Complete Active Space Self-consistent Field Wave Function Research Articles

A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions.

In this work, we present a one-step second-order converger for state-specific (SS) and state-averaged (SA) complete active space self-consistent field (CASSCF) wave functions. Robust convergence is achieved through step restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid numerical instabilities, an exponential parameterization of variational configuration parameters is employed, which works with a nonredundant orthogonal complement basis. This is a common approach for SS-CASSCF and is extended to SA-CASSCF wave functions in this work. Our implementation is integral direct and based on intermediates that are formulated in either the sparse atomic-orbital or small active molecular-orbital basis. Thus, it benefits from a combination with efficient integral decomposition techniques, such as the resolution-of-the-identity or the chain-of-spheres for exchange approximations. This facilitates calculations on large molecules, such as a Ni(II) complex with 231 atoms and 5154 basis functions. The runtime performance of TRAH-CASSCF is competitive with the other state-of-the-art implementations of approximate and full second-order algorithms. In comparison with a sophisticated first-order converger, TRAH-CASSCF calculations usually take more iterations to reach convergence and, thus, have longer runtimes. However, TRAH-CASSCF calculations still converge reliably to a true minimum even if the first-order algorithm fails.

An algorithm to correct for the CASSCF active space in multiscale QM/MM calculations based on geometry ensembles

AbstractWhen the excitation energies of an ensemble of geometries, computed by the complete active space self‐consistent field (CASSCF) or other CAS‐based methods, are convoluted to obtain the absorption spectrum, it is advisable that all the considered geometries have the same molecular orbitals within the active space. In this work, we present an algorithm that evaluates the molecular orbital overlap matrix between a previously selected reference geometry, with the desired active space, and each of the sampled geometries. Based on the value of the overlap matrix elements, the algorithm determines whether one or more pairs of molecular orbitals of the sampled geometry have to be swapped for a subsequent CASSCF calculation. We have applied the developed algorithm to CASSCF and CASPT2 calculations for sets of geometries of the five canonical nucleobases in vacuum and in aqueous solvent. The algorithm shows a very good efficacy since it recovered the correct active space for 90% of the geometries which presented undesired molecular orbitals in the active space after the first CASSCF wavefunction optimization. In addition, the importance of having the same orbitals within the active space for all the geometries is discussed based on the corrected and uncorrected density of states for the nucleobases.

Are Multicentre Bond Indices and Related Quantities Reliable Predictors of Excited-State Aromaticity?

Systematic scrutiny is carried out of the ability of multicentre bond indices and the NOEL-based similarity index dAB to serve as excited-state aromaticity criteria. These indices were calculated using state-optimized complete active-space self-consistent field wavefunctions for several low-lying singlet and triplet states of the paradigmatic molecules of benzene and square cyclobutadiene and the inorganic ring S2N2. The comparison of the excited-state indices with aromaticity trends for individual excited states suggested by the values of magnetic aromaticity criteria show that whereas the indices work well for aromaticity reversals between the ground singlet and first triplet electronic states, addressed by Baird’s rule, there are no straightforward parallels between the two sets of data for singlet excited states. The problems experienced while applying multicentre bond indices and dAB to singlet excited states are explained by the loss of the information inherently present in wavefunctions and/or pair densities when calculating the first-order density matrix.

Low-lying electronic terms of diatomic molecules AB (A = Sc–Ni, B = Cu/Ag/Au)

Low-lying electronic terms of 24 heteronuclear diatomic molecules AB (A = Sc–Ni, B = Cu/Ag/Au) have been systematically studied. Scalar relativistic effects were included by use of the spin-free Douglas–Kroll–Hess (DKH) Hamiltonian. The complete active space self-consistent field (CASSCF) method, followed by multi-reference configuration interaction (MRCI), was used to construct full potential energy curves (PECs). Spectroscopic constants as well as dipole moments are also reported. Spin-orbit coupling was subsequently calculated perturbatively via the spin-orbit terms of the Breit–Pauli Hamiltonian based on the CASSCF wavefunctions. Full spin-orbit coupled PECs were thus constructed for the low-lying terms of NiCu and NiAg. In addition, Kramers-restricted configuration interaction (KRCI) with the exact 2-component (X2C) Hamiltonian was utilised for the atoms and for the Cu-containing diatomic molecules. The influence of relativistic effects, spin-orbit coupling, core correlation effects and basis set incompleteness was probed for some selected cases. It is shown that for 23 out of the 24 diatomic molecules considered here a direct correspondence exists between the ground state terms (GSTs) of the monocations and those of the diatomic molecules with and .

