Assessing the performance of density functional theory for the electronic structure of metal-salens: the 3d(0)-metals

A series of metal-salen complexes of the 3d(0) metals Sc(III), Ti(IV), V(V), Cr(VI), and Mn(VII) have been explored using high-level electronic structure methods including coupled-cluster theory with singles, doubles, and perturbative triples as well as complete active-space third-order perturbation theory. The performance of three common density functional theory approaches has been assessed for both the geometries and the relative energies of the low-lying electronic states. The nondynamical correlation effects are demonstrated to be extremely large in all of the systems examined. Although density functional theory provides reasonable results for some of the systems, the overall agreement is quite poor. This said, the density functional theory approaches are shown to outperform the single-reference perturbation theory and coupled-cluster theory approaches for cases of strong nondynamical correlation.     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Modeling the peroxide/superoxide continuum in 1:1 side-on adducts of O2 with Cu

The character of singlet (C(3)N(2)H(5))CuO(2) ranges smoothly between copper(III) peroxide and copper(II) superoxide with variation of the electronic character of the supporting beta-diketiminate ligand. Over the range of the variation, multireference second-order perturbation theory predicts the (1)A(1) singlet state always to be lower in energy than the lowest triplet state ((3)B(1)). The multideterminantal character of the biradical-like superoxide mesomer causes density functional theory sometimes to fail badly in predicting the relative energies of these same states, although its predictions of other properties, such as geometry, are of good quality.     

Assessing the performance of density functional theory for the electronic structure of metal-salens: the M06 suite of functionals and the d⁴-metals

We have systematically investigated the electronic structure of the d? metal-salen complexes including the Cr(II)-, Mn(III)-, Fe(IV)-, Mo(II)-, Tc(III)-, and Ru(IV)-salen complexes. Density functional theory (DFT) has been employed, using the BP86 and B3LYP functionals, and the entire M05 and M06 suites of meta-generalized gradient functionals. These results are compared to robust complete active-space self-consistent field (CASSCF) optimized geometries and complete active-space third-order perturbation theory (CASPT3) energies for the lowest singlet, triplet, and quintet states. Although the M06 and M06-L DFT functionals have been generally recommended for computations on complexes that contain main group and transition metals, none of the M0-functionals appear statistically better than the B3LYP functional for the computation of spin-state energy gaps. DFT- and CASSCF-optimized geometries normally agree to within 0.3 ? least root mean squared deviation (LRMSD) for the singlet and triplet structures and less than 0.1 ? LRMSD for the quintet structures. It can be concluded that no DFT functional tested here can be considered reliable over all metal-salen complexes and it is highly recommended that the accuracy of any given DFT functional should be assessed on a case-by-case basis.     

An assessment of pure,hybrid, meta,and hybrid‐meta GGA density functional theory methods for open‐shell systems: The case of the nonheme iron enzyme 8R–LOX

The performance of a range density functional theory functionals combined in a quantum mechanical (QM)/molecular mechanical (MM) approach was investigated in their ability to reliably provide geometries, electronic distributions, and relative energies of a multicentered open‐shell mechanistic intermediate in the mechanism 8R–Lipoxygenase. With the use of large QM/MM active site chemical models, the smallest average differences in geometries between the catalytically relevant quartet and sextet complexes were obtained with the B3LYP^* functional. Moreover, in the case of the relative energies between ⁴II and ⁶II , the use of the B3LYP^* functional provided a difference of 0.0 kcal mol^–1. However, B3LYP^± and B3LYP also predicted differences in energies of less than 1 kcal mol^–1. In the case of describing the electronic distribution (i.e., spin density), the B3LYP^*, B3LYP, or M06‐L functionals appeared to be the most suitable. Overall, the results obtained suggest that for systems with multiple centers having unpaired electrons, the B3LYP^* appears most well rounded to provide reliable geometries, electronic structures, and relative energies. © 2012 Wiley Periodicals, Inc.     

