The singlet-triplet gap in trimethylenmethane and the ring-opening of methylenecyclopropane: a multireference Brillouin-Wigner coupled cluster study

We performed an ab initio study of the singlet-triplet gap in trimethylenmethane (TMM) and of the ring-opening of methylenecyclopropane by the multireference BWCC method. Since the singlet states of TMM and intermediates between TMM and methylenecyclopropane have a strong multiconfigurational character, it is necessary to use a multireference method. The cc-pVDZ and cc-pVTZ basis sets were used. We compared our results with experiments, where available, and with previous calculations performed by MCSCF and spin-flip coupled-cluster-type methods.     

Effects of ethynyl substituents on the electronic structure of cyclobutadiene

The effects of ethynyl substitution on the electronic structure of cyclobutadiene are investigated in this work. Ethynyl substituted cyclobutadienes may be involved in Bergman cyclization reactions and are possible intermediates in the formation of fullerenes and graphitic sheets. Prediction of the electronic structure of cyclobutadiene is challenging for single-reference ab initio methods because of Jahn-Teller distortions and the diradical character of the singlet state. The equation-of-motion spin-flip coupled-cluster with single and double excitations (EOM-SF-CCSD) method accurately describes diradical states and is used to determine vertical and adiabatic singlet-triplet energy splittings in the substituted cyclobutadienes. The adiabatic singlet-triplet gaps decrease upon substituent addition, but the singlet states remain lower in energy. However, the results are affected by spin-contamination of the reference state and deteriorate when an unrestricted HF reference is employed. Additional insights in the electronic structure of cyclobutadienes are obtained by analyzing natural charges and spin densities. The substituents pull the charge out of the cyclobutadiene ring; however, the natural charges and spin densities are found to be nearly independent of the geometry and spin state.     

Taming the Antiferromagnetic Beast: Computational Design of Ultrashort Mn−Mn Bonds Stabilized by N-Heterocyclic Carbenes

The development of complexes featuring low-valent, multiply bonded metal centers is an exciting field with several potential applications. In this work, we describe the design principles and extensive computational investigation of new organometallic platforms featuring the elusive manganese-manganese bond stabilized by experimentally realized N-heterocyclic carbenes (NHCs). By using DFT computations benchmarked against multireference calculations, as well as MO- and VB-based bonding analyses, we could disentangle the various electronic and structural effects contributing to the thermodynamic and kinetic stability, as well as the experimental feasibility, of the systems. In particular, we explored the nature of the metal-carbene interaction and the role of the ancillary η⁶ coordination to the generation of Mn₂ systems featuring ultrashort metal-metal bonds, closed-shell singlet multiplicities, and positive adiabatic singlet-triplet gaps. Our analysis identifies two distinct classes of viable synthetic targets, whose electrostructural properties are thoroughly investigated.     

Analysis and interpretation of metal-radical coupling in a series of square planar nickel complexes: correlated Ab initio and density functional investigation of [Ni(L(ISQ))(2)] (L(ISQ)=3,5-di-tert-butyl-o-diiminobenzosemiquinonate(1-))

This paper reports a detailed theoretical study of the interaction between a central low-spin d(8) nickel ion and two N,N-coordinating diiminobenzosemiquinonate(1-) ligands in a square planar arrangement. Such complexes have recently attracted much attention due to their unusual bonding patterns, structures, optical, and magnetic properties. Geometry optimizations using various levels of density functional theory (DFT) result in excellent agreement with the experimentally determined structure and in particular reproduce the quinoidal distortions in the aromatic rings well. A detailed analysis of the orbital structure reveals that the complex features essentially two strongly interacting ligand radicals which interact with each other via an efficient superexchange mechanism that is mediated by a back-bonding interaction to the central metal. An analysis of the broken symmetry DFT wave function is presented and a new index for the diradical character is proposed which shows that [Ni(L(ISQ))(2)] has a diradical character of approximately 77%. These results are in full agreement with elaborate multireference post-Hartree-Fock ab initio calculations for [Ni(L(ISQ))(2)] using the difference dedicated configuration interaction (DDCI) method as well as second-order multireference M?ller-Plesset (MR-MP2) theory, which give diradical characters of 65-80%. On the basis of these calculations our best estimate for the singlet-triplet gap in this system is 3096 cm(-)(1). This very large value results from an efficient mixing of the ionic configurations into the mainly singlet diradical ground state which is feasible because the semiquinonate SOMOs are delocalized and, therefore, have moderate on-site Coulomb repulsion parameters. As pointed out in the discussion, this represents an interesting difference to the case of magnetically interacting transition metal ions which typically show much smaller magnetic exchange couplings.     

