Complete Active Space Self-consistent Field Research Articles

First-principles molecular dynamics simulation study on Ti/Mn ions in aqueous sulfuric acid for use in redox flow battery

The effect of the Ti4+ ion on the structural and chemical features of the Mn3+ ion in aqueous sulfuric acid was investigated using first-principles molecular dynamics (FPMD) simulation and second-order perturbation theory (CASPT2) with a complete active space self-consistent field (CASSCF) reference function. The focus was on the role of the Ti ion in the MnO2 formation reaction from the Mn3+ ion. The simulations showed that Mn3+ forms two types of complexes, [Mn(H2O)4(SO4)2]1− and [Mn(H2O)6]3+ in aqueous sulfuric acid with Ti ions where the population of the former was found to be higher than that of the latter. We found that when the HSO4− ion was coordinated to a Ti4+ ion, it released one proton, which increases proton concentration in the solution. Detailed quantum chemical calculations on the isolated Mn complexes show that if the Mn complexes interact with a hydronium ion, the stability of Mn3+ ion is increased to a large extent. Such a result implies that the increased local proton concentration due to Ti4+ ions hinders formation of MnO2 particle.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures.

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Computational Description of Alkylated Iron-Sulfur Organometallic Clusters.

The radical S-adenosyl methionine (SAM) enzyme superfamily has widespread roles in hydrogen atom abstraction reactions of crucial biological importance. In these enzymes, reductive cleavage of SAM bound to a [4Fe-4S]1+ cluster generates the 5'-deoxyadenosyl radical (5'-dAdo•) which ultimately abstracts an H atom from the substrate. However, overwhelming experimental evidence has surprisingly revealed an obligatory organometallic intermediate Ω exhibiting an Fe-C5'-adenosyl bond, whose properties are the target of this theoretical investigation. We report a readily applied, two-configuration version of broken symmetry DFT, denoted 2C-DFT, designed to allow the accurate description of the hyperfine coupling constants and g-tensors of an alkyl group bound to a multimetallic iron-sulfur cluster. This approach has been validated by the excellent agreement of its results both with those of multiconfigurational complete active space self-consistent field computations for a series of model complexes and with the results from electron nuclear double-resonance/electron paramagnetic resonance spectroscopic studies for the crystallographically characterized complex, M-CH3, a [4Fe-4S] cluster with a Fe-CH3 bond. The likewise excellent agreement between spectroscopic results and 2C-DFT computations for Ω confirm its identity as an organometallic complex with a bond between an Fe of the [4Fe-4S] cluster and C5' of the deoxyadenosyl moiety, as first proposed.

Magneto-Structural Analysis of Hydroxido-Bridged CuII2 Complexes: Density Functional Theory and Other Treatments

A selection of dimeric Cu(II) complexes with bidentate N,N′ ligands with the general formula [Cu(L)(X)(μ-OH)]2·nH2O and [Cu(L)(μ-OH)]2X2·nH2O were magneto-structurally analyzed using the Density Functional Theory (DFT). A Broken Symmetry-Density Functional Theory (BS-DFT) study was undertaken for these complexes with relevant decomposition schemes that gave insight into the effect of the nature of the ligand and coordination environment on the DFT-predicted coupling constants (J). The impact of the spin population, which correlates well with the Cu-O-Cu bridging angles and the calculated coupling constant (J) values, was studied. The models were further refined using a complete active space self-consistent field (CASSCF) while expanding the active space from 2 orbitals 2 electrons (2,2) to 10 orbitals 18 electrons (18,10). These models were approximated using multireference methods (n-electron valence state perturbation theory and difference dedicated configuration interaction), and a better approximation of J values was found as expected. Orbitals involved in the superexchange pathway were also visualized.

Analysis of the Ability of C6H5I to Phosphoresce.

The heavy atom effect is a widely utilized strategy to enhance the phosphorescence intensity of organic molecules. Among the preferred choices, heavy halogen atoms such as bromine (Br) or iodine (I) have gained popularity. However, the incorporation of these heavy atoms can introduce challenges due to the presence of unstable excited states that undergo dissociation upon excitation. This study focuses on investigating the excited states of the C6H5I molecule, with particular emphasis on the intricate interplay of spin-orbital coupling effects, employing multireference ab initio methodologies. The absence of phosphorescence in the C6H5I molecule is attributed to the efficient energy transfer to dissociative excited states and the near-zero spin-orbital coupling between stable triplet sub-levels and the ground singlet state. To gain insights into the explicit dynamics of the excited states, the research employed Ehrenfest dynamics driven by real-time time-dependent density functional theory (TDDFT). Furthermore, the study explored the complete active space compositions and various post-CASSCF (complete active space self-consistent field) approaches.

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.

Efficient analytical gradients of property-based diabatic states: Geometry optimizations for localized holes.

