Valence Bond Configuration Interaction Research Articles

Origin of Ferromagnetic Exchange Coupling in Donor–Acceptor Biradical Analogues of Charge-Separated Excited States

A new donor-acceptor biradical complex, TpCum,MeZn(SQ-VD) (TpCum,MeZn+ = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. The magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with JSQ-VD = +77 cm-1 (H = -2JSQ-VDŜSQ·ŜVD) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in TpCum,MeZn(SQ-VD) can be compared with that of the related donor-acceptor biradical complex TpCum,MeZn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where JSQ-NN ≅ +550 cm-1. This represents a dramatic reduction in the biradical exchange by a factor of ∼7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQSOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in TpCum,MeZn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VDLUMO and NNLUMO) with the SOMO of the SQ radical (SQSOMO) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the TpCum,MeZn(SQ-VD) ground state, and the intrinsically weaker mixing between the VDLUMO and the SQSOMO compared to that observed for TpCum,MeZn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet-triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.

Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

Spectroscopic Signatures of Resonance Inhibition Reveal Differences in Donor-Bridge and Bridge-Acceptor Couplings.

The torsional dependence of the ground state magnetic exchange coupling (J) and the corresponding electronic coupling matrix element (HDA) for eight transition metal complexes possessing donor-acceptor (D-A) biradical ligands is presented. These biradical ligands are composed of an S = 1/2 metal semiquinone (SQ) donor and an S = 1/2 nitronylnitroxide (NN) acceptor, which are coupled to each other via para-phenylene, methyl-substituted para-phenylenes, or a bicyclo[2.2.2]octane ring. The observed trends in electronic absorption and resonance Raman spectral features are in accord with a reduction in electronic and magnetic coupling between D and A units within the framework of our valence bond configuration interaction model. Moreover, our spectroscopic results highlight different orbital mechanisms that modulate coupling in these complexes, which is not manifest in the ferromagnetic JSQ-B-NN values. The work provides new detailed insight into the effects of torsional rotations which contribute to inhomogeneities in experimentally determined exchange couplings, electron transfer rates, and electron transport conductance measurements.

Resonant inelastic X-ray scattering determination of the electronic structure of oxyhemoglobin and its model complex

Hemoglobin and myoglobin are oxygen-binding proteins with S = 0 heme {FeO2}8 active sites. The electronic structure of these sites has been the subject of much debate. This study utilizes Fe K-edge X-ray absorption spectroscopy (XAS) and 1s2p resonant inelastic X-ray scattering (RIXS) to study oxyhemoglobin and a related heme {FeO2}8 model compound, [(pfp)Fe(1-MeIm)(O2)] (pfp = meso-tetra(α,α,α,α-o-pivalamido-phenyl)porphyrin, or TpivPP, 1-MeIm = 1-methylimidazole) (pfpO2), which was previously analyzed using L-edge XAS. The K-edge XAS and RIXS data of pfpO2 and oxyhemoglobin are compared with the data for low-spin FeII and FeIII [Fe(tpp)(Im)2]0/+ (tpp = tetra-phenyl porphyrin) compounds, which serve as heme references. The X-ray data show that pfpO2 is similar to FeII, while oxyhemoglobin is qualitatively similar to FeIII, but with significant quantitative differences. Density-functional theory (DFT) calculations show that the difference between pfpO2 and oxyhemoglobin is due to a distal histidine H bond to O2 and the less hydrophobic environment in the protein, which lead to more backbonding into the O2 A valence bond configuration interaction multiplet model is used to analyze the RIXS data and show that pfpO2 is dominantly FeII with 6-8% FeIII character, while oxyhemoglobin has a very mixed wave function that has 50-77% FeIII character and a partially polarized Fe-O2 π-bond.