The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.     

Density functional theory with fractional orbital occupations

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H(2) and N(2), and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.     

Conformational analysis of singlet-triplet state mixing in Paternò-Büchi diradicals

Conformational dependence of spin-orbit coupling (SOC) in flexible Paternò-Büchi (PB) diradicals has been studied with high-level ab initio methods using both (i) one-electron spin-orbit Hamiltonian with parametrized (effective) nuclear charges in conjunction with a state-averaged MCSCF wave function as implemented by Robb in Gaussian 98 and (ii) complete one- and two-electron SOC with a fully optimized MCSCF triplet wave function and frozen core singlet as implemented by Furlani in the GAMESS computational package. The ab initio results revealed two distinct areas of elevated SOC values, one corresponding to the region whereby a cisoid conformation in the C-C-O-C fragment brings the two odd-electron orbitals closer to each other, and the other area corresponding to the partially eclipsed conformation lacking direct overlap between the spin centers. In this second region the 1,4-electronic communication is mediated by the oxygen's 2p-lone pair, which is suitably oriented to play the role of a "relay-antenna". The other critical factor affecting the rate of intersystem crossing (ISC)--singlet-triplet energy separation--was computed utilizing a multireference CASSCF-MP2 method to include dynamic correlation effects. The largest singlet-triplet energy gap, approximately 2 kcal/mol, was found for a gauche conformer (also a minimum SOC conformation). Rotation about the central C-O bond either toward the fully eclipsed (0 degrees ) or the partially eclipsed (120 degrees ) conformations decreases the singlet-triplet gap while increasing the value of the SOC matrix element. These computational findings support the Griesbeck model for stereochemistry of triplet PB reactions and provide a rigorous basis for predicting the probability of ISC in diradicals separated by a partially conjugated spacer.     

Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory

Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.     

Vibrational spectra and structure of cyclopentane and its isotopomers

The infrared and Raman spectra of vapor, liquid, and solid state cyclopentane and its d(1), 1,1-d(2), 1,1,2,2,3,3-d(6), and d(10) isotopomers have been recorded and analyzed. The experimental work was complemented by ab initio and density functional theory (DFT) calculations. The computations confirm that the two conformational forms of cyclopentane are the twist (C(2)) and bent (C(s)) structures and that they differ very little in energy, less than about 10 cm(-1) (0.1 kJ/mol). The bending angle for the C(s) form is 41.5° and the dihedral angle of twisting is 43.2° for the C(2) form. A reliable and complete vibrational assignment for each of the isotopomers has been achieved for the first time, and these agree very well with the DFT (B3LYP/cc-pVTZ) computations. The ab initio CCSD/cc-pVTZ calculations predict a barrier to planarity of 1887 cm(-1), which is in excellent agreement with the experimental value of 1808 cm(-1).     

Electronic structure of the alkyne-bridged dicobalt hexacarbonyl complex Co(2) micro-C(2)H(2) (CO)(6): evidence for singlet diradical character and implications for metal-metal bonding

A series of ab initio calculations are presented on the alkyne-bridged dicobalt hexacarbonyl cluster Co2 micro-C2H2 (CO)6, indicating that this compound has substantial multireference character, which we interpret as evidence of singlet diradical behavior. As a result, standard theoretical methods such as restricted Hartree-Fock (RHF) or Kohn-Sham (RKS) density functional theory cannot properly describe this compound. We have therefore used complete active space (CAS) methods to explore the bonding in and spectroscopic properties of Co2 micro-C2H2 (CO)6. CAS methods identify significant population of a Co-Co antibonding orbital, along with Co-pi* back-bonding, and a relatively large singlet-triplet energy splitting. Analysis of the electron density and related quantities, such as energy densities and atomic overlaps, indicates a small but significant amount of covalent bonding between cobalt centers.     

