Complete Active Space Self-consistent Field Research Articles

Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor.

Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.

Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor.

Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.

XMS-CASPT2//XMS-CASPT2 and XMS-CASPT2//CASSCF at comparison: The impact of dynamic correlation in the excited state optimization of nitronaphthalene.

Here, analytical extended multi-state complete active space second-order perturbation method (XMS-CASPT2) gradients are used to rationalize the decreasing triplet quantum yield trend in 2-nitronaphthalene, 1-nitronaphthalene, and 2-methyl-1-nitronaphthalene, a series of nitro-substituted aromatic compounds. Comparison with the XMS-CASPT2//CASSCF (where CASSCF stands for complete active space self-consistent field method) results highlights the importance of dynamic correlation in geometry optimization and challenges the validity of an XMS-CASPT2//CASSCF approach: XMS-CASPT2 S1 minima leads to planar structures, while CASSCF optimizations trigger a pyramidalization of the nitro group. The XMS-CASPT2 results correlate the reported decreasing triplet quantum yield trend in these species to a decrease in S1 to T2 population transfer and an increase in S1-S0 decay, while no such correlation is observed when using XMS-CASPT2//CASSCF data.

Multireference Ab Initio Calculations on Excited Electronic States of Carbazole-Based Organic Compounds for Thermally Activated Delayed Fluorescence.

The emerging technology of organic light-emitting diodes takes advantage of the thermally activated delayed fluorescence (TADF) mechanism for improved efficiency. Carbazole-based organic molecules are suitable for TADF emission because of charge transfer excitations between the electron-donor carbazole and an electron-acceptor unit. Computational design of new TADF molecules with the desired properties is challenging because charge-transfer excitations cannot be predicted accurately by time-dependent density functional theory. Four groups of carbazole-based donor-acceptor molecules have been studied using multireference ab initio methods to understand the nature of excited electronic states. The state-averaged complete active space self-consistent field (SA-CASSCF) and the N-electron valence state perturbation theory (NEVPT2) were used to calculate energies and oscillator strengths for multiple excited electronic states. The number of active electrons and orbitals and the number of excited states included in state-averaged CASSCF were selected such that the accuracy of ab initio predictions could be improved systematically. The procedure introduced here for the calculation of multiple excited electronic states of TADF candidates can be used to accelerate the computational search for efficient TADF materials.

Nature of partial sigma bond.

This study investigates the formation of partial sigma (σ) covalent bonds in experimentally synthesizable biradicals formed from hydrogenated and fluorinated C8, C20, and C60 cage structures, by assessing their stability, geometry, and bonding character in singlet and triplet states using restricted B3LYP-D3/6-31+G(d,p) theory, natural bond orbital (NBO) analysis, and complete active space self-consistent field (CASSCF) method. The results show that these partial σCC bonds have Wiberg bond orders of 0.38 to 0.48 and bond lengths ranging from 2.62 Å to 5.93 Å. Cage size influences the characteristics of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), with electrons favoring more antibonding orbitals in smaller cages where electrons reside more on the exterior of the cage and favoring bonding orbitals in larger ones where electrons are more in the interior. Fluorination enhances electron density on bonding orbitals. The analysis further clarified that the differentiation between antibonding and bonding features of HOMOs and LUMOs extends beyond merely electron transfer from s- to p-atomic orbitals, also noting possible interactions of the same symmetry repel. The study also introduces hyperconjugation from α-position CH bonds as a factor in stabilizing partial σ-bond formation. The results also caution against the use of broken symmetry methodology in unrestricted SCF wavefunctions for biradicals, such as those in this study as it may cause large spin contamination and thus errors in the calculated electronic properties results.

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces.

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Assessment of Iron-Based Spin-Orbit Coupling Effects in Pt-Fe Heterobimetallic Lantern Complexes via 57Fe Mössbauer Spectroscopy.

A series of heterobimetallic lantern complexes, [PtFe(SOCR)4(pyX)] where R = Me, X = H (1), X = NH2 (2), X = SMe (3); R = Ph, X = H (4), X = NH2 (5), X = SMe (6), have been prepared and characterized spectroscopically. Compounds 1, 4, and 5 are reported herein for the first time. The high-spin iron(II) sites of 1-6 have been investigated using 57Fe Mössbauer spectroscopy. Although the isomer shift of these species is nearly identical, their quadrupole splitting exhibits a much larger variation. Moreover, the zero-field Mössbauer spectra of 3-5 show surprising changes over time which are likely indicative of small structural distortions. The field dependent Mössbauer study of 1 and 6 revealed a zero field splitting (ZFS) characterized by a relatively large and positive D value. The combined Density Functional Theory (DFT) and ab initio Complete Active Space Self-Consistent Field (CASSCF) investigation of 1-6 indicates that their ground state is best described using a linear combination of {|xz⟩, |yz⟩} states. Our theoretical analysis suggests that the ZFSs and magnitude of the quadrupole splitting of 1-6 are determined by the spin-orbit coupling of the three lowest orbital states which have a T2g parentage.

