Complete Active Space Research Articles

Quantum Information-Assisted Complete Active Space Optimization (QICAS).

We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.

Theoretical insights into the photophysics of an unnatural base Z: A MS-CASPT2 investigation.

We have employed the highly accurate multistate complete active space second-order perturbation theory (MS-CASPT2) method to investigate the photoinduced excited state relaxation properties of one unnatural base, namely Z. Upon excitation to the S2 state of Z, the internal conversion to the S1 state would be dominant. From the S1 state, two intersystem crossing paths leading to the T2 and T1 states and one internal conversion path to the S0 state are possible. However, considering the large barrier to access the S1 /S0 conical intersection and the strong spin-orbit coupling between S1 and T2 states (>40 cm-1 ), the intersystem crossing to the triplet manifolds is predicted to be more preferred. Arriving at the T2 state, the internal conversion to the T1 state and the intersystem crossing back to the S1 state are both possible considering the S1 /T2 /T1 three-state intersection near the T2 minimum. Upon arrival at the T1 state, the deactivation to S0 can be efficient after overcoming a small barrier to access T1 /S0 crossing point, where the spin-orbit coupling (SOC) is as large as 39.7 cm-1 . Our present work not only provides in-depth insights into the photoinduced process of unnatural base Z, but can also help the future design of novel unnatural bases with better photostability.

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.

The Co-N bond cleavage in the adenosyncobalamin cofactor in advance to glutamate mutase and methylmalonyl-CoA mutase processes

The in vivo experiments show that the adenosylcobalamin cofactor in glutamate mutase and methylmalonyl-CoA mutase processes lose its dimethylbenzimidazole axial ligand before starting the enzymatic processes. Complete active space self-consistent field geometry optimization of the vitamin B12 active forms plus substrates joint models have been performed. These joint models include the adenosylcobalamin cofactor, the carboxyl negative ion model of the studied processes’ active substrates, and the histidine molecule. Partial electronic density is transferred from the highest occupied substrate molecular orbitals to the lowest unoccupied antibonding molecular orbitals, which consist of corrin ring and dimethylbenzimidazole ligand common molecular orbitals during the multi-configurational self-consistent field molecular orbital mixing process. As a result, the Co-N axial bond is permanently elongated during the complete active space self-consistent field geometry optimization until its complete rupture and until the removal of the dimethylbenzimidazole ligand from the central cobalt atom and the corrin ring is complete. The Co-N bond cleavage in the adenosylcobalamin cofactors in the studied processes is running as no energy barrier process under the influence of their active substrates and histidine molecule.

Magnetic Exchange Coupling in Macrocyclic Cobalt (II) Complexes: The Influence of Bridging Ligands and Choice of the Computational Methodologies

AbstractExchange‐coupled spin states of cobalt complexes represent the key to understanding the challenging nature of the magnetism of cobalt dimer. In this study, we introduce a comprehensive investigation of the nature of magnetic super‐exchange coupling interactions between two metallic centers in a macro ligand cobalt dimer. More importantly, we provide a detailed comparison between a series of bridging ligands and study their role in the magnetic exchange coupling constant in cobalt dimer with tetraaza macrocycle ligand scaffold. By varying the types of bridging and terminal ligands, we explored the nature of magnetic coupling in 24 species of cobalt dimers, which allowed us to draw a magneto‐structure relationship and monitor the effect of bridging/terminal ligands on the overall magnetism. We employed different density functional theory (DFT) methodologies and complete active space self‐consistent field (CASSCF) in our investigation. The results show that there are comprehensible functional dependencies, and the choice of exchange‐correlation functional is critical for calculating the magnetic properties. Using the experimental values of the exchange coupling, we found that hybrid functionals with 10–20 % Hartree‐Fock exchange integrals give acceptable accuracy. Furthermore, we adjusted the percentage of HF integrals to estimate the optimum value required to be included in the hybrid functionals. Finally, we used CASSCF to gain deeper understanding of the magnetic coupling for the valence magnetic electrons and to achieve the true ground state wavefunction, which is not feasible with conventional DFT calculations. However, the CASSCF calculations poorly underestimate the magnetic coupling, which can be significantly improved by including the dynamic correlations, as implemented in the NEVPT2 methodology.

Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size.

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives.

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

ExoMol line lists – LIII: empirical rovibronic spectra of yttrium oxide

ABSTRACT Empirical line lists BRYTS for the open shell molecule 89Y16O (yttrium oxide) and its isotopologues are presented. The line lists cover the six lowest electronic states: $X\, {}^{2}\Sigma ^{+}$, $A\, {}^{2}\Pi$, $A^{\prime }\, {}^{2}\Delta$, $B\, {}^{2}\Sigma ^{+}$, $C\, {}^{2}\Pi$, and $D\, {}^{2}\Sigma ^{+}$ up to 60 000 cm−1 (<0.167 $\mu$m) for rotational excitation up to J = 400.5. An ab initio spectroscopic model consisting of potential energy curves (PECs), spin–orbit, and electronic angular momentum couplings is refined by fitting to experimentally determined energies of YO, derived from published YO experimental transition frequency data. The model is complemented by empirical spin-rotation and Λ-doubling curves and ab initio dipole moment and transition dipole moment curves computed using multireference configuration interaction (MRCI). The ab initio PECs computed using the complete basis set limit extrapolation and the coupled-cluster CCSD(T) method with its higher quality provide an excellent initial approximation for the refinement. Non-adiabatic coupling curves for two pairs of states of the same symmetry A/C and B/D are computed using a state-averaged complete active space self-consistant field theory (CASSCF) and used to build diabatic representations for the $A\, {}^{2}\Pi$, $C\, {}^{2}\Pi$, $B\, {}^{2}\Sigma ^{+}$, and $D\, {}^{2}\Sigma ^{+}$ curves. The experimentally derived energies of 89Y16O utilized in the fit are used to replace the corresponding calculated energy values in the BRYTS line list. Simulated spectra of YO show excellent agreement with the experiment, where it is available. Calculated lifetimes of YO are tuned to agree well with the experiment, where available. The BRYTS YO line lists are available from the ExoMol database (www.exomol.com).

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.

Experimental and Theoretical Studies of Hyperthermal N + O2 Collisions.

The dynamics of hyperthermal N(4S) + O2 collisions were investigated both experimentally and theoretically. Crossed molecular beams experiments were performed at an average center-of-mass (c.m.) collision energy of ⟨Ecoll⟩ = 77.5 kcal mol-1, with velocity- and angle-resolved product detection by a rotatable mass spectrometer detector. Nonreactive (N + O2) and reactive (NO + O) product channels were identified. In the c.m. reference frame, the nonreactively scattered N atoms and reactively scattered NO molecules were both directed into the forward direction with respect to the initial direction of the reagent N atoms. On average, more than 90% of the available energy (⟨Eavl⟩ = 77.5 kcal mol-1) was retained in translation of the nonreactive products (N + O2), whereas a much smaller fraction of the available energy for the reactive pathway (⟨Eavl⟩ = 109.5 kcal mol-1) went into translation of the NO + O products, and the distribution of translational energies for this channel was broad, indicating extensive internal excitation in the nascent NO molecules. The experimentally derived c.m. translational energy and angular distributions of the reactive products suggested at least two dynamical pathways to the formation of NO + O. Quasiclassical trajectory (QCT) calculations were performed with a collision energy of Ecoll = 77 kcal mol-1 using two sets of potential energy surfaces, denoted as PES-I and PES-II, and these theoretical results were compared to each other and to the experimental results. PES-I is a reproducing kernel Hilbert space (RKHS) representation of multireference configurational interaction (MRCI) energies, while PES-II is a many-body permutation invariant polynomial (MB-PIP) fit of complete active space second order perturbation (CASPT2) points. The theoretical investigations were both consistent with the experimental suggestion of two dynamical pathways to produce NO + O, where reactive collisions may proceed on the doublet (12A') and quartet (14A') surfaces. When analyzed with this theoretical insight, the experimental c.m. translational energy and angular distributions were in reasonably good agreement with those predicted by the QCT calculations, although minor differences were observed which are discussed. Theoretical translational energy and angular distributions for the nonreactive N + O2 products matched the experimental translational energy and angular distributions almost quantitatively. Finally, relative yields for the nonreactive and reactive scattering channels were determined from the experiment and from both theoretical methods, and all results are in reasonable agreement.