Assessing the performance of ab initio classical valence bond methods for hydrogen transfer reactions

Ab initio classical valence bond theory in terms of localized orbitals has several advantages over electronic structure methods based on canonical delocalized Hartree-Fock molecular orbitals, with two key distinctions being greater applicability to inherently multiconfigurational systems (also called multireference systems or strongly correlated systems) and great interpretability in terms of covalent and ionic valence bond configurations (also called valence bond structures). This can be especially advantageous for applications to chemical reactions. However, until now only limited work tested the quantitative accuracy for the energetics of chemical reactions. The present study provides such tests and validations for a representative test set of six barrier heights corresponding to forward and reverse barriers of three hydrogen transfer reactions. In particular, we test the valence bond self-consistent-field theory (VBSCF) and three post-VBSCF methods that use VBSCF as a reference function for adding dynamic correlation, in particular valence bond configuration interaction (VBCI), breathing orbital valence bond (BOVB), and valence bond second-order perturbation theory (VBPT2). The VBSCF method itself is, as expected, not quantitatively accurate, with a mean unsigned error (MUE) for the six barrier heights of ∼17kcal/mol. But the post-VBSCF methods are found to be quite successful. Depending on the basis set, and valence bond structure selection we obtain MUEs (in kcal/mol) as low as 3.7 for VBCI, 4.5 for BOVB, and (using a bigger basis-set) 1.3 for VBPT2. These compare well, on the same data set, with 1.6 for coupled clusters with singles and doubles (CCSD) and 1.5 for multireference second order perturbation theory based on a complete active space self-consistent field reference function (MRPT2). We discuss the results in terms of the pros and cons of each of these methods.

L-Edge X-ray Absorption Spectroscopic Investigation of {FeNO}6: Delocalization vs Antiferromagnetic Coupling.

NO is a classic non-innocent ligand, and iron nitrosyls can have different electronic structure descriptions depending on their spin state and coordination environment. These highly covalent ligands are found in metalloproteins and are also used as models for Fe-O2 systems. This study utilizes iron L-edge X-ray absorption spectroscopy (XAS), interpreted using a valence bond configuration interaction multiplet model, to directly experimentally probe the electronic structure of the S = 0 {FeNO}6 compound [Fe(PaPy3)NO]2+ (PaPy3 = N,N-bis(2-pyridylmethyl)amine-N-ethyl-2-pyridine-2-carboxamide) and the S = 0 [Fe(PaPy3)CO]+ reference compound. This method allows separation of the σ-donation and π-acceptor interactions of the ligand through ligand-to-metal and metal-to-ligand charge-transfer mixing pathways. The analysis shows that the {FeNO}6 electronic structure is best described as FeIII-NO(neutral), with no localized electron in an NO π* orbital or electron hole in an Fe dπ orbital. This delocalization comes from the large energy gap between the Fe-NO π-bonding and antibonding molecular orbitals relative to the exchange interactions between electrons in these orbitals. This study demonstrates the utility of L-edge XAS in experimentally defining highly delocalized electronic structures.

Iron L-edge X-ray absorption spectroscopy of oxy-picket fence porphyrin: experimental insight into Fe-O2 bonding.

The electronic structure of the Fe-O(2) center in oxy-hemoglobin and oxy-myoglobin is a long-standing issue in the field of bioinorganic chemistry. Spectroscopic studies have been complicated by the highly delocalized nature of the porphyrin, and calculations require interpretation of multideterminant wave functions for a highly covalent metal site. Here, iron L-edge X-ray absorption spectroscopy, interpreted using a valence bond configuration interaction multiplet model, is applied to directly probe the electronic structure of the iron in the biomimetic Fe-O(2) heme complex [Fe(pfp)(1-MeIm)O(2)] (pfp ("picket fence porphyrin") = meso-tetra(α,α,α,α-o-pivalamidophenyl)porphyrin or TpivPP). This method allows separate estimates of σ-donor, π-donor, and π-acceptor interactions through ligand-to-metal charge transfer and metal-to-ligand charge transfer mixing pathways. The L-edge spectrum of [Fe(pfp)(1-MeIm)O(2)] is further compared to those of [Fe(II)(pfp)(1-MeIm)(2)], [Fe(II)(pfp)], and [Fe(III)(tpp)(ImH)(2)]Cl (tpp = meso-tetraphenylporphyrin) which have Fe(II)S = 0, Fe(II)S = 1, and Fe(III)S = 1/2 ground states, respectively. These serve as references for the three possible contributions to the ground state of oxy-pfp. The Fe-O(2) pfp site is experimentally determined to have both significant σ-donation and a strong π-interaction of the O(2) with the iron, with the latter having implications with respect to the spin polarization of the ground state.