Automatic Active Space Selection for Calculating Electronic Excitation Energies Based on High-Spin Unrestricted Hartree–Fock Orbitals

Multireference perturbation theory (MR-PT2, e.g., MS-CASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) use a multiconfigurational wave function as the reference wave function, and this can be generated, for example, by the complete active space self-consistent field (CASSCF) method or restricted active space self-consistent field (RASSCF) method. The MR-PT2 and MC-PDFT methods have proved successful in many previous studies, but their performance depends on the quality of the reference wave function, and the quality of a CASSCF or RASSCF wave function depends on the active space. Even for a given number of active electrons and active orbitals, the orbitals obtained at the end of the self-consistent field iterations of the CASSCF calculation may be different for different sets of initial guess orbitals. Consequently, it is a worthwhile goal to automate active space selection, including the choice of orbitals to start the iterations, and here we examine the question of whether we can devise a broadly applicable automatic scheme for producing guess orbitals that lead to an active space that gives accurate excitation energies. Such a scheme depends on the target number of excitation energies that one is trying to calculate, and here our target is the first two spin-conserving excited electronic states of a closed-shell molecule or a doublet radical. For this target, we propose a scheme called ABC2 to automatically select an active space for MC-PDFT calculations and MS-CASPT2 calculations; the scheme uses high-spin-state unrestricted Hartree-Fock (UHF) natural orbitals as guess orbitals. A novel feature of the ABC2 scheme is that it contains a reliability test that should be passed for the results to be considered reliable. This test requires that the MC-PDFT or CASPT2 excitation energy be within 1.1 eV of the CASSCF excitation energy for the result to be considered reliable. We evaluated the performance of ABC2 for the two lowest excitation energies (or only the lowest when an accurate value of the second lowest state is not available) of 16 singlet systems and 10 doublet systems. We compared the performance of ABC2 to that of our previous ABC scheme, which finds active orbitals through a more expensive (multiconfigurational) excited-state calculation, to the use of ground-state UHF natural orbitals, and to the default scheme in OpenMolcas. We found that the new scheme is more robust than previous methods for a variety of systems.

A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function.

A perturbation theory-based algorithm for the iterative orbital update in complete active space self-consistent-field (CASSCF) calculations is presented. Following Angeli et al. (J. Chem. Phys. 2002, 117, 10525), the first-order contribution of singly excited configurations to the CASSCF wave function is evaluated using the Dyall Hamiltonian for the determination of a zeroth-order Hamiltonian. These authors employ an iterative diagonalization of the first-order density matrix including the first-order correction arising from single excitations, whereas the present approach uses the single-excitation amplitudes directly for the construction of the exponential of an anti-Hermitian matrix resulting in a unitary matrix which can be used for the orbital update. At convergence, the single-excitation amplitudes vanish as a consequence of the generalized Brillouin's theorem. It is shown that this approach in combination with direct inversion of the iterative subspace (DIIS) leads to very rapid convergence of the CASSCF iteration procedure. © 2019 Wiley Periodicals, Inc.

Crystal Field Splittings in Lanthanide Complexes: Inclusion of Correlation Effects beyond Second Order Perturbation Theory.

State-averaged complete active space self-consistent field (CASSCF) calculations and a subsequent spin-orbit calculation mixing the CASSCF wave functions (CASSCF/state-interaction with spin-orbit coupling) is the conventional approach used for ab initio calculations of crystal-field splittings and magnetic properties of lanthanide complexes. However, this approach neglects dynamical correlation. Complete active space second-order perturbation theory (CASPT2) can be used to account for dynamical correlation but suffers from the well-known problems of multireference perturbation theory, e.g., intruder state problems. Variational multireference configuration interaction (MRCI) calculations do not show these problems but are usually not feasible due to the large size of real lanthanide complexes. Here, we present a quasi-local projected internally contracted MRCI approach which makes MRCI calculations of lanthanide complexes feasible and allows assessing the influence of dynamical correlation beyond second-order perturbation theory. We apply the method to two well-studied molecules, namely, [Er{N(SiMe3)2}3] and {C(NH2)3}5[Er(CO3)4]·11H2O.

