Active Space Second-order Perturbation Theory Research Articles

Ab Initio Calculation of UV-vis Absorption of Parent Mg, Fe, Co, Ni, Cu, and Zn Metalloporphyrins.

Relativistic restricted active space (RAS) second-order multireference perturbation theory (MRPT2) methods, incorporating spin-orbit (SO) coupling perturbatively via state interaction (SO-MRPT2/RASSCF), were used to reproduce the absorption spectra of parent metalloporphyrins containing the Mg2+, Zn2+, Co2+, Ni2+, Cu2+, or FeCl2+ ions in the 12,500-40,000 cm-1 region. Particular attention was paid to the interaction between the porphyrin ring and the metal 3d electrons in states of different multiplicities (we used metal 3d and double d-shell or 3d' orbitals). For this class of compounds, the N-electron valence state perturbation theory (NEVPT2) method is superior to the complete active space perturbation theory (CASPT2) and successfully reproduces the energies of all four characteristic transitions (Q, B, N, and L) of closed-shell metalloporphyrins. Inclusion of SO coupling was found to have very little effect on excitation energies and oscillator strengths. For FeCl2+ porphyrin, we treated ligand-to-metal charge-transfer (LMCT; π,d), metal ligand field (d,d), and metal-to-ligand charge-transfer (MLCT; d,π*) transitions within the same framework. The broad and intense spectral features associated with its B (Soret) band are attributed to multiconfigurational LMCT (d,π*) bands involving strong metal-ligand orbital mixing.

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.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections.

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Toward a Stochastic Complete Active Space Second-Order Perturbation Theory.

In this work, an internally contracted stochastic complete active space second-order perturbation theory, stochastic-CASPT2, is reported. The method relies on stochastically sampled reduced density matrices (RDMs) up to rank four and contractions thereof with the generalized Fock matrix. A new protocol for calculating higher-order RDMs in full configuration interaction quantum Monte Carlo (FCIQMC) has been designed based on (1) restricting sampling of the corresponding excitations to a deterministic subspace, (2) averaging the RDMs from independent dynamics and (3) projecting them onto the closest positive semi-definite matrix. Our protocol avoids previously encountered numerical conditioning problems in the orthogonalization of the perturber overlap matrix stemming from numerical noise. The chromium dimer CASSCF(12,12)/CASPT2 binding curve is computed as a proof of concept.

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.

Interpreting the Cu-O2 Antibonding Nature in Two Cu-O2 Complexes from Cu L-Edge X-ray Absorption Spectra.

Cu-O2 structures play important roles in bioinorganic chemistry and enzyme catalysis, where the bonding between the Cu and O2 parts serves as a fundamental research concern. Here, we performed a multiconfigurational study on the copper L2,3-edge X-ray absorption spectra (XAS) of two copper enzyme model complexes to gain a better understanding of the antibonding nature from the clearly interpreted structure-spectroscopy relation. We obtained spectra in good agreement with the experiments by using the restricted active space second-order perturbation theory (RASPT2) method, which facilitated reliable chemical analysis. Spectral feature interpretations were supported by computing the spin-orbit natural transition orbitals. All major features were assigned to be mainly from Cu 2p to antibonding orbitals between Cu 3d and O2 π*, Cu 3d-πO-O* (type A), and a few also to mixed antibonding/bonding orbitals between Cu 3d and O2 π, Cu 3d ± πO-O (type M). Our calculations provided a clear illustration of the interactions between Cu 3d and O2 π*/π orbitals that are carried in the metal L-edge XAS.

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.

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.

A Combined Wave Function and Density Functional Approach for K-Edge X-ray Absorption Near-Edge Spectroscopy: A Case Study of Hydrated First-Row Transition Metal Ions.

The prediction of X-ray absorption spectra (XAS) of transition metal complexes has important and broad application areas in chemistry and biology. In this letter, we have investigated the predictive ability of multiconfiguration pair-density functional theory (MC-PDFT) for X-ray absorption spectra by calculating the metal K pre-edge features of aquated 3d transition metal ions in common oxidation states. MC-PDFT results were compared with experimentally measured spectra as well as analyzed against results from restricted active-space second-order perturbation theory (RASPT2) and time-dependent density functional theory (TDDFT). As expected, TDDFT performs well for excited states that can be accurately represented by singly excited configurations but fails for excited states where higher order excitations become important. On the other hand, both RASPT2 and MC-PDFT provide quantitatively accurate results for all excited states irrespective of their character. While core-level spectroscopy with RASPT2 is accurate, it is computationally expensive. Our results show that MC-PDFT performs equally well with significantly lower computational cost and is an encouraging alternate approach for X-ray spectroscopies.