A TDDFT study of the low-lying excitation energies of polycyclic cinnolines and their carbocyclic analogues

The low-lying excited states of 21 compounds of polycyclic cinnoline, monoaza-hydrocarbon and their corresponding polycyclic aromatic hydrocarbon (PAH) analogues have been investigated in the framework of time-dependent density functional theory (TDDFT). The gradient corrected BLYP, hybrid B3LYP and B3P86 functionals together with 6-31G (d) basis set have been used. The hybrid-type B3LYP and B3P86 systematically overestimate the excitation energies for states with dominating ionic character (corresponding to group III band), with a mean absolute deviation (MAD) of 0.33 eV (B3LYP) and 0.34 eV (B3P86), respectively. However, they can accurately predict the excitation energies for states with covalent character (corresponding to group II and I bands). The MAD for group II (B3LYP: 0.05 eV; B3P86: 0.05 eV) and I bands (B3LYP: 0.12 eV; B3P86: 0.12 eV) are significantly smaller. The BLYP outperforms B3LYP and B3P86 for group III band (MAD: 0.09 eV), but has a worse performance for group II (MAD: 0.15 eV) and I (MAD: 0.13 eV) bands. Comparison of the lowest-lying excited states for polycyclic cinnolines with those of the corresponding PAH analogues, the first excited states of polycyclic cinnolines mainly result from n→π₀* transitions. Therefore, in non-polar solvents, the spectra of some polycyclic cinnolines exhibit an additional absorption band at longer wavelengths.     

Ground and excited states of the monomer and dimer of certain carboxylic acids

The ground-state properties of the monomer and the dimer of formic acid, acetic acid, and benzoic acid have been investigated using Hartree-Fock (HF) and density functional theory (DFT) methods using the 6-311++G(d,p) basis set. Some of the low-lying excited states have been studied using the time-dependent density functional theory (TDDFT) with LDA and B3LYP functionals and also employing complete-active-space-self-consistent-field (CASSCF) and multireference configuration interaction (MRCI) methodologies. DFT calculations predict the ground-state geometries in quantitative agreement with the available experimental results. The computed binding energies for the three carboxylic acid dimers are also in accord with the known thermodynamic data. The TDDFT predicted wavelengths corresponding to the lowest energy n-pi* transition in formic acid (214 nm) and acetic acid (214 nm) and the pi-pi* transition in benzoic acid (255 nm) are comparable to the experimentally observed absorption maxima. In addition, TDDFT calculations predict qualitatively correctly the blue shift (4-5 nm) in the excitation energy for the pi-pi* transition in going from the monomer to the dimer of formic acid and acetic acid and the red shift (approximately 19 nm) in pi-pi* transition in going from benzoic acid monomer to dimer. This also indicates that the electronic interaction arising from the hydrogen bonds between the monomers is marginal in all three carboxylic acids investigated.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.     

Ground and excited state properties of photoactive platinum(IV) diazido complexes: theoretical considerations