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 MASH simulation of the photoexcited dynamics of cyclobutanone.

In response to a community prediction challenge, we simulate the nonadiabatic dynamics of cyclobutanone using the mapping approach to surface hopping (MASH). We consider the first 500fs of relaxation following photoexcitation to the S2 state and predict the corresponding time-resolved electron-diffraction signal that will be measured by the planned experiment. 397 abinitio trajectories were obtained on the fly with state-averaged complete active space self-consistent field using a (12,11) active space. To obtain an estimate of the potential systematic error, 198 of the trajectories were calculated using an aug-cc-pVDZ basis set and 199 with a 6-31+G* basis set. MASH is a recently proposed independent trajectory method for simulating nonadiabatic dynamics, originally derived for two-state problems. As there are three relevant electronic states in this system, we used a newly developed multi-state generalization of MASH for the simulation: the uncoupled spheres multi-state MASH method (unSMASH). This study, therefore, serves both as an investigation of the photodissociation dynamics of cyclobutanone, and also as a demonstration of the applicability of unSMASH to abinitio simulations. In line with previous experimental studies, we observe that the simulated dynamics is dominated by three sets of dissociation products, C3H6 + CO, C2H4 + C2H2O, and C2H4 + CH2 + CO, and we interpret our predicted electron-diffraction signal in terms of the key features of the associated dissociation pathways.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

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.

Zero-Field Splitting Tensor of the Triplet Excited States of Aromatic Molecules: A Valence Full-π Complete Active Space Self-Consistent Field Study.

A method to predict the D tensor in the molecular frame with multiconfigurational wave functions in large active space was proposed, and the spin properties of the lowest triplets of aromatic molecules were examined with full-π active space; such calculations were challenging because the size of active space grows exponentially with the number of π electrons. In this method, the exponential growth of complexity is resolved by the density matrix renormalization group (DMRG) algorithm. From the D tensor, we can directly determine the direction of the magnetic axes and the ZFS parameters, D- and E-values, of the phenomenological spin Hamiltonian with their signs, which are not usually obtained in ESR experiments. The method using the DMRG-CASSCF wave function can give correct results even when the sign of D- and E-values is sensitive to the accuracy of the prediction of the D tensor and existing methods fail to predict the correct magnetic axes.

Photochemical Mechanisms of Hydroxyquinoline Benzimidazole: Insights from Electronic Structure Calculations and Nonadiabatic Dynamics Simulations.

Excited-state intramolecular double proton transfer (ESIDPT) has received much attention because of its widespread existence in the life reactions of living organisms, and materials with this property are significant for their special luminescent properties. In this work, the complete active space self-consistent field (CASSCF) and OM2/multireference configuration interaction (OM2/MRCI) methods have been employed to study the static electronic structure calculations of the photochemistry and the possibility of ESIDPT process of hydroxyquinoline benzimidazole (HQB) molecule, along with the nonadiabatic dynamics simulations. The computational results show that the HQB molecule is relaxed to the S1-ENOL minimum after being excited to the Franck-Condon point in the S1 state. Subsequently, during the nonadiabatic deactivation process, the OH···N proton transfer and the twisting of benzimidazole occur before arriving at the single proton transfer conical intersection S1S0-KETO. Finally, the system can either return to the initial ground-state structure S0-ENOL or to the single proton transfer ground-state structure S0-KETO, both of which have almost the same probability. The dynamics simulations also show that no double proton transfer occurs. The excited-state lifetime of HQB is fitted to 1.1 ps, and only 64% of the dynamic trajectories return to the ground state within the 2.0 ps simulation time. We hope the detailed reaction mechanism of the HQB molecule will provide new insights into similar systems.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions.

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Metal-Free Activation of Molecular Oxygen by Quaternary Ammonium-Based Ionic Liquid: A Detail Mechanistic Study.

