Active Space Self-consistent Field Method Research Articles

Electronic structure and optical spectral analysis of the MnO42- anion with consideration of site and Jahn-Teller distortion.

The ground state of 3d1 MnO42- was studied by density functional theory (DFT) and complete active space self-consistent field (CASSCF) methods in terms of a variety of molecular point group structures to ascertain the site and Jahn-Teller (JT) distortion effect. Modeling results from UB3LYP/6-31+G(d) calculations with natural bond orbital analysis show the four Mn-O bonds are coordinate covalent. The one-electron matrix elements from CASSCF(AILFT) (abinitio ligand field theory) with a second order perturbation treatment were used to calculate the parameters of the angular overlap model. These allowed the calculation of JT stabilization energies and first and second order JT coupling constants for MnO42- with C2v and D2d symmetry. Absorption spectra and excited state transition energies were calculated assuming the lattice distorted geometry was C2v with time-dependent DFT (TDDFT) using the unrestricted coulomb-attenuating UCAM-B3LYP density functional and with the spin-adapted spin-flip DFT using the UBH&HLYP density functional, both with the AUG-CC-PVTZ basis set. The mean absolute deviation of the calculations from experimental excited states for the ligand field and ligand-to-metal charge transfer (LMCT) bands was better than 0.1eV. Several new assignments for LMCT excited states were made on the basis of the TDDFT excitation results.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Can Iron-Porphyrins Behave as Single-Molecule Magnets?

The study of magnetic properties, especially the magnetic anisotropy of iron-porphyrin complexes employing multiconfigurational methods, is quite challenging due to many strongly correlated electrons in nearly degenerate orbitals. However, a prerequisite for observing the magnetic anisotropy and slow magnetization relaxation, the zero-field splitting parameter, D, was experimentally observed decades ago for halide-based axially ligated penta-coordinate Fe(III)-porphyrins. In these complexes, the signs of D were reported mostly as positive; in a few cases, inconclusive signs of the D parameter were also mentioned. However, no ab initio calculations have been reported to shed light on this. Deciphering the electronic structure of these penta-coordinated complexes employing the complete active space self-consistent field method and N-electron valence second-order perturbation theory, we confirm the positive D values. However, a negative D value is highly desired to observe the single-molecule magnet properties without an external magnetic field, which we observed in the Fe(II)-porphyrin complexes with axial imidazole ligands instead of halide ligands. The detailed analysis of the multireference wave functions unravels the role of axial ligands in determining the sign and magnitude of the D parameters.

Comparative Study of Uracil Excited-State Photophysics in Water and Acetonitrile via RMS-CASPT2-Driven Quantum-Classical Trajectories.

We present a nonadiabatic molecular dynamics study of the ultrafast processes occurring in uracil upon UV light absorption, leading to electronic excitation and subsequent nonradiative decay. Previous studies have indicated that the mechanistic details of this process are drastically different depending on whether the process takes place in the gas phase, acetonitrile, or water. However, such results have been produced using quantum chemical methods that did not incorporate both static and dynamic electron correlation. In order to assess the previously proposed mechanisms, we simulate the photodynamics of uracil in the three environments mentioned above using quantum-classical trajectories and, for solvated uracil, hybrid quantum mechanics/molecular mechanics (QM/MM) models driven by the rotated multistate complete active space second-order perturbation (RMS-CASPT2) method. To do so, we exploit the gradient recently made available in OpenMolcas and compare the results to those obtained using the complete active space self-consistent field (CASSCF) method only accounting for static electron correlation. We show that RMS-CASPT2 produces, in general, a mechanistic picture different from the one obtained at the CASSCF level but confirms the hypothesis advanced on the basis of previous ROKS and TDDFT studies thus highlighting the importance of incorporating dynamic electron correlation in the investigation of ultrafast electronic deactivation processes.

Pathways of two-body dissociation of BrCNq+ (q = 2, 3) induced by electron collision.

Pathways of two-body fragmentation of BrCNq+ (q = 2, 3) have been explored by combined experimental and theoretical studies. In the experiment, the BrCN molecule is ionized by 1keV electron impact and the created fragment ions are detected using an ion momentum imaging spectrometer. Six two-body fragmentation channels are identified. By measuring the momentum vectors of the fragment ions, the kinetic energy release (KER) distributions for these channels have been determined. Theoretically, the potential energy curves of BrCNq+ (q = 2, 3) as a function of Br-C and C-N internuclear distances are calculated by the complete active space self-consistent field method. By comparing the measured KER and theoretical predictions, pathways for the fragmentation channels are assigned. The relative branching ratios of the channels are also determined.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic.