Recently synthesized by the group of Sadler, the platinum(IV) diazido complexes [Pt(N(3))(2)(OH)(2)(L')(L')] (L' and L' are N-donor ligands) have potential to be used as photoactivatable metallodrugs in cancer chemotherapy. In the present study optimized structures and UV-Vis electronic spectra of trans,trans,trans- and cis,trans,cis-[Pt(N(3))(2)(OH)(2)(NH(3))(2)] (1t and 1c, respectively) as well as cis,trans,cis-[Pt(N(3))(2)(OH)(2)(L)(2)] (L = NH(3), NH(2)CH(3), NF(3), PH(3), PF(3), H(2)O, CO, OH(-), CN(-), py, imid; 2c-11c) and cis,trans-[Pt(N(3))(2)(OH)(2)(bpy)] (12c) complexes were predicted using density functional theory (DFT). The ground state electronic structures of all complexes were analyzed with the help of the natural bond orbital analysis (NBO). The electronic spectra of 1c and 1t were computed using time-dependent density functional theory (TDDFT) with five different density functionals and the ab initio CASSCF/CASPT2 method (for the five lowest energy transitions). The best agreement with available experiments was found in the case of the long-range corrected ωB97X functional. The electronic transitions were characterized by the analysis of the natural transition orbitals (NTO). The low-lying excited singlet states of 1t and 1c have significant azide-to-platinum(IV) charge-transfer character (LMCT). Geometry optimization of the three lowest singlet excited states performed using TDDFT results in the simultaneous dissociation of two azide ligands with the formation of the azidyl radicals N(3)˙ and photoreduction of Pt(IV) to Pt(II). Variation of the ligand L does not strongly affect the nature and the relative energies of the low-lying states. It is shown that the replacement of the OH(-) groups in 1c by OPh(-) ligands results in the red shift of the intense N(3)(-)→Pt LMCT band and the appearance of transitions with significant intensity in the visible region of the spectrum. The dissociative nature of the low-lying unoccupied orbitals remains unaffected. These theoretical results may suggest new experimental routes for the improvement of the photochemical activity of Pt(IV) diazido complexes.     

Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order M?ller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.     

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.     

Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel

We extend our previous formulation of time-dependent four-component relativistic density-functional theory [J. Gao, W. Liu, B. Song, and C. Liu, J. Chem. Phys. 121, 6658 (2004)] by using a noncollinear form for the exchange-correlation kernel. The new formalism can deal with excited states involving moment (spin)-flipped configurations which are otherwise not accessible with ordinary exchange-correlation functionals. As a first application, the global potential-energy curves of 16 low-lying omega omega-coupled electronic states of the AuH molecule have been investigated. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are grossly in good agreement with those of ab initio multireference second-order perturbation theory and the available experimental data.     

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. II. Electronic structure and photoluminescence spectra

The influence of the choice of the exchange-correlation functional (semilocal gradient corrected or hybrid functionals) on the electronic properties of metal-exchanged zeolites has been investigated for Cu- and Co-exchanged chabazite. The admixture of exact exchange in hybrid functionals increases the fundamental gap of purely siliceous chabazite, leading to better agreement with experiment and many-body perturbation theory for close-packed SiO(2) polymorphs where detailed experimental information is available. For the metal-exchanged chabazite the increased exchange splitting strongly influences the position of the cation states relative to the framework bands-in general, gradient-corrected functionals locate the occupied cation states close to the valence-band maximum of the framework, while hybrid functionals shift the occupied cation states to larger binding energies and the empty states to higher energies within the fundamental gap. The photoluminescence spectra have been analyzed using fixed-moment total-energy calculations for excited spin states in structurally relaxed and frozen geometries. The geometrical relaxation of the excited states leads to large differences in excitation and emission energies which are more pronounced in calculations using hybrid functionals. Due to the stronger relaxation effects calculated with hybrid functionals, the large differences in the electronic spectra calculated with both types of functionals are not fully reflected in the photoluminescence spectra.     

Application of an efficient multireference approach to free-base porphin and metalloporphyrins: ground, excited, and positive ion states

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is applied to determine the geometries of the ground state of free-base porphin and its metal derivatives, magnesium and zinc porphyrins. The vertical excitation energies and ionization potentials are computed at these optimized geometries using an IVO-based version of multireference Mo?ller-Plesset (IVO-MRMP) perturbation theory. The geometries and excitation energies obtained from the IVO-CASCI and IVO-MRMP methods agree well with experiment and with other correlated many-body methods. We also provide the ground state vibrational frequencies for free-base porphin and Mg-porphyrin. All frequencies are real in contrast to self-consistent field treatments which yield an imaginary frequency. Ground state normal mode frequencies (scaled) of free-base porphin and magnesium porphyrin from IVO-CASCI and complete active space self-consistent field methods are quite similar and are consistent with Becke-Slater-Hartree-Fock exchange and Lee-Yang-Parr correlation density functional theory calculations and with experiment. In addition, geometries are determined for low-lying excited state triplets and for positive ion states of the molecules. To our knowledge, no prior experimental and theoretical data are available for these excited state geometries of magnesium and zinc porphyrins. Given that the IVO-CASCI and IVO-MRMP computed geometries and excitation energies agree favorably with experiment and with available theoretical data, our predicted excited state geometries should be equally accurate.     