On the Fluorescence Properties and Nonradiative Transitions in Medium-Sized All-Trans Polyenes.

The nonadiabatic photodynamics of all-trans linear polyenes with N = 4-8 conjugated double bonds is studied from an electronic structure perspective. Excitation energies and stationary points for the 1Bu and 2Ag singlet states have been computed by using the state-average complete active space (SA-CASSCF) method and its second-order perturbation theory variant (MS-CASPT2). The dependence of the two low-lying excited states on the "chain length" N has been elucidated. In addition, the 1Bu-2Ag crossing seam has been mapped out in a suitable two-dimensional coordinate space and its minimum within the subspace has been determined. This minimum is found to increase substantially and monotonously in energy with increasing N. This increase is discussed and interpreted in relation to the fluorescence properties of these systems. In particular, it allows to understand the crossover from S1(2Ag) fluorescence for smaller N to S2(1Bu) (or dual) fluorescence for larger N.

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.

Magnetic Properties of Tetravalent Pu in the Perovskites BaPuO3 and SrPuO3.

BaPuO3 and SrPuO3 were synthesized, and their structures were refined in the orthorhombic space group Pbnm, a common distortion from the classic Pm3̅m cubic perovskite. Magnetic-susceptibility measurements, obtained as a function of temperature over the range of 1.8-320 K, exhibit temperature-dependent behavior, with evidence of long-range magnetic order at temperatures higher than their lanthanide and actinide analogues: BaPuO3 below 164(1) K and SrPuO3 below 76(1) K. Effective moments of 1.66(10)μB for BaPuO3 and 1.84(8)μB for SrPuO3 were obtained by fitting their paramagnetic susceptibilities using the Curie-Weiss law. Both are below the free-ion value of 2.68 μB expected for a Pu4+ 5I4 ground level. Ab initio wave function calculations, performed at the relativistic complete active space level including spin-orbit coupling and with an embedded cluster approach that neglects interactions between Pu centers, were used to generate embedded-cluster Pu4+ magnetic susceptibilities. The calculations agree well with experimental data at higher temperatures, providing evidence that a single-ion representation is sufficient to account for the observed paramagnetic behavior without the need to invoke charge transfer, disproportionation, strong covalent bonding, or other more complex electronic behavior.

Theoretical Understanding on the Facilitated Photoisomerization of a Carbonyl Supported Borane System.

Boron compound BOMes2 containing an internal B-O bond undergoes highly efficient photoisomerization, followed by sequential structural transformations, resulting in a rare eight-membered B, O-heterocycle (S. Wang, et al. Org. Lett.2019, 21, 5285-5289). In this work, the detailed reaction mechanisms of such a unique carbonyl-supported tetracoordinate boron system in the first excited singlet (S1) state and the ground (S0) state were investigated by using the complete active space self-consistent field and its second-order perturbation (MS-CASPT2//CASSCF) method combined with time-dependent density functional theory (TD-DFT). Moreover, an imine-substituted tetracoordinated organic boron system (BNMes2) was selected for comparative study to explore the intrinsic reasons for the difference in reactivity between the two types of compounds.Steric factorwasfound to influence the photoisomerization activity of BNMes2 and BOMes2. These results rationalize the experimental observations and can provide helpful insights into understanding the excited-state dynamics of heteroatom-doped tetracoordinate organoboron compounds, which facilitates the rational design of boron-based materials with superior photoresponsive performances.

Excited-state van der Waals potential energy surfaces for the NO A2Σ+ + CO2X1Σg+ collision complex.