Ab initio nonorthogonal valence bond methods

AbstractModern classical valence bond (VB) methods provide clear interpretation and chemical insights by employing covalent and ionic VB structures explicitly. This review focuses on a methodical development of current modern classical VB methods. As a basic method of the classical VB theory, the VB self‐consistent field (VBSCF) method provides a compact wave function, mainly containing static correlation. On the basis of the VBSCF method, the development of classical VB methods can be divided into two aspects—one focuses on improvement of computational accuracy, such as the breathing orbital VB (BOVB), VB configuration interaction (VBCI), and VB second‐order perturbation theory (VBPT2) methods; the other focuses on extending VB approaches to molecules and reactions in solvated or biological environments, including the VB polarizable continuum model (VBPCM), VB solvation model (VBSM), VB effective fragment potential (VBEFP), and VB/molecular mechanics (VB/MM) methods. These improved methods have the advantage of VB theory and provide intuitive chemical insights into medium‐sized chemical problems. Finally, the further development of modern classical VB methods is briefly discussed.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

A benchmark quantum Monte Carlo study of the ground state chromium dimer

AbstractWe report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Theoretical Insights into the Magnetostructural Correlations in Mn3-Based Single-Molecule Magnets

Density functional theory (DFT) and the valence bond configuration interaction (VBCI) model have been applied to the oximato-based Mn(III)(3)O single-molecule magnets (SMMs), allowing one to correlate the Mn(III)-Mn(III) exchange coupling energy (J) with the bridging geometry in terms of two structural angles: the Mn-O-N-Mn torsion angle (γ) and the Mn(3) out-of-plane shift of O (angle δθ). Using DFT, a two-dimensional (γ, δθ) energy surface of J is derived and shown to yield essentially good agreement with the reported J values deduced from magnetic susceptibility data on trigonal oximato-bridged Mn(3) SMMs. VBCI is used to understand and analyze the DFT results. It is shown that the exchange coupling in these systems is governed by a spin-polarization mechanism inducing a pronounced and dominating ferromagnetic exchange via the oximato bridge as opposed to kinetic exchange, which favors a weaker and antiferromagnetic exchange via the bridging oxide. In the light of these results, a discussion of the exchange coupling in the Mn(6) family of the SMM with a record demagnetization barrier is given.

Ferromagnetic nanoscale electron correlation promoted by organic spin-dependent delocalization.