Quantum chemical characterization of the generation of high-valent oxoruthenium species of Keggin type polyoxometalates: electronic structure and bonding features

High-valent transition-metal-substituted Keggin-type polyoxometalates (POMs) are active and robust oxidation catalyst. The important oxidized intermediates of these POM complexes are very difficult to be characterized by using the experimental method, and thus no detail information is available on such species. In the present paper, density functional theory (DFT) calculations have been carried out to characterize the electronic structures of a series of mono-ruthenium-substituted Keggin-type POMs. We find that the aquaruthenium(II/III/IV) species possess d(xy)(2)d(xz)(2)d(yz)(2), d(xy)(2)d(xz)(2)d(yz)(1), and d(xy)(2)d(xz)(1)d(yz)(1) electronic configuration, respectively, and hydroxyl/oxoruthenium(IV/V/VI) species possess d(xy)(2)d(xz)(1)π*(yz)(1), d(xy)(2)π*(xz)(1)π*(yz)(1), d(xy)(1)π*(xz)(1)π*(yz)(1), and d(xy)(1)π*(xz)(1)π*(yz)(0) electronic configuration, respectively. Mulliken spin population shows that spin density is localized on the ruthenium center in aquaruthenium(II/III/IV) POM complexes, and the RuO(a) unit in hydroxyl/oxoruthenium(IV/V/VI) POM complexes. The O(a) atom has substantial radical character in oxoruthenium(IV/V) species, and the radical character of the O(a) atom are significantly weakened in the oxoruthenium(VI) species. The relevant energy of the important Ru-O(a)π*-antibonding unoccupied orbitals with high RuO(a) compositions of oxoruthenium(IV/V/VI) POM complexes decrease in the order: oxoruthenium(IV) > oxoruthenium(V) > oxoruthenium(VI). The pH-independent multiple reduction energies for Ru(III/II), Ru(V/IV), and Ru(VI/V) couples are calculated, which is in agreement with the experimental data.     

Theoretical study of the electronic spectra of small molecules that incorporate analogues of the copper-cysteine bond

The copper-sulfur bond that binds cysteinate to the metal center is a key factor in the spectroscopy of blue copper proteins. We present theoretical calculations describing the electronically excited states of small molecules, including CuSH, CuSCH(3), (CH(3))(2)SCuSH, (imidazole)-CuSH, and (imidazole)(2)-CuSH, derived from the active site of blue copper proteins that contain the copper-sulfur bond in order to identify small molecular systems that have electronic structure that is analogous to the active site of the proteins. Both neutral and cationic forms are studied since these represent the reduced and oxidized forms of the protein, respectively. For CuSH and CuSH(+), excitation energies from time-dependent density functional theory with the B97-1 exchange-correlation functional agree well with the available experimental data and multireference configuration interaction calculations. For the positive ions, the singly occupied molecular orbital is formed from an antibonding combination of a 3d orbital on copper and a 3p(π) orbital on sulfur, which is analogous to the protein. This leads several of the molecules to have qualitatively similar electronic spectra to the proteins. For the neutral molecules, changes in the nature of the low lying virtual orbitals leads the predicted electronic spectra to vary substantially between the different molecules. In particular, addition of a ligand bonded directly to copper results in the low-lying excited states observed in CuSH and CuSCH(3) to be absent or shifted to higher energies.