We present efficient analytical gradients of property-based diabatic states and couplings using a Lagrangian formalism. Unlike previous formulations, the method achieves a computational scaling that is independent of the number of adiabatic states used to construct the diabats. The approach is generalizable to other property-based diabatization schemes and electronic structure methods as long as analytical energy gradients are available and integral derivatives with the property operator can be formed. We also introduce a scheme to phase and reorder diabats to ensure their continuity between molecular configurations. We demonstrate this for the specific case of Boys diabatic states obtained from state-averaged complete active space self-consistent field electronic structure calculations with GPU acceleration in the TeraChem package. The method is used to test the Condon approximation for the hole transfer in an explicitly solvated model DNA oligomer.

Sulfur-Containing Radical Anions Formed by Photolysis of Thiosulfate: Quantum-Chemical Analysis.

The photochemistry of sodium thiosulfate (S2O32-) in aqueous solutions is rather complicated. Several sulfur-containing radical anions are formed upon photoexcitation. Any of them are rather common (SO3•-, SO2•-, and SO5•-); others are rare (S2O3•-, •S4O63-, and S•-) or never documented (S2O5•-). In order to support the identification of intermediate radical anions, quantum-chemical (QM─quantum mechanical) calculations of the geometric and electronic structures of S2O3•-, S2O5•-, and •S4O63- were performed. Two different approaches, time-dependent density functional theory and complete active space self-consistent field, were applied to identify the method optimal for the reproduction of the experimental electronic absorption spectra. Several of the most commonly used functionals were considered. The best agreement with the experimentally observed spectra of reference compounds (common sulfur-containing anions and radical anions) was achieved for the WB97X-D3 functional. Using this approach, satisfactory agreement between experimental and calculated spectra of S2O3•-, S2O5•-, and •S4O63- was achieved. It was shown that S2O5•- and •S4O63- can exist in two isomeric forms with different spectral properties. These isomers are S2O3O2•-; SO3SO2•- for the case of S2O5•- and (S2O3)2•3-; (S3O32-...SO3•-) for the case of •S4O63-.

Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory.

State-specific electronic structure theory provides a route toward balanced excited-state wave functions by exploiting higher-energy stationary points of the electronic energy. Multiconfigurational wave function approximations can describe both closed- and open-shell excited states and avoid the issues associated with state-averaged approaches. We investigate the existence of higher-energy solutions in complete active space self-consistent field (CASSCF) theory and characterize their topological properties. We demonstrate that state-specific approximations can provide accurate higher-energy excited states in H2 (6-31G) with more compact active spaces than would be required in a state-averaged formalism. We then elucidate the unphysical stationary points, demonstrating that they arise from redundant orbitals when the active space is too large or symmetry breaking when the active space is too small. Furthermore, we investigate the singlet-triplet crossing in CH2 (6-31G) and the avoided crossing in LiF (6-31G), revealing the severity of root flipping and demonstrating that state-specific solutions can behave quasi-diabatically or adiabatically. These results elucidate the complexity of the CASSCF energy landscape, highlighting the advantages and challenges of practical state-specific calculations.

Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as the impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the nonembedding limit using a linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ∼2.18 eV and ∼1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.

Laser cooling with intermediate state of spin–orbit coupling of LuF molecule

This work presents a theoretical study of the laser cooling feasibility of the molecule LuF, in the fine structure level of approximation. An ab-initio complete active space self-consistent field (CASSCF)/MRCI with Davidson correction calculation has been done in the Λ(±) and Ω(±) representations. The corresponding adiabatic potential energy curves and spectroscopic parameters have been investigated for the low-lying electronic states. The calculated values of the internuclear distances of the X3Σ0+ and (1)3Π0+ states show the candidacy of the molecule LuF for direct laser cooling. Since the existence of the intermediate (1)3Δ1 state cannot be ignored, the investigation has been done by taking into consideration the two transitions (1)3Π0+−(1)3Δ1 and (1)3Π0+ −X3Σ0+. The calculation of the Franck–Condon factors, the radiative lifetimes, the total branching ratio, the slowing distance, and the laser cooling scheme study prove that the molecule LuF is a good candidate for Doppler laser cooling.

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.

Excited-State Aromaticity Reversals in Naphthalene and Anthracene.

Aromaticity reversals between the electronic ground (S0) and low-lying singlet (S1, S2) and triplet (T1, T2, T3) states of naphthalene and anthracene are investigated by calculating the respective off-nucleus isotropic magnetic shielding distributions using complete-active-space self-consistent field (CASSCF) wavefunctions involving gauge-including atomic orbitals (GIAOs). The shielding distributions around the aromatic S0, antiaromatic S1 (1Lb), and aromatic S2 (1La) states in naphthalene are found to resemble the outcomes of fusing together the respective S0, S1, and S2 shielding distributions of two benzene rings. In anthracene, 1La is lower in energy than 1Lb, and as a result, the S1 state becomes aromatic, and the S2 state becomes antiaromatic; the corresponding shielding distributions are found to resemble extensions by one ring of those around the S2 and S1 states in naphthalene. The lowest antiaromatic singlet state of either molecule is found to be significantly more antiaromatic than the respective T1 state, which shows that it would be incorrect to assume that the similarity between the (anti)aromaticities of the S1 and T1 states in benzene, cyclobutadiene, and cyclooctatetraene would be maintained in polycyclic aromatic hydrocarbons.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models.