We describe the electronic structure and the origin of ferromagnetic exchange coupling in two new metal complexes, NN-SQ-Co(III)(py)(2)Cat-NN (1) and NN-Ph-SQ-Co(III)(py)(2)Cat-Ph-NN (2) (NN = nitronylnitroxide radical, Ph = 1,4-phenylene, SQ = S = (1)/(2) semiquinone radical, Cat = S = 0 catecholate, and py = pyridine). Near-IR electronic absorption spectroscopy for 1 and 2 reveals a low-energy optical band that has been assigned as a Psi(u) --> Psi(g) transition involving bonding and antibonding linear combinations of delocalized dioxolene (SQ/Cat) valence frontier molecular orbitals. The ferromagnetic exchange interaction in 1 is so strong that only the high-spin quartet state (S(T) = (3)/(2)) is thermally populated at temperatures up to 300 K. The temperature-dependent magnetic susceptibility data for 2 reveals that an excited state spin doublet (S(T) = (1)/(2)) is populated at higher temperatures, indicating that the phenylene spacer modulates the magnitude of the magnetic exchange. The valence delocalization within the dioxolene dyad of 2 results in ferromagnetic alignment of two localized NN radicals separated by over 22 A. The ferromagnetic exchange in 1 and 2 results from a spin-dependent delocalization (double exchange type) process and the origin of this strong electron correlation has been understood in terms of a valence bond configuration interaction (VBCI) model. We show that ferromagnetic coupling promoted by organic mixed-valency provides keen insight into the ability of single molecules to communicate spin information over nanoscale distances. Furthermore, the strong interaction between the itinerant dioxolene electron and localized NN electron spins impacts our ability to understand the exchange interaction between delocalized electrons and pinned magnetic impurities in technologically important dilute magnetic semiconductor materials. The long correlation length (22 A) of the itinerant electron that mediates this coupling indicates that high-spin pi-delocalized organic molecules could find applications as nanoscale spin-polarized electron injectors and molecular wires.

Non-Hermitian Multiconfiguration Molecular Mechanics.

We present a new version of the multiconfiguration molecular mechanics (MCMM) algorithm for fitting potential energy surfaces of complex reactive systems. The main improvement consists in allowing the valence bond configuration interaction matrix to be non-Hermitian, which broadens the range of geometries over which the potential energy surface can be fit accurately. A second improvement is that the new algorithm has simpler gradients and Hessians and executes faster. The performance of the new algorithm is evaluated using the example of two model reactions.

Fe L- and K-edge XAS of Low-Spin Ferric Corrole: Bonding and Reactivity Relative to Low-Spin Ferric Porphyrin

Corrole is a tetrapyrrolic macrocycle that has one carbon atom less than a porphyrin. The ring contraction reduces the symmetry from D(4h) to C(2v), changes the electronic structure of the heterocycle, and leads to a smaller central cavity with three protons rather than the two of a porphyrin. The differences between ferric corroles and porphyrins lead to a number of differences in reactivity including increased axial ligand lability and a tendency to form 5-coordinate complexes. The electronic structure origin of these differences has been difficult to study experimentally as the dominant porphyrin/corrole pi --> pi* transitions obscure the electronic transitions of the metal. Recently, we have developed a methodology that allows for the interpretation of the multiplet structure of Fe L-edges in terms of differential orbital covalency (i.e., the differences in mixing of the metal d orbitals with the ligand valence orbitals) using a valence bond configuration interaction model. Herein, we apply this methodology, combined with a ligand field analysis of the Fe K pre-edge to a low-spin ferric corrole, and compare it to a low-spin ferric porphyrin. The experimental results combined with DFT calculations show that the contracted corrole is both a stronger sigma donor and a very anisotropic pi donor. These differences decrease the bonding interactions with axial ligands and contribute to the increased axial ligand lability and reactivity of ferric corroles relative to ferric porphyrins.

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest-lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self-consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9-12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O(2) molecule, the ground state (3)Sigma(-) possesses both a sigma bond and 3-electron pi bonds. However, here the polar sigma bond contributes the most to the overall bonding. It is augmented by a fractional (19%) contribution of three-electron pi bonding that arises from pi charge transfer from fluorine to nitrogen. In the singlet (1)Delta and (1)Sigma(+) excited states the pi-bonding component is classically covalent, and it contributes 28% and 37% to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that pi bonding contributes at least 24, 35 and 42 kcal mol(-1) to the total bonding energies of the (3)Sigma(-), (1)Delta and (1)Sigma(+) states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.