Fast and reliable ab initio calculation of crystal field splittings in lanthanide complexes.

Ab initio calculations of crystal field splittings and magnetic properties of lanthanide complexes are usually performed using state-averaged complete active space self-consistent field (CASSCF) calculations and a subsequent spin-orbit calculation mixing the CASSCF wave functions (CASSCF/state interaction with spin-orbit coupling). Because this approach becomes very time-consuming for large molecules, simplifications have been proposed in the literature to determine the state-averaged orbitals by configuration-averaged Hartree-Fock (CAHF) instead of CASSCF. We present an approach which is an extension of the CAHF method. We combine the techniques of local density fitting with CAHF and achieve a significant speedup compared to CASSCF without loss in accuracy. To assess the performance of our method, we apply it to three well-known molecules, namely, Er[N(SiMe3)2]3, Er(trensal), and the double-decker (NBu4)+ [Er(Pc)2]-.

The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function.

An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.

Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO π bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

Localization of molecular orbitals on fragments

A non-iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single-determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments-in-molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree-Fock or Kohn-Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals.

Photoelectron Spectroscopic Study of the Oxyallyl Diradical

The photoelectron spectrum of the oxyallyl (OXA) radical anion has been measured. The radical anion has been generated in the reaction of the atomic oxygen radical anion (O(•-)) with acetone. Three low-lying electronic states of OXA have been observed in the spectrum. Electronic structure calculations have been performed for the triplet states ((3)B(2) and (3)B(1)) of OXA and the ground doublet state ((2)A(2)) of the radical anion using density functional theory (DFT). Spectral simulations have been carried out for the triplet states based on the results of the DFT calculations. The simulation identifies a vibrational progression of the CCC bending mode of the (3)B(2) state of OXA in the lower electron binding energy (eBE) portion of the spectrum. On top of the (3)B(2) feature, however, the experimental spectrum exhibits additional photoelectron peaks whose angular distribution is distinct from that for the vibronic peaks of the (3)B(2) state. Complete active space self-consistent field (CASSCF) method and second-order perturbation theory based on the CASSCF wave function (CASPT2) have been employed to study the lowest singlet state ((1)A(1)) of OXA. The simulation based on the results of these electronic structure calculations establishes that the overlapping peaks represent the vibrational ground level of the (1)A(1) state and its vibrational progression of the CO stretching mode. The (1)A(1) state is the lowest electronic state of OXA, and the electron affinity (EA) of OXA is 1.940 ± 0.010 eV. The (3)B(2) state is the first excited state with an electronic term energy of 55 ± 2 meV. The widths of the vibronic peaks of the X̃ (1)A(1) state are much broader than those of the ã (3)B(2) state, implying that the (1)A(1) state is indeed a transition state. The CASSCF and CASPT2 calculations suggest that the (1)A(1) state is at a potential maximum along the nuclear coordinate representing disrotatory motion of the two methylene groups, which leads to three-membered-ring formation, i.e., cyclopropanone. The simulation of b̃ (3)B(1) OXA reproduces the higher eBE portion of the spectrum very well. The term energy of the (3)B(1) state is 0.883 ± 0.012 eV. Photoelectron spectroscopic measurements have also been conducted for the other ion products of the O(•-) reaction with acetone. The photoelectron imaging spectrum of the acetylcarbene (AC) radical anion exhibits a broad, structureless feature, which is assigned to the X̃ (3)A'' state of AC. The ground ((2)A'') and first excited ((2)A') states of the 1-methylvinoxy (1-MVO) radical have been observed in the photoelectron spectrum of the 1-MVO ion, and their vibronic structure has been analyzed.