Anharmonic vibrational spectroscopy calculations with electronic structure potentials: comparison of MP2 and DFT for organic molecules

Density functional theory (DFT) technique is the most commonly used approach when it comes to computation of vibrational spectra of molecular species. In this study, we compare anharmonic spectra of several organic molecules such as allene, propyne, glycine, and imidazole, computed from ab initio MP2 potentials and DFT potentials based on commonly used BLYP and B3LYP functionals. Anharmonic spectra are obtained using the direct vibrational self-consistent field (VSCF) method and its correlation-corrected extension (CC-VSCF). The results of computations are compared with available experimental data. It is shown that the most accurate vibrational frequencies are obtained with the MP2 method, followed by the DFT/B3LYP method, while DFT/BLYP results are often unsatisfactory. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Molecular dynamics and metadynamics simulations of [2 + 2] photocycloaddition

Triplet state mechanism of [2 + 2] photocycloaddition forming a cyclobutane ring from two ethylenes is investigated in the context of photocatalysis. High‐level ab initio calculations are combined with ab initio adiabatic molecular dynamics and ab initio metadynamics for rare events modeling. In a photocatalytic scheme, a reactant reaches the triplet state either via intersystem crossing (ISC) or triplet sensitization. The model system adopts a biradical structure, which represents energy intersection with the ground state. The system either completes cyclization or undergoes fragmentation into two olefinic units. The potential and free energy surfaces of the cyclobutane/ethylenes system are mapped with multireference approaches describing possible reaction pathways. To obtain a full picture of a double bond photoreactivity, ab initio adiabatic dynamical calculations were used to estimate reaction yields and to model the effects of excess energy. The potential use of density functional theory based approaches for [2 + 2] photocycloaddition was investigated for future simulations and design of realistic photocatalytic systems. Dynamical aspects of [2 + 2] photocycloaddition via a triplet state manifold are investigated by combining ab initio multireference methods and ab initio molecular dynamics and metadynamics. The reaction pathways are studied for a model system of two ethylenes forming a cyclobutane ring to provide a basis for further studies on design of photocatalytic systems.     

SPOCK.CI: a multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.     

Potential energy surfaces for rearrangements of Berson trimethylenemethanes

In this research, thermal rearrangements of the Berson trimethylenemethanes (Berson-TMMs) have been investigated by employing density functional theory (DFT) and high-level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order M?ller-Plesset perturbation theory (MRMP2), multireference configuration interaction singles and doubles (MRCISD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The relevant portions of the lowest-energy, singlet-spin potential energy surface of the C(4)H(6) (parent TMM), C(6)H(8) (Berson-TMMa), and C(8)H(12) (Berson-TMMc) chemical systems have been explored in order to determine the reaction energies and activation parameters accurately, with the ultimate objective of providing a theoretical account of experiments by Berson on TMMc. The nature of the orthogonal and the planar structures of the parent TMM have been clarified in this study. We have concluded that the orthogonal TMM (1)B(1) minimum has a C(2v) symmetry structure, and there is no pyramidalization in the unique methylene group. It lies at 13.9 kcal mol(-1) above the triplet minimum (3)B(2) at MRCISD level. The closed-shell (1)A(1) state of the planar TMM is not a true minimum but a transition structure (TS) for 180° rotation of the unique methylene group in the orthogonal TMM minimum. It lies at 3.0 kcal mol(-1) above (1)B(1). The planar structures are also involved in the interchange of equivalent orthogonal TMMs (o(1), o(2), o(3)). Many features of the parent TMM are retained in TMMa and TMMc, despite the constraints imposed by the five-membered ring in the latter species. Thus, ring closure to the bicyclic molecules 3a (3c) and 5a (5c) takes place similarly to that in the parent TMM. Likewise, planar TMMa (TMMc) structures are TSs, while orthogonal ones are true minima. The adiabatic singlet-triplet gaps are also similar, being 14.7 (13.0) and 16.5 (16.2) kcal mol(-1) in the orthogonal (o(1)) and planar TMMa (TMMc), respectively. It has been shown here that the substantial reductions in the ring-opening barriers of MCP derivatives 3a (3c) and 5a (5c) can be largely attributed to ring strain in the former and π-bond strain in the latter species.     

Ab initio multireference configuration-interaction theoretical study on the low-lying spin states in binuclear transition-metal complex: magnetic exchange of [(NH3)5Cr(mu-OH)Cr(NH3)5]5+ and [Cl3FeOFeCl3]2-

The magnetic exchange interaction behavior and energy spectrum of low-lying spin states are investigated by using ab initio multireference configuration-interaction method for the representative binuclear transition-metal complexes [(NH(3))(5)Cr(mu-OH)Cr(NH(3))(5)](5+) and [Cl(3)FeOFeCl(3)](2-). Our calculations for the nonmodeling real title complexes found that under the appropriate basis sets and active space, ab initio method at multireference configuration-interaction level of theory is able to give accurate energy spectrum of low-lying spin states within reachable computation demand nowadays and the deviation of magnetic exchange interaction to Lande interval rule can be described by the biquadratic correction in terms of Heisenberg spin Hamiltonian. As a methodology comparison, density-functional theory combined with broken-symmetry approach provides an alternative yet efficient approach to produce accurate numerical results, but there are dependences on the particular chosen exchange-correlation functionals and system dependent. The spin population analyses at complete active space self-consistent-field level of the theory provide an instructively understanding and prediction for the magnetic interaction mechanism.     