Basic exchange model: Comparison of Anderson and valence bond configuration interaction approaches and an alternative exchange expression

The application of the Anderson [Phys. Rev. 115, 2 (1959)] and valence bond configuration interaction (VBCI) methods on a basic exchange model is investigated to assess their ability to calculate the exchange energy under a variety of physical situations, represented by the model parameters. The model comprises two metal orbitals and a central ligand orbital. We show that the validity of the Anderson method is not restricted to cases in which $U⪡\ensuremath{\Delta}$ if the ``repulsion assisted transfer'' term is included in the exchange expressions. We discuss the influence of the Coulomb repulsion in the metal and ligand orbitals on the Anderson method, pointing out some deficiencies of the Anderson orbitals. In cases of strong metal-ligand covalency, the VBCI method fails due to its perturbational character. The modified Anderson exchange performs better in some of these cases, depending on the specific situation. Based on the concept of a strict separation of covalent and exchange effects, we derive an exchange expression that overcomes all the discussed difficulties of the Anderson and VBCI methods.

Donor−Acceptor Biradicals as Ground State Analogues of Photoinduced Charge Separated States

A Valence Bond Configuration Interaction (VBCI) model is used to relate the intraligand magnetic exchange interaction (J) to the electronic coupling matrix element (HAB) in Tp(Cum,MeZn)(SQNN), a compound that possesses a Donor-Acceptor (D-A) SemiQuinone-NitronylNitroxide (SQNN) biradical ligand. Within this framework, an SQ --> NN charge transfer state mixes with the ground state and stabilizes the spin triplet (S = 1). This charge-transfer transition is observed spectroscopically and probed using resonance Raman spectroscopy. In addition, the temperature-dependent electronic absorption spectrum of the Ni(II) complex, Tp(Cum,MeNi)(SQNN), has been studied. Exchange coupling between the S = 1 Ni(II) ion and S = 1 SQNN provides a mechanism for observing the formally spin-forbidden, ligand-based 3GC --> 1CTC transition. This provides a means of determining U, the mean GC --> CTC energy, and a one-center exchange integral, K(0). The experimental determination of J, U, and K(0) permits facile calculation of HAB, and we show that this methodology can be extended to determine the electronic coupling matrix element in related SQ-Bridge-NN molecules. As magnetic susceptibility measurements are easily acquired in the solid state, H(AB) may be effectively determined for single molecules in a known geometry, provided a crystal structure exists for the biradical complex. Thus, SQ-Bridge-NN molecules possess considerable potential for probing both geometric and electronic structure contributions to the magnitude of the electronic coupling matrix element associated with a given bridge fragment.

Fe L-edge X-ray absorption spectroscopy of low-spin heme relative to non-heme Fe complexes: delocalization of Fe d-electrons into the porphyrin ligand.

Hemes (iron porphyrins) are involved in a range of functions in biology, including electron transfer, small-molecule binding and transport, and O2 activation. The delocalization of the Fe d-electrons into the porphyrin ring and its effect on the redox chemistry and reactivity of these systems has been difficult to study by optical spectroscopies due to the dominant porphyrin pi-->pi(*) transitions, which obscure the metal center. Recently, we have developed a methodology that allows for the interpretation of the multiplet structure of Fe L-edges in terms of differential orbital covalency (i.e., differences in mixing of the d-orbitals with ligand orbitals) using a valence bond configuration interaction (VBCI) model. Applied to low-spin heme systems, this methodology allows experimental determination of the delocalization of the Fe d-electrons into the porphyrin (P) ring in terms of both P-->Fe sigma and pi-donation and Fe-->P pi back-bonding. We find that pi-donation to Fe(III) is much larger than pi back-bonding from Fe(II), indicating that a hole superexchange pathway dominates electron transfer. The implications of the results are also discussed in terms of the differences between heme and non-heme oxygen activation chemistry.