Theoretical investigations for electronic structures and photodissociation of bromine molecule

We have theoretically studied the nonadiabatic transitions among the lower states with W = 1u symmetry {1u (Lindeman and Wiesenfeld, 1979) to 1u (Alexander et al., 2000)} in the photodissociation of Br2 using the complete active space self-consistent field (CASSCF) computations and the time-independent Schrodinger equations. The CASSCF wave function is formed from a complete distribution of a number of active electrons in a set of active orbitals, which in general constitute a subset of the total occupied space. From the configuration analysis of the CASSCF wave functions, we found that the nonadiabatic transition between 1u(Bracker et al., 1999) and 1u (Lindeman and Wiesenfeld, 1979) is a noncrossing type, while that between 1u (Bracker et al., 1999) and B3P0+u is a crossing type. The spectroscopic constants for the X1Sg+, A3P1u and B3P0+u states of Br2 have been calculated. The absorption cross-section for the ground and the lower excited states in the photodissociation of Br2 molecule has been presented as well as the numerical estimates of nonadiabatic transition probabilities. Also, the five highest occupied and the five lowest unoccupied orbitals of Br2 have been calculated. Key words: Nonadiabatic transitions, broimine molecule, photodissociation.

Ab initio investigation of the ground X2A′ [ X2A1] and low-lying excited electronic states of C 2B

Ab initio single- and multi-reference approaches, i.e. restricted open-shell Hartree–Fock (ROHF), coupled-cluster singles-and-doubles with approximate triples correction [CCSD(T)], complete active space self-consistent field (CASSCF), 2nd-order CAS perturbation theory (CASPT2), multi-reference singles-and-doubles configuration-interaction (MRSDCI), and density-functional B3LYP – in the cc-pVQZ basis set – have been employed to investigate the structure of the ground X 2 A′ [ X 2 A 1] state of the triatomic C 2B. We found that the ground state of the cyclic C 2B is prone to symmetry breaking along the asymmetric stretching coordinate. Single-reference highly correlated CCSD(T)/aug-cc-pVQZ method (as well as ‘static’-correlated CASSCF, and B3LYP) predicts two equivalent global minima of the adiabatic potential energy function, with the barrier between the minima of about 20 cm −1 at C 2v geometry. Wavefunctions almost free from SB are obtained using the MRSDCI approach based on the CASSCF and state-averaged (SA) CASSCF wavefunctions. Highly correlated multi-reference full-valence (FV) CASPT2 model exactly predicts a C 2v equilibrium geometry; however, the highest level FV-CAS-MRSDCI/aug-cc-pVQZ method predicts lower-symmetry structure. We found that this effect is not artifactual as stated in Leonard et al. (2000) [5]. SB arises from a pseudo-Jahn–Teller effect (PJTE), the non-adiabatic interaction with the first excited 1 2 B 2 state, which has the same symmetry as the asymmetric stretching coordinate in the ground state. Several low-lying excited electronic states have been optimized using SA-CAS-MRSDCI/aug-cc-pVTZ procedure. The first excited doublet is 1 2 B 2 (0.95 eV), and the lowest-lying quartet state 1 4 B 2 (1.74 eV). The vertical excitation spectra and transition matrix elements for six low-lying doublet and four quartet states were calculated using full valence SA-CAS-MRSDCI/aug-cc-pVTZ procedure.

Theoretical Description of the Structure and Magnetic Properties of Nitroxide−Cu(II)−Nitroxide Spin Triads by Means of Multiconfigurational Ab Initio Calculations

