cluster expansions of the single-determinant Hartree-Fock wave function: the processes of bond breaking and forming are inherently multi-configurational and require an accurate description of non-dynamical electron correlation. To this end, we present a systematic ab initio approach for computing BDEs that is based on three components: 1) multi-reference single and double excitation configuration interaction (MRSDCI) for the electronic energies; 2) a two-parameter scheme for extrapolating MRSDCI energies to the complete basis set limit; and 3) DFT-B3LYP calculations of minimum-energy structures and vibrational frequencies to account for zero point energy and thermal corrections. We validated our methodology against a set of reliable experimental BDE values of CC and CH bonds of hydrocarbons. The goal of chemical accuracy is achieved, on average, without applying any empirical corrections to the MRSDCI electronic energies. We then use this composite scheme to make predictions of BDEs in a large number of hydrocarbon molecules for which there are no experimental data, so as to provide needed thermochemical estimates for fuel molecules.

Theoretical Study of the Photochemistry of a Reversible Three‐State Bis‐Thiaxanthylidene Molecular Switch

The ground- and the lowest singlet excited-state potential energy surfaces of the bis-thiaxanthylidene (3) molecular switch are investigated using a density functional method specifically designed to treat molecular systems typified by strong non-dynamic electron correlation. The results of the theoretical calculations suggest that the unique ability of substituted bis-thiaxanthylidenes to switch between three states of luminescence-non-fluorescent state, blue fluorescent state, and red fluorescent state-can be explained by specific features on the excited state potential energy surface: the potential barrier around the Franck-Condon point of the anti-folded conformer and the existence of conical intersection in the vicinity of the syn-folded conformer. It is suggested that the twisted conformer, if made more stable via chemical modification, should fluoresce in the near-infrared region (λ≈740-760 nm), thus offering a possibility for a four-state switching of luminescence in a single-component molecular system.

Natural Orbital Functional Theory and Reactivity Studies of Diradical Rearrangements: Ethylene Torsion as a Case Study

Natural orbital functional theory (NOFT) in its PNOF3 and PNOF4 implementations is used to investigate the potential energy surface (PES) of ethylene torsion. This rearrangement is taken as a case study to illustrate the satisfactory performance of the Piris Natural Orbital Functional (PNOF) toward rearrangements sensible to non-dynamical electron correlation or near-degeneracy effects. We show that the fulfillment of the G-positivity condition, as implemented in PNOF4, is key to yield a correct description of structures with significant diradical character. We have found that PNOF4 yields an accurate description of these delicate PES and predicts the correct trends of the occupation numbers as compared with multiconfigurational wavefunction methods.

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: Löwdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.

Antiferromagnetic interactions in the quarter-filled organic conductor (EDO-TTF)2PF6

The ground state electronic structure of the high-temperature (HT) and the low-temperature (LT) phases of (EDO-TTF)(2)PF(6) is investigated using the embedded cluster approach in combination with the density functional method designed to describe the strong non-dynamic electron correlation. It is found that, in the HT phase, the unpaired electron spins located on pairs of neighbouring EDO-TTF molecules are antiferromagnetically coupled along the stacking direction with the Heisenberg exchange integral J = -655 cm(-1). In the LT phase, the unpaired spins located on the cationic EDO-TTF molecules are coupled antiferromagnetically with J values strongly alternating along the stacking axis of the crystal thus rendering it diamagnetic. The parameters of the extended Hubbard model are evaluated and the conductance properties of the two phases are estimated using these parameters. It is suggested to investigate the charge and spin excitations in the two phases of (EDO-TTF)(2)PF(6) with the use of angle-resolved photoemission spectroscopy.

Isomerization of Bicyclo[1.1.0]butane by Means of the Diffusion Quantum Monte Carlo Method

The isomerization of bicyclo[1.1.0]butane which comprises species with different multireference character is studied by means of the diffusion quantum Monte Carlo method (DMC). Accurate multireference DMC calculations are presented. It can be shown that at most three configuration state functions are required to achieve a balanced description of dynamical and nondynamical electron correlation. A general scheme is described that promotes efficient error cancellation in multireference DMC calculations.

The ‘tailored’ CCSD(T) description of the automerization of cyclobutadiene

An alternative route to extend the CCSD(T) approach to multireference problems is presented. The well-known defect of the CCSD(T) model in describing the non-dynamic electron correlation effects is remedied by ‘tailoring’ the underlying coupled-cluster singles and doubles (CCSD) approach and applying the perturbative triples correction to it. The TCCSD(T) approach suggested in the paper has the same computational demands as the CCSD(T) method, though being mostly free from its drawbacks pertinent to multireference (quasidegenerate) situations. To test the approach we calculate the potential energy surface for the automerization of cyclobutadiene where the transition state exhibits a strong multireference character.

ChemInform Abstract: Ab initio Studies of Structure and Hyperfine Coupling in Cyclohexadienyl and Hydroxycyclohexadienyl Radicals.