Excited state van der Waals (vdW) potential energy surfaces (PESs) of the NO A2Σ+ + CO2X1Σg+ system are thoroughly investigated using coupled cluster theory and complete active space perturbation theory to second order (CASPT2). First, it is shown that pair natural orbital coupled cluster singles and doubles with perturbative triples yields comparable accuracy compared to CCSD(T) for molecular properties and vdW-minima at a fraction of computational cost of the latter. Using this method in conjunction with highly diffuse basis sets and counterpoise correction for basis set superposition error, the PESs for different intermolecular orientations are investigated. These show numerous vdW-wells, interconnected for all geometries except one, with a maximum depth of up to 830 cm-1; considerably deeper than those on the ground state surface. Multi-reference effects are investigated with CASPT2 calculations. The long-range vdW-surfaces support recent experimental observations relating to rotational energy transfer due the anisotropy in the potentials.

An embedded cluster CASPT2 study of the Ce:YVO4 spectrum.

Multiconfigurational theory, in combination with the embedded cluster approach, is a precise and abinitio approach to describe the electronic structure of solids. In this work, the spectrum of a Ce(III) dopant in YVO4 has been studied by complete active space perturbation theory of the second order (CASPT2), with the host material represented as a set of abinitio model potentials and point-charges. We assess the sensitivity of the spectrum to the size of both the embedded cluster size as well as the size of the electronic basis set. A comparison of our best computational model with experimental results shows that the embedding approach is robust and can accurately model the spectrum of low-concentration dopants in complex host materials.

Ultrafast internal conversion and photochromism in gas-phase salicylideneaniline.

Salicylideneaniline (SA) is an archetypal system for excited-state intramolecular proton transfer (ESIPT) in non-planar systems. Multiple channels for relaxation involving both the keto and enol forms have been proposed after excitation to S1 with near-UV light. Here, we present transient absorption measurements of hot gas-phase SA, jet-cooled SA, and SA in Ar clusters using cavity-enhanced transient absorption spectroscopy (CE-TAS). Assignment of the spectra is aided by simulated TAS spectra, computed by applying time-dependent complete active space configuration interaction (TD-CASCI) to structures drawn from nonadiabatic molecular dynamics simulations. We find prompt ESIPT in all conditions followed by the rapid generation of the trans keto metastable photochrome state and fluorescent keto state in parallel. Increasing the internal energy increases the photochrome yield and decreases the fluorescent yield and fluorescent state lifetime observed in TAS. In Ar clusters, internal conversion of SA is severely hindered, but the photochrome yield is unchanged. Taken together, these results are consistent with the photochrome being produced via the vibrationally excited keto population after ESIPT.

On the aromaticity and stability of benzynes in the ground and lowest-lying triplet excited states.

In this work, we have revisited the aromaticity of benzyne isomers at the unrestricted density functional theory level (UDFT) using the energetic, magnetic, and delocalization criteria. In addition, this last criterion has also been analyzed employing complete active space (CASSCF) calculations. The results show conservation of aromaticity in these monocycles. Additionally it is observed that this trend is maintained in polycyclic aromatic hydrocarbon derivatives such as biradical didehydrophenanthrenes. Do these results imply a violation of Baird's rule? The answer is No, because this conservation in aromaticity is due to the loss of hydrogen atoms affects only the electronic σ skeleton and exerts a minor influence on the π cloud. Additionally, we have analyzed the relative stability of benzyne isomers and their relationship with experimental ΔES-T values. According to the literature, the stability of the benzynes in the singlet state is due to an effective interaction between the electrons of the biradical centers; however, this effect is completely reversed in the triplet state, which explains why the para isomer has the lowest ΔES-T gap.

Long-range ab initio potential energy surface for the ground electronic state of the ozone molecule with the accurate dissociation asymptote

In this work an excellent agreement was achieved between the empirical (9230.08 ± 4.85 cm−1) and theoretical (9230.70 cm−1) values of the first dissociation limit (De) of O3. Ab initio multireference calculations were performed for the first time using the extended complete active space [CAS(24,15)] reference in the icMRCI(Q) method combined with the extrapolation to the complete basis set limit [CBS(56Z)] and with the inclusion of the spin–orbit coupling between 9 multiplet electronic states approaching De. Finally, the full-dimensional potential energy surface was developed in the scattering coordinates for the long-range region toward De at this level of theory.