Most oxidation processes in common organic synthesis and chemical biology require transition metal catalysts or metalloenzymes. Herein, we report a detailed mechanistic study of a metal-free oxygen (O2) activation protocol on benzylamine/alcohols using simple quaternary alkylammonium-based ionic liquids to produce products such as amide, aldehyde, imine, and in some cases, even aromatized products. NMR and various control experiments established the product formation and reaction mechanism, which involved the conversion of molecular oxygen into a hydroperoxyl radical via a proton-coupled electron transfer process. Detection of hydrogen peroxide in the reaction medium using colorimetric analysis supported the proposed mechanism of oxygen activation. Furthermore, first-principles calculations using density functional theory (DFT) revealed that reaction coordinates and transition state spin densities have a unique spin conversion of triplet oxygen leading to formation of singlet products via a minimum energy crossing point. In addition to DFT, domain-based local pair natural orbital coupled cluster, (DLPNO-CCSD(T)), and complete active space self-consistent field, CASSCF(20,14) methods complemented the above findings. Partial density of states analysis showed stabilization of π* orbital of oxygen in the presence of ionic liquid, making it susceptible to hydrogen abstraction in a mild, metal-free condition. Inductively coupled plasma atomic emission spectroscopic (ICP-AES) analysis of reactant and ionic liquids clearly showed the absence of any significant transition metal contamination. The current results described the origin of O2 activation within the context of molecular orbital (MO) theory and opened up a new avenue for the use of ionic liquids as inexpensive, multifunctional and high-performance alternative to metal-based catalysts for O2 activation.

Isomerization dynamics of a novel cis/trans‐only merocyanine

AbstractMerocyanines (MC) usually adopt ring opened zwitterionic structures that are interconvertible with their ring‐closed spiropyran photoisomers. By methylating the phenolate oxygen, and thereby blocking the ring‐closure reaction, a cis/trans‐only MC photoswitch was obtained, yielding a perfect candidate for a detailed examination of the cis/trans isomerization mechanism for this class of compounds. This photoswitch displays outstanding properties including excellent photoreaction quantum yields and photoswitching turnovers. Due to the central polymethine bridge of MC, in principle eight cis (C)/trans/(T) isomers are possible. Density Functional Theory (DFT) calculations revealed the CCT and TTT‐isomers of the studied compound as most stable cis and trans ground state isomers, respectively. UV/vis transient absorption studies combined with conical intersection computations with the complete active space self‐consistent field (CASSCF) method show that both trans/cis‐ and cis/trans‐photoisomerizations are initiated by a rotation of the central doubled bond fragment. A hot ground state species is then formed, which undergoes a second isomerization. Thus, the cis/trans reaction proceeds via a CCT‐CTT‐TTT sequence and the reverse reaction via TTT‐TCT‐CCT.

Theoretical Prediction of Core-Level Binding Energies: Analysis of Unexpected Errors.

The analysis of the C(1s) and O(1s) core-level binding energies (CLBEs) of selected molecules computed by means of total energy Hartree-Fock (ΔSCF-HF) differences shows that in some cases, the calculated values for the C(1s) are larger than the experiment, which is unexpected. The origin of these unexpected errors of the Hartree-Fock ΔSCF BEs is shown to arise from static, nondynamical, electron correlation effects which are larger for the ion than for the neutral system. Once these static correlation effects are included by using complete active space self-consistent field (CASSCF) wave functions that include internal correlation terms, the resulting ΔSCF BEs are, as expected, smaller than measured values.

Spectroscopic and Theoretical Investigation of High-Spin Square-Planar and Trigonal Fe(II) Complexes Supported by Fluorinated Alkoxides.

The electronic structures and spectroscopic behavior of three high-spin FeII complexes of fluorinated alkoxides were studied: square-planar {K(DME)2}2[Fe(pinF)2] (S) and quasi square-planar {K(C222)}2[Fe(pinF)2] (S') and trigonal-planar {K(18C6)}[Fe(OC4F9)3] (T) where pinF = perfluoropinacolate and OC4F9 = tris-perfluoro-t-butoxide. The zero-field splitting (ZFS) and hyperfine structure parameters of the S = 2 ground states were determined using field-dependent 57Fe Mössbauer and high-field and -frequency electron paramagnetic resonance (HFEPR) spectroscopies. The spin Hamiltonian parameters were analyzed with crystal field theory and corroborated by density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) calculations. Whereas the ZFS tensor of S has a small rhombicity, E/D = 0.082, and a positive D = 15.17 cm-1, T exhibits a negative D = -9.16 cm-1 and a large rhombicity, E/D = 0.246. Computational investigation of the structural factors suggests that the ground-state electronic configuration and geometry of T's Fe site are determined by the interaction of [Fe(OC4F9)3]- with {K(18C6)}+. In contrast, two distinct countercations of S/S' have a negligible influence on their [Fe(pinF)2]2- moieties. Instead, the distortions in S' are likely induced by the chelate ring conformation change from δλ, observed for S, to the δδ conformation, determined for S'.