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues.

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

Approximate Excited-State Geometry Optimization with the State-Averaged Adaptive Sampling Configuration Interaction Algorithm with Large Active Spaces.

The selected configuration interaction (SCI) wave function is a useful approximation to the full configuration interaction (FCI) one. The adaptive sampling CI (ASCI) method is a deterministic SCI method. By combining ASCI and orbital optimization, the ASCI self-consistent field (ASCI-SCF) method, which is an approximation of the complete active space self-consistent field (CASSCF) method, can be formulated as well. However, their applicability has been tested mainly on the systems in their electronically ground states. In this work, we implement the state-average (SA) ansatz in ASCI-SCF calculations to calculate excited states. We also derive expressions for the approximate analytical gradient and implement them as a computer program. We demonstrate the applicability of the current method for calculating vertical and adiabatic excitation energies and optimizing the molecular geometries of thermally activated delayed fluorescence (TADF) molecules.

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding.

The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

Understanding the Excited-State Relaxation Mechanisms of Xanthophyll Lutein by Multi-configurational Electronic Structure Calculations.

The contradictory behaviors in light harvesting and non-photochemical quenching make xanthophyll lutein the most attractive functional molecule in photosynthesis. Despite several theoretical simulations on the spectral properties and excited-state dynamics, the atomic-level photophysical mechanisms need to be further studied and established, especially for an accurate description of geometric and electronic structures of conical intersections for the lowest several electronic states of lutein. In the present work, semiempirical OM2/MRCI and multi-configurational restricted active space self-consistent field methods were performed to optimize the minima and conical intersections in and between the 1Ag-, 2Ag-, 1Bu+, and 1Bu- states. Meanwhile, the relative energies were refined by MS-CASPT2(10,8)/6-31G*, which can reproduce correct electronic state properties as those in the spectroscopic experiments. Based on the above calculation results, we proposed a possible excited-state relaxation mechanism for lutein from its initially populated 1Bu+ state. Once excited to the optically bright 1Bu+ state, the system will propagate along the key reaction coordinate, i.e., the stretching vibration of the conjugated carbon chain. During this period of time, the 1Bu- state will participate in and forms a resonance state between the 1Bu- and 1Bu+ states. Later, the system will rapidly hop to the 2Ag- state via the 1Bu+/2Ag- conical intersection. Finally, the lutein molecule will survive in the 2Ag- state for a relatively long time before it internally converts to the ground state directly or via a twisted S1/S0 conical intersection. Notably, though the photophysical picture may be very different in solvents and proteins, the current theoretical study proposed a promising calculation protocol and also provided many valuable mechanistic insights for lutein and similar carotenoids.

Molecular properties of TCNQ and anions

The purpose of the work is to calculate accurate values of molecular properties of tetracyanoquinodimethane (TCNQ) and anions using the complete active space self-consistent field and complete active space second-order perturbation theory methods. The accuracy has been evaluated using several basis sets and active spaces. The calculated properties have, in many cases, been confirmed by experimental data (within parentheses), e.g., 9.54 eV (9.61 eV) and 3.36 eV (3.38 eV) for the ionization potential and electron affinity, respectively, of TCNQ; 3.12 eV (3.01 eV) and 3.54 eV (3.42 or 3.60 eV) for transition energies to the two lowest-lying excited singlet states of TCNQ; − 0.03, 0.46 and 1.44 eV (0, 0.5 and 1.4 eV) for electronic energies in electron attachment of TCNQ forming hbox {TCNQ}^-; and 3.88 eV (3.71 eV) for the transition energy to the second lowest-lying excited singlet state of hbox {TCNQ}^{2-}. Further, the calculations have brought insight into some experimental observations, e.g., the shape of the fluorescence spectrum of TCNQ at 3–4 eV.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues.

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔEspin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both ΔEspin (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

Iron(II) Complexes with Porphyrin and Tetrabenzoporphyrin: CASSCF/MCQDPT2 Study of the Electronic Structures and UV-Vis Spectra by sTD-DFT.

The geometry and electronic structures of iron(II) complexes with porphyrin (FeP) and tetrabenzoporphyrin (FeTBP) in ground and low-lying excited electronic states are determined by DFT (PBE0/def2-TZVP) calculations and the complete active space self-consistent field (CASSCF) method, followed by the multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2) approach to determine the dynamic electron correlation. The minima on the potential energy surfaces (PESs) of the ground (3A2g) and low-lying, high-spin (5A1g) electronic states correspond to the planar structures of FeP and FeTBP with D4h symmetry. According to the results of the MCQDPT2 calculations, the wave functions of the 3A2g and 5A1g electronic states are single determinant. The electronic absorption (UV-Vis) spectra of FeP and FeTBP are simulated within the framework of the simplified time-dependent density functional theory (sTDDFT) approach with the use of the long-range corrected CAM-B3LYP function. The most intensive bands of the UV-Vis spectra of FeP and FeTBP occur in the Soret near-UV region of 370-390 nm.