The structural, electronic and magnetic properties of two different models of the heterospin polymer chain complexes of Cu2+ hexafluoroacetylacetonate with two pyrazole-substituted nitronyl nitroxides Cu(hfac)2L(R) have been studied by means of multiconfigurational perturbation theory based on a CASSCF (complete active space self-consistent field) wave function, i.e. the CASPT2 method. Our calculations reveal the presence of two minima in the electronic energy curve along the Cu-O(L) bond, separated by only 6 kcal/mol, and corresponding to the X-ray structures of the CuO6 centers in Cu(hfac)2L(Pr) at 115 and 293 K, respectively. The two energetic minima are characterized by a different electronic structure, thus giving rise to a different three-spin exchange coupling and explaining the thermally induced spin transitions in this family of compounds. The concomitant variations in the magnetic properties, i.e. g factors and magnetic moments mu(eff)(T) were calculated and compared with the experimental data of Cu(hfac)2L(Pr). Even if the correspondence is only qualitative, our calculations provide a convincing explanation of the observed magnetic peculiarities. In particular, at low temperatures, the predicted ground-state is 2A(u), well separated from the 2A(g), 4A(u) states and therefore exclusively populated. Its calculated g factors, g(parallel) = 1.848, g(perpendicular) = 1.965, 1.974, qualitatively correspond to the observed g < 2 signals in the low-temperature EPR spectra. The previously assumed formal spin assignment >N-O*-Cu-*O-N < for these linear spin triads is challenged by our calculations, pointing instead to a more important role of the end-standing NO in the exchange interactions with Cu(II).

A study of the fixed-node error in quantum Monte Carlo calculations of electronic transitions: The case of the singlet n→π∗ (CO) transition of the acrolein

We report fixed-node diffusion Monte Carlo (FN-DMC) calculations of the singlet n-->pi( *) (CO) vertical transition of acrolein. The impact of the fixed-node approximation on the excitation energy is investigated. To do that, trial wave functions corresponding to various nodal patterns are used. They are constructed by using either a minimal complete-active-space self-consistent field (CASSCF) calculation involving an oxygen lone pair n and the pi( *) (CO) molecular orbitals or a more complete set involving all the molecular orbitals expected to play a significant role in the excitation process. Calculations of both states have been performed with molecular orbitals optimized separately for each state via standard "state specific" CASSCF calculations or by using a common set of optimized orbitals ["state averaged" CASSCF calculations] whose effect is to introduce some important correlation between the nodal patterns of the two electronic states. To investigate the role of the basis set three different basis of increasing size have been employed. The comparative study based on the use of all possible combinations of basis sets, active spaces, and type of optimized molecular orbitals shows that the nodal error on the difference of energies is small when chemically relevant active space and state-averaged-type CASSCF wave functions are used, although the fixed-node error on the individual total energies involved can vary substantially. This remarkable result obtained for the acrolein suggests that FN-DMC calculations based on a simple strategy (use of standard ab initio wave functions and no Monte Carlo optimization of molecular orbital parameters) could be a working computational tool for computing electronic transition energies for more general systems.

Reexamination of the Lyman-Birge-Hopfield transition ofN2: Configuration-interaction generalized oscillator strengths

Generalized oscillator strengths (GOS) for the dipole forbidden quadrupole allowed Lyman-Birge-Hopfield (LBH) valence transition of ${\mathrm{N}}_{2}$ have been calculated. Complete active space self-consistent-field (CAS) and multireference configuration interaction (MRCI) wave functions of several types have been used and their effects on the computed GOS profiles discussed. Orthogonal and nonorthogonal molecular orbitals have been employed. The latter allows the explicit inclusion of relaxation effects in the excited state leading to a clear spectra interpretation. Hartree-Fock (HF) and CAS wave functions have been compared as a previous step before the MRCI calculations. Differences between the respective GOS profiles were found, with the CAS MRCI GOS curve being slightly closer to experiment than the HF MRCI one. Agreement between the present theoretical CAS MRCI GOS profile employing nonorthogonal orbitals and recent experimental results are very favorable, being the best one among available theoretical calculations in the literature.