The hyperfine coupling constants in cyclohexadienyl radical and its derivative formed by substituting a hydroxy group for one of the methylene hydrogens are studied by ab initio computational methods. Couplings to all of the carbon atoms and to the hydrogens within the five carbon conjugated segment are described reasonably well with a simple spin polarization model implemented by single excitation configuration interaction. However, the methylene hydrogen coupling and its large drop upon hydroxy substitution are significantly underestimated. Treatment of strong nondynamical electron correlation in the {pi} space leads to only small improvements in the coupling constants. Extensive recovery of dynamical electron correlation together with very large basis sets, will probably be required for quantitative description of the methylene hydrogen couplings. The geometry relaxation accompanying hydroxy substitution is found to be small and to partially counteract the large drop in methylene hydrogen coupling. It is concluded that the drop is due to disruption of the electronic structure through changes in direct delocalization of the unpaired electron, indirect spin polarization, and higher order electron correlations contributions to the hyperfine coupling. 45 refs., 1 fig., 3 tabs.

Björn O. Roos (1937-2010)

Björn O. Roos (1937-2010)

Efficient self-consistent DFT calculation of nondynamic correlation based on the B05 method

Becke's B05 method of describing nondynamic electron correlation in Density Functional Theory is implemented self-consistently with computational efficiency. Important modifications of the method are proposed in order to make the self-consistency feasible. Resolution-of-identity technique is used to reduce dramatically the cost of the required exact-exchange energy density. The method is briefly validated on a variety of properties. It describes accurately for the first time the subtle energetics of the NO dimer, an exemplary system of strong nondynamic correlation. The efficient algorithm for the exact-exchange energy density can be applied to other functionals that use this quantity.

Localized orbital corrections for the calculation of barrier heights in density functional theory.

This work describes the extension of a previously reported empirical localized orbital correction model for density functional theory (DFT-LOC) for atomization energies, ionization potentials, electron affinities, and reaction enthalpies to the correction of barrier heights for chemical reactions of various types including cycloadditions, cycloreversions, dipolar cycloadditions, S(N)2's, carbon radical reactions, hydrogen radical reactions, sigmatropic shifts, and electrocyclizations. The B3LYP localized orbital correction version of the model (B3LYP-LOC) reduces the number of outliers and overall mean unsigned error (MUE) vs. experiment or ab initio values from 3.2 to 1.3 kcal/mole for barrier heights and from 5.1 to 1.1 kcal/mole for reaction enthalpies versus B3LYP. Furthermore, the new model has essentially zero additional computational cost beyond standard DFT calculations. Although the model is heuristic and is based on multiple linear regression to experimental or ab initio data, each of the parameters is justified on chemical grounds and provides insight into the fundamental limitations of DFT, most importantly the failure of current DFT methods to accurately account for nondynamical electron correlation.

Energy Gaps in the 4f135d1 Manifold and Multiple Spontaneous Emissions in Yb2+-Doped CsCaBr3

Multiple spontaneous 4f(13)5d(1) --> 4f(14) emissions are predicted in Yb(2+)-doped CsCaBr(3) crystals by ab initio quantum chemical calculations. Four emission bands are found at 23,900, 26,600, 34,600, and 43,900 cm(-1) that should be experimentally observable at low temperatures. The first, third, and fourth bands are slow, electric dipole forbidden emissions that can be described as spin-forbidden. The second band is a fast, electric dipole-allowed emission that cannot be described as spin-allowed, but as spin-enabled; its radiative emission lifetime is 400 ns. Large energy gaps (23 900, 4600, 4000 cm(-1), respectively), relative to the maximum local phonon energies calculated (around 185 cm(-1)), are found below the emitting levels of the slow bands, which indicates that these states should be significantly stable and multiphonon relaxation to the lower states should be negligible. A smaller gap (2600 cm(-1)) separates the states of the fast band, which should result in a temperature dependent competition between radiative and nonradiative decay. Differential correlation between 4f-4f and 4f-5d pairs, splitting of the 5d shell by interactions with the host, and spin-orbit effects within the 4f(13) subshell, are found to be responsible for the existence of the gaps, which, in turn, split the absorption spectrum into four groups of separate bands, three of which could lie below the host absorption threshold. The quantum chemical methods employed make use of explicit wave functions expanded in terms of flexible basis sets, multiconfigurational self-consistent-field and multireference second-order perturbation methods to account for nondynamic and dynamic electron correlation, scalar and relativistic terms in the (YbBr(6))(4-) defect cluster Hamiltonian, and quantum mechanical embedding potentials to represent the host crystal.

A diagnostic for determining the quality of single-reference electron correlation methods

It was recently proposed that the Euclidian norm of the t1 vector of the coupled-cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appropriate. This diagnostic T1 is defined for use with self-consistent-field molecular orbitals and is invariant to the same orbital rotations as the coupled-cluster energy. T1 is investigated for several different chemical systems which exhibit a range of multireference behavior and is shown to be an excellent measure of the importance of nondynamical electron correlation and is far superior to C0 from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T1 (i.e., >0.02) probably indicates the need for a multireference electron correlation procedure.

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.