Proton Reaction Path in Base Pairs of DNA Molecule According to the Complete Active Space Self-Consistent Field Method

The double proton transfer reaction paths in AT and CG base pairs of DNA molecule are calculated in the Complete Active Space Self-Consistent Field method and compared with the same paths in Density Functional Theory with B3LYP approximation approach. We found that an essential increase of an activation energy, which significantly reduces the probability of spontaneous mutations in DNA via double proton transfer. There exist two transition points on the singlet potential energy surface divided by a flat region for GC base pair. The applicability of various quantum-chemical methods for description of double proton transfer reactions was discussed.

Electron and ion spectroscopy of azobenzene in the valence and core shells.

Azobenzene is a prototype and a building block of a class of molecules of extreme technological interest as molecular photo-switches. We present a joint experimental and theoretical study of its response to irradiation with light across the UV to x-ray spectrum. The study of valence and inner shell photo-ionization and excitation processes combined with measurement of valence photoelectron-photoion coincidence and mass spectra across the core thresholds provides a detailed insight into the site- and state-selected photo-induced processes. Photo-ionization and excitation measurements are interpreted via the multi-configurational restricted active space self-consistent field method corrected by second order perturbation theory. Using static modeling, we demonstrate that the carbon and nitrogen K edges of azobenzene are suitable candidates for exploring its photoinduced dynamics thanks to the transient signals appearing in background-free regions of the NEXAFS and XPS.

Intermolecular-Type Conical Intersections in Benzene Dimer.

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

A Theoretical Account of the Coupling between Metal- and Ligand-centred Spins.

This study addresses the magnetic interaction between paramagnetic metal ions and the radical ligands taking the [CuII (hfac)2 (imVDZ)] and [MII (hfac)2 (pyDTDA)] (imVDZ=1,5-dimethyl-3-(1-methyl-2-imidazolyl)-6-oxoverdazyl; hfac=(1,1,1,5,5,5)hexafluroacetylacetonate; pyDTDA=4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl), (M=Cu, Ni, Co, Fe, Mn) compounds as reference systems. The coupling between the metal and ligand spins is quantified in terms of the exchange coupling constant (J) in the platform of density functional theory (DFT) and the wave function-based complete active space self-consistent field (CASSCF) method. Application of DFT and broken symmetry (BS) formalism results ferromagnetic coupling for all the transition metal complexes except the Mn(II) complex. This DFT-BS prediction of magnetic nature matches with the experimental finding for all the complexes other than the Fe(II)-pyDTDA complex, for which an antiferromagnetic coupling between high spin iron and the thiazyl ligand has been reported. However, evaluation of spin state energetics through the multiconfigurational wave function-based method produces the S=3/2 ground spin state for the iron-thiazyl in parity with experiment. Electronic structure analyses find the overlap between the metal- and ligand-based singly occupied molecular orbitals (SOMOs) to be one of the major reasons attributing to different extent of exchange coupling in the systems under investigation.

The ionic and ground states of gamma-pyrone. The photoionization spectrum studied by synchrotron radiation and interpreted by configuration interaction and density functional calculations.

A synchrotron-based photoionization spectrum up to 27eV represents a considerable improvement in resolution over early He(I) and He(II) spectra. Symmetry-adapted coupled cluster calculations of the ionic state sequence give the sequence of state vertical ionization energies (VIE) as 12B2 < 12B1 < 12A2 < 22B1 < 12A1. Generally, these symmetry-adapted cluster configuration interactions VIE match reasonably well with the experimental spectrum over this wide energy range. Density functional calculations of the corresponding adiabatic terms (AIE) were also performed. Higher energy ionic states were determined by complete active space self-consistent field methods; these include all π-ionizations and some σ-ionic states. These were analyzed by Franck-Condon (FC) procedures and compared with an experiment. The spectral onset is complex, where two states, later shown to be the 12B2 and 12B1 states, are strongly overlapping. The superposition of the FC vibrational structure in the 12B2 and 12B1 states accounts for most of the peaks arising at the onset of the photoelectron spectra. However, the small separation between these two ionic states makes vibronic interaction fairly inevitable. In the absence of Herzberg-Teller analyses for ionic states, we have sought and determined a transition state between the 12B2 and 12B1 states, showing that vibronic coupling does occur. The lack of degradation in the vibrational envelope of the higher of the two states contrasts with our previous work on the halogenobenzenes, where overlapping state envelopes led to considerable widening of the line width at half-height of the higher energy states.