CASPT2 study on electronic states of the dichlorodifluoromethane cation

We studied the eight lowest-lying states of the CF 2 Cl 2 + ion, which were observed in the PE spectra by Pradeep and Shirley, using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods. The CASPT2 calculations predict the equilibrium geometries, adiabatic ( T 0) and vertical ( T v) excitation energies, relative energies ( T v ′ ) at the geometry of the molecule, and the CASSCF calculations predict vibrational frequencies. On the basis of the CASPT2 T 0 calculations, we assign the X, A, B, C, D, E, F, and G states of the CF 2 Cl 2 + ion to 1 2B 2, 1 2A 2, 1 2B 1, 1 2A 1, 2 2B 2, 2 2B 1, 2 2A 1, and 2 2A 2, respectively. Our A 2A 2 and B 2B 1 assignments are in line with the assignments of Pradeep and Shirley, but our F(2) 2A 1 and G(2) 2A 2 assignments are different from the F(2) 2A 2 and G(2) 2A 1 assignments presented in the experimental papers. The CASPT2 T 0 values for 1 2B 1 and 2 2B 2 are in good agreement with the available experimental values, and the CASPT2 T v ′ values are in very good (for 1 2B 2, 1 2A 2, 1 2B 1, 1 2A 1, and 2 2B 2) or reasonable (for 2 2B 1, 2 2A 1, and 2 2A 2) agreement with the experimental values. The CASSCF wavefunction of the 2 2A 1 state at the geometry of the molecule and the CASSCF wavefunctions of the 2 2B 2, 2 2B 1, and 2 2A 2 states at the CASPT2 geometries are found to have multi-configurational character. The CASSCF frequency values of the total symmetric modes in the 1 2B 2, 1 2A 2, 1 2B 1, and 2 2B 2 states are comparable with available experimental data.

Spin−Spin Contributions to the Zero-Field Splitting Tensor in Organic Triplets, Carbenes and BiradicalsA Density Functional and Ab Initio Study

An evaluation study for the direct dipolar electron spin-spin (SS) contribution to the zero-field splitting (ZFS) tensor in electron paramagnetic resonance (EPR) spectroscopy is presented. Calculations were performed on a wide variety of organic systems where the SS contribution to the ZFS dominates over the second-order spin-orbit coupling (SOC) contribution. Calculations were performed using (hybrid) density functional theory (DFT), as well as complete active space self-consistent field (CASSCF) wave functions. In the former case, our implementation is an approximation, because we use the two-particle reduced spin-density matrix of the noninteracting reference system. In the latter case, the SS contribution is approximated by a mean-field method which, nevertheless, gives accurate results, compared to the approximation free computation of the SS part in a CASSCF framework. For the case of the triplet dioxygen molecule, it was shown that restricted open-shell density functional theory (RODFT), as well as CASSCF, can provide accurate spin-spin couplings while spin-unrestricted DFT leads to much larger errors. Furthermore, 15 organic radicals, including several 1,3 and 1,5 diradicals, dinitroxide biradicals, and even a chlorophyll a model system, were examined as test cases to demonstrate the accuracy and efficiency of our approach within a DFT framework. Accurate D values with root-mean-square deviations of 0.0035 cm(-1) were obtained. Furthermore, all trends, including those due to substituent effects, were correctly reproduced. In a different set of calculations, the polyacenes benzene, naphthalene, anthracene, and tetracene were studied. Applying DFT, the absolute D values were noticeably underestimated, but it was possible to correctly reproduce the trend to smaller D values with larger size of the systems. Finally, it was demonstrated that our approach is also well-suited for the study of carbenes. The smaller organic radicals of this work were also studied, through the use of CASSCF wave functions. This was a special advantage in the case of the triplet polyacenes, where the CASSCF approach gave better results than the DFT method. In comparing spin-restricted and spin-unrestricted results, it was shown through a natural orbital analysis and comparison to high-level ab initio calculations that even small amounts of spin polarization introduced by the unrestricted calculations lead to large deviations between the unrestricted Kohn-Sham (UKS) and restricted open-shell Kohn-Sham (ROKS) approaches. It is challenging to understand why the ROKS results show much better correlation with the experimental data.

Scalable correlated electronic structure theory

The approach taken in Ames to advance high-level electronic structure theory has been a combination of the development and implementation of new and novel methods with the continuing development of strategies to optimize scalable computing. This work summarizes advances on both fronts. Several new methods have been implemented under the Distributed Data Interface (DDI), most recently including analytic Hessians for both Hatree- Fock and CASSCF (complete active space self-consistent field) wavefunctions, gradients for restricted open shell second order perturbation theory, and the fragment molecular orbital method (FMO). Exciting new method developments include the FMO method and the CEEIS (Correlation Energy Extrapolation by Intrinsic Scaling) method for efficiently approaching the exact energy for atomic and molecular systems.