Character of the electronic ground state and of charge-transfer excited states in ionic solids: An ab initio cluster model approach

The electronic structure of the ground electronic state and of some special charge-transfer excited states in ionic solids is examined from the ab initio cluster model approach. Different ab initio wave functions, including a frozen orbital approach, the Hartree–Fock self-consistent field, and multireference configuration interaction wave functions, are considered and analyzed using different theoretical techniques. We explicitly consider some alkaline–earth oxides such as CaO, a more difficult case such as A1₂O₃, a transition-metal oxide such as NiO, and a system with a more complicated structure such as KNiF₃. Analysis of ab initio wave functions in terms of valence bond components shows that all these compounds are largely ionic, thus supporting the simple picture arising from the ionic model. However, the nature of the excited states is more complex. Alkaline–earth oxides lowest excited states are essentially described as charge-transfer excitations dominated by a single resonant valence bond structure and the calculated energy difference is comparable to the experimental optical gap. In the case of A1₂O₃, the electronic spectra presents excitonic features and the local charge-transfer excitation excited states provide a reasonable representation of these phenomena. Finally, several different valence bond structures are present in the lowest electronic states of KNiF₃. © 1994 John Wiley & Sons, Inc.     

Thermal rearrangements of 1-ethynyl-2-methylcyclopropane: a computational study

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-ethynyl-2-methylcyclopropane is carried out employing density functional theory (DFT), with the B3LYP functional, and high-level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order M?ller-Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. In all computations Pople's polarized triple-ζ split valence basis set, 6-311G(d,p), is utilized. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of the experiments by Hopf, Ellis and Frey, Huntsman et al., and Berson. The computational results herein on the target system show that the thermal aromatization reaction does not proceed via conversion of 1,2,5-hexatriene (2) to 1,3,5-hexatriene (10a) as proposed by Hopf. Indeed, the reaction proceeds via conversion of 5 and 6 to bicyclo[3.1.0]hexene (9) as suggested by Huntsman et al.     

The fulvenediyls and related biradicals: Molecular and electronic structure

The structures, stabilities, and electronic properties of the nine fulvenediyls have been investigated and compared to the isomeric benzynes using density functional theory (DFT) and ab initio multireference configuration interaction methods (MRCI). Given the significant biradical character of several singlet fulvenediyls, the BLYP method reproduces the relative energies of these systems rather accurately. In contrast, some triplet states (3A'-12, 3A'-13, and 3B2-14) suffer from artifactual symmetry breaking towards a nonplanar geometry at the DFT level. The structures and properties of the title biradicals are readily rationalized within the framework of through-space and through-bond molecular orbital interactions. The degree of coupling between the formally unpaired electrons strongly depends on the number and arrangement of intervening sigma-bonds, and often parallels the trends observed for annellated arynes of similar topology. In some cases, novel structural patterns can be identified that are characteristic of five-membered-ring systems. These similarities and differences between five- and six-membered-ring arynes are discussed on the basis of molecular orbital arguments.     

Critical examination of the supermolecule density functional theory calculations of intermolecular interactions

The results of calculations employing twelve different combinations of exchange and correlation functionals are compared with results of ab initio calculations for two different configurations of the water dimer and three different configurations of the thymine-adenine complex. None of the density functional theory (DFT) treatments could properly reproduce the results of coupled-cluster calculations for all configurations examined. The DFT approaches perform well when the interaction energy is dominated by the electrostatic component and the dispersion energy is less important. Two mechanisms that compensate for the missing dispersion component were identified. The first one is the decrease of the magnitude of the intermolecular exchange-repulsion and the second one is the increase of the magnitude of the attractive deformation energy. For some functionals both effects are observed together, but for some other ones only the second effect occurs. The three correlation functionals that were examined were found to make only very small contributions to the deformation energy. The examination of angular and distance dependence of the interactions shows that the currently available DFT approaches are not suitable for developing intermolecular potential energy surfaces. They could however be used to find global minima on potential energy surfaces governed by intermolecular electrostatic interactions. Additional single point ab initio calculations are recommended as the means of validating optimized structures.