X-ray Absorption Edge Spectroscopy and Computational Studies on LCuO2 Species: Superoxide−CuII versus Peroxide−CuIII Bonding

The geometric and electronic structures of two mononuclear CuO2 complexes, [Cu(O2){HB(3-Ad-5-(i)Prpz)3}] (1) and [Cu(O2)(beta-diketiminate)] (2), have been evaluated using Cu K- and L-edge X-ray absorption spectroscopy (XAS) studies in combination with valence bond configuration interaction (VBCI) simulations and spin-unrestricted broken symmetry density functional theory (DFT) calculations. Cu K- and L-edge XAS data indicate the Cu(II) and Cu(III) nature of 1 and 2, respectively. The total integrated intensity under the L-edges shows that the 's in 1 and 2 contain 20% and 28% Cu character, respectively, indicative of very covalent ground states in both complexes, although more so in 1. Two-state VBCI simulations also indicate that the ground state in 2 has more Cu (/3d8) character. DFT calculations show that the in both complexes is dominated by O2(n-) character, although the O2(n-) character is higher in 1. It is shown that the ligand L plays an important role in modulating Cu-O2 bonding in these LCuO2 systems and tunes the ground states of 1 and 2 to have dominant Cu(II)-superoxide-like and Cu(III)-peroxide-like character, respectively. The contributions of ligand field (LF) and the charge on the absorbing atom in the molecule (Q(mol)M) to L- and K-edge energy shifts are evaluated using DFT and time-dependent DFT calculations. It is found that LF makes a dominant contribution to the edge energy shift, while the effect of Q(mol)M is minor. The charge on the Cu in the Cu(III) complex is found to be similar to that in Cu(II) complexes, which indicates a much stronger interaction with the ligand, leading to extensive charge transfer.

Ground States, Excited States, and Metal−Ligand Bonding in Rare Earth Hexachloro Complexes: A DFT-Based Ligand Field Study

Metal (4f)-ligand (Cl 3p) bonding in LnCl(6)(3-) (Ln = Ce to Yb) complexes has been studied on the basis of 4f-->4f and Cl,3p-->4f charge-transfer spectra and on the analysis of these spectra within the valence bond configuration interaction model to show that mixing of Cl 3p into the Ln 4f ligand field orbitals does not exceed 1%. Contrary to this, Kohn-Sham formalism of density functional theory using currently available approximations to the exchange-correlation functional tends to strongly overestimate 4f-3p covalency, yielding, for YbCl(6)(3-), a much larger mixing of Cl 3p-->4f charge transfer into the f(13) ionic ground-state wave function. Thus, ligand field density functional theory, which was recently developed and applied with success to complexes of 3d metals in our group, yields anomalously large ligand field splittings for Ln, the discrepancy with experiment increasing from left to the right of the Ln 4f series. It is shown that eliminating artificial ligand-to-metal charge transfer in Kohn-Sham calculations by a procedure described in this work leads to energies of 4f-4f transitions in good agreement with experiment. We recall an earlier concept of Ballhausen and Dahl which describes ligand field in terms of a pseudopotential and give a thorough analysis of the contributions to the ligand field from electrostatics (crystal field) and exchange (Pauli) repulsion. The close relation of the present results with those obtained using the first-principles based and electron density dependent effective embedding potential is pointed out along with implications for applications to other systems.

XMVB: A program for ab initio nonorthogonal valence bond computations

An ab initio nonorthogonal valence bond program, called XMVB, is described in this article. The XMVB package uses Heitler-London-Slater-Pauling (HLSP) functions as state functions, and calculations can be performed with either all independent state functions for a molecule or preferably a few selected important state functions. Both our proposed paired-permanent-determinant approach and conventional Slater determinant expansion algorithm are implemented for the evaluation of the Hamiltonian and overlap matrix elements among VB functions. XMVB contains the capabilities of valence bond self-consistent field (VBSCF), breathing orbital valence bond (BOVB), and valence bond configuration interaction (VBCI) computations. The VB orbitals, used to construct VB functions, can be defined flexibly in the calculations depending on particular applications and focused problems, and they may be strictly localized, delocalized, or bonded-distorted (semidelocalized). The parallel version of XMVB based on MPI (Message Passing Interface) is also available.