We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.

Dihydropyrene/Cyclophanediene Photoswitching Mechanism Revisited with Spin-Flip Time-Dependent Density Functional Theory: Nature of the Photoisomerization Funnel at Stake!

The complex photoisomerization mechanism of the dihydropyrene (DHP) photochromic system is revisited using spin-flip time-dependent density functional theory (SF-TD-DFT). The photoinduced ring-opening reaction of DHP into its cyclophanediene isomer involves multiple coupled electronic states of different character. A balanced treatment of both static and dynamic electron correlations is required to determine both the photophysical and photochemical paths in this system. The present results provide a refinement of the mechanistic picture provided in a previous complete active space self-consistent field plus second-order perturbation theory (CASPT2//CASSCF) study based on geometry optimizations at the CASSCF level. In particular, the nature of the conical intersection playing the central role of the photochemical funnel is different. While at the CASSCF level, the crossing with the ground state involves a covalent doubly excited state leading to a three-electron/three-center bond conical intersection, SF-TD-DFT predicts a crossing between the ground state and a zwitterionic state. These results are supported by multi-state CASPT2 calculations. This study illustrates the importance of optimizing conical intersections at a sufficiently correlated level of theory to describe a photochemical path involving crossings between covalent and ionic states.

Origin of the Distinctive Electronic Structure of Co- and Fe-Porphyrin-Nitrene and Its Effect on Their Nitrene Transfer Reactivity

Metal-bound nitrene species are the crucial intermediate in catalytic nitrene transfer reactions exhibited by engineered enzymes and molecular catalysts. The electronic structure of such species and its correlation with nitrene transfer reactivity have not been fully understood yet. This work presents an in-depth electronic structure analysis and nitrene transfer reactivity of two prototypical metal-nitrene species derived from CoII(TPP) and FeII(TPP) (TPP = meso-tetraphenylporphyrin) complexes and tosyl azide nitrene precursor. Parallel to the well-known "cobalt(III)-imidyl" electronic structure of the Co-porphyrin-nitrene species, the formation mechanism and electronic structure of the elusive Fe-porphyrin-nitrene have been established using density functional theory (DFT) and multiconfigurational complete active-space self-consistent field (CASSCF) calculations. Electronic structure evolution analysis for the metal-nitrene formation step and CASSCF-derived natural orbitals advocates that the electronic nature of the metal-nitrene (M-N) core of Fe(TPP) is strikingly different from that of the Co(TPP). Specifically, the "imidyl" nature of the Co-porphyrin-nitrene [(TPP)CoIII-•NTos] (Tos = tosyl) (I1Co) is contrasted by the "imido-like" character of the Fe-porphyrin-nitrene [(TPP)FeIV[Formula: see text]NTos] (I1Fe). This difference between Co- and Fe-nitrene has been attributed to the additional interactions between Fe-dπ and N-pπ orbitals in Fe-nitrene, which is further complemented by the shortened Fe-N bond length of 1.71 Å. This stronger M-N bond in Fe-nitrene compared to the Co-nitrene is also reflected in the higher exothermicity (ΔΔH = 16 kcal/mol) of the Fe-nitrene formation step. The "imido-like" character renders a relatively lower spin population on the nitrene nitrogen (+0.42) in the Fe-nitrene complex I1Fe, which undergoes the nitrene transfer to the C═C bond of styrene with a considerably higher enthalpy barrier (ΔH‡ = 10.0 kcal/mol) compared to the Co congener I1Co (ΔH‡ = 5.6 kcal/mol) possessing a higher nitrogen spin population (+0.88) and a relatively weaker M-N bond (Co-N = 1.80 Å).

Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

ContextIn 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description.MethodsTo obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.

An exotic 3-center/4-electron carbon–carbon pi long-bond: Is it tangible?

Centrosymmetric species with AB2 boding motif where central atom (A) is relatively more electronegative than the end ligands (B atoms) have been predicted to exhibit an unusual form of three-center/four-electron (3c/4e) long-bonding where bonding/antibonding interactions occur between the two end ligands (B–B) bypassing the central atom albeit via sharing the latter’s lone pair. Such a long-bond of sigma- and pi-type has so far been predicted as single bonds and mainly as linear (B–A–B) bonding motifs. This work, through computations based on density-functional theory (DFT) and natural bond orbital (NBO) analysis, reveals pi-type long-bonding between carbon atoms separated by more than 2 angstroms in the gas-phase chain species, namely CnX (X = O,N; n = 2,4,6,8). Notably, this work, through DFT and NBO analysis, not only successfully predicts pi-type long-bonding in linear and nonlinear CnX species (mainly those where X is the central atom) but is also able to reveal multiple pi long-bonds particularly in the triplet-C2O as well as a pi long-bond in an isomer of C8N where N is not the central atom. However, preliminary computations using complete active space self-consistent field (CASSCF) multi-reference method performed in this work could only confirm antibonding pi long-bond orbital, whereas the validity of bonding pi long-bond orbital of the proposed long-bond could not be ascertained through the CASSCF.

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.