How does multi-reference computation change the catalysis chemistry? DFT and CASPT2 studies of the Cu-catalysed coupling reactions between aryl iodides and β-diketones.

The molecular mechanism of a Cu-catalysed coupling reaction was theoretically studied using density functional theory (DFT) and the complete active space self-consistent field method followed by the second-order perturbation theory (CASSCF/CASPT2) to investigate the effects of the strong electron correlation of the Cu centre on the reaction profile. Both DFT and CASSCF/CASPT2 calculations showed that the catalytic cycle proceeds via an oxidative addition (OA) reaction, followed by a reductive elimination (RE) reaction, where OA is the rate-determining step. Although the DFT-calculated activation energies of the OA and RE steps are highly dependent on the choice of functionals, the CASSCF/CASPT2 results are less affected by the choice of DFT-optimised geometries. Therefore, with a careful assessment based on the CASSCF/CASPT2 single-point energy evaluation, an optimal choice of the DFT geometry is of good qualitative use for energetics at the CASPT2 level of theory. Based on the changes in the electron populations of the 3d orbitals during the OA and RE steps, the characteristic features of the DFT-calculated electronic structure were qualitatively consistent with those calculated using the CASSCF method. Further electronic structure analysis by the natural orbital occupancy of the CASSCF wavefunction showed that the ground state is almost single-reference in this system and the strong electron correlation effect of the Cu centre can be dealt with using the MP2 or CCSD method, too. However, the slightly smaller occupation numbers of the 3dπ orbital in the course of reactions suggested that the electron correlation effect of the Cu(III) centre appears through the interaction between the 3dπ orbital and the C-I antibonding σ* orbital in the OA step, and between the 3dπ orbital and the Cu-C antibonding σ* orbital in the RE step.

Understanding electrostatics and covalency effects in highly anisotropic organometallic sandwich dysprosium complexes [Dy(CmRm)2] (where R = H, SiH3, CH3 and m = 4 to 9): a computational perspective.

In this article, we have thoroughly studied the electronic structure and 4f-ligand covalency of six mononuclear dysprosium organometallic sandwich complexes [Dy(CmRm)2]n+/- (where R = H, SiH3, CH3; m = 4 to 9; n = 1, 3) using both the scalar relativistic density functional and complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) method to shed light on the ligand field effects in fine-tuning the magnetic anisotropy of these complexes. Energy decomposition analysis (EDA) and ab initio-based ligand field theory AILFT calculations predict the sizable 4f-ligand covalency in all these complexes. The analysis of CASSCF/NEVPT2 computed spin-Hamiltonian (SH) parameters indicates the stabilization of mJ |±15/2〉 for [Dy(C4(SiH3)4)2]- (1), [Dy(C5(CH3)5)2]+ (2) and [Dy(C6H6)2]3+ (3) complexes with the Ucal value of 1867.5, 1621.5 and 1070.8 cm-1, respectively. On the other hand, we observed mJ |±9/2〉 as the ground state for [Dy(C7H7)2]3- (4) and [Dy(C8H8)2]- (5) complexes with significantly smaller Ucal values of 237.1 and 38.6 cm-1 respectively. For the nine-membered ring [Dy(C9H9)2]+ (6) complex, we observed the stabilization of the mJ |±1/2〉 ground state, with the first excited state being located ∼29 cm-1 higher in energy. AILFT-NEVPT2 ligand field splitting analysis indicates that the presence of π-type 4f-ligand interactions in complexes 1-3 help generate the axial-ligand field, while the δ-type interactions in complexes 4-5 generate the equatorial ligand field despite the ligands approaching from the axial direction. As the ring size increases, φ-type interactions dominate, generating a pure equatorial ligand field stabilising mJ |±1/2〉 as the ground state for 6. Calculations suggest that the nature of the ligand field mainly governs the Ucal values in the following order: 4f-Lσ > 4f-Lπ > 4f-Lδ > 4f-Lφ. Calculations were performed by replacing ligands with CHELPG charges to access the crystal field (CF) effects which suggests the stabilization of pure mJ |±15/2〉 in all the charge-embedded models (1Q-6Q). Our findings point out that the crystal field and ligand field effects complement each other and generate a giant barrier for magnetic relaxation in the small ring complexes 1-3, while a relatively weak crystal field and adverse 4f-Lδ/4f-Lφ interactions diminish the SMM behaviour in the large ring complexes 4-6.