Electron Trap Depths in Cubic Lutetium Oxide Doped with Pr and Ti, Zr or Hf─From Ab Initio Multiconfigurational Calculations.

We propose a universal approach to model intervalence charge transfer (IVCT) and metal-to-metal charge transfer (MMCT) transitions between ions in solids. The approach relies on already well-known and reliable ab initio RASSCF/CASPT2/RASSI-SO calculations for a series of emission center coordination geometries (restricted active space self-consistent field, complete active space second-order perturbation theory, and restricted active space state interaction with spin-orbit coupling). Embedding with ab initio model potentials (AIMPs) is used to represent the crystal lattice. We propose a way to construct the geometries via interpolation of the coordinates obtained using solid-state density functional theory (DFT) calculations for the structures where the activator metal is at specific oxidation (charge) states of interest. The approach thus takes the best of two worlds: the precision of the embedded cluster calculations (including localized excited states) and the geometries from DFT, where the effects of ionic radii mismatch (and eventual nearby defects) can be modeled explicitly. The method is applied to the Pr activator and Ti, Zr, Hf codopants in cubic Lu2O3, in which the said ions are used to obtain energy storage and thermoluminescence properties. Electron trap charging and discharging mechanisms (not involving a conduction band) are discussed in the context of the IVCT and MMCT role in them. Trap depths and trap quenching pathways are analyzed.

Analytic first-order derivatives of CASPT2 with IPEA shift.

Complete active space second-order perturbation theory (CASPT2) is useful for accurately predicting properties of complex electronic structures, but it is well known that it systematically underestimates excitation energies. The underestimation can be corrected using the ionization potential-electron affinity (IPEA) shift. In this study, analytic first-order derivatives of CASPT2 with the IPEA shift are developed. CASPT2-IPEA is not invariant with respect to rotations among active molecular orbitals, and two additional constraint conditions are necessary in the CASPT2 Lagrangian to formulate analytic derivatives. The method developed here is applied to methylpyrimidine derivatives and cytosine, and minimum energy structures and conical intersections are located. By comparing energies relative to the closed-shell ground state, we find that the agreement with experiments and high-level calculations is indeed improved by the inclusion of the IPEA shift. The agreement of geometrical parameters with high-level calculations may also be improved in some cases.

Importance of Dispersion in the Molecular Geometries of Mn(III) Spin-Crossover Complexes

The computational investigation of the molecular geometries of a pair of manganese(III) spin-crossover complexes is reported. For the geometry of the quintet high-spin state, density functionals significantly overestimate Mn-Namine bond distances, although the geometry for the triplet intermediate-spin state is well described. Comparisons with several wave function-based methods demonstrate that this error is due to the limited ability of commonly used density functionals to recover dispersion beyond a certain extent. Among the methods employed for geometry optimization, restricted open-shell Møller-Plesset perturbation theory (MP2) appropriately describes the high-spin geometry but results in a slightly shorter Mn-O distance in both spin states. On the other hand, extended multistate complete active space second-order perturbation theory (XMS-CASPT2) provides a good description of the geometry for the intermediate-spin state but also sufficiently recovers dispersion, performing well for the high-spin state. Despite the fact that the electronic structure of both spin states is dominated by one-electron configuration, XMS-CASPT2 offers a balanced approach, leading to molecular geometries with much better agreement with experiment than MP2 and DFT. A scan along the Mn-Namine bond demonstrates that for these complexes coupled cluster methods (i.e., DLPNO-CCSD(T)) also yield bond distances in agreement with experiment while multiconfiguration pair density functional theory (MC-PDFT) is unable to recover dispersion well enough, analogous to single-reference DFT.

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.

Chemical Bonding in Isoelectronic NdO2and SmO22+

Neodymium dioxide (NdO2) and samarium dioxide cation (SmO22+) are isoelectronic molecules. Here we used calculations of the spin-orbit-free wave functions to study and compare their geometries, spin states, and bonding. We used Kohn-Sham density functional theory with the B97-1 exchange-correlation functional to optimize the geometries and found that the two molecules have different ground spin states and structures. NdO2 favors a linear ONdO triplet structure, and SmO22+ favors a linear SmOO2+ quintet structure. We then used state-averaged complete-active-space self-consistent-field (SA-CASSCF) calculations to investigate the bonding characteristics of NdO2 and SmO22+ in various geometries. We found that in NdOO, one electron is transferred from Nd to O, while in SmO22+, there is no electron transfer between Sm and O. The SA-CASSCF calculation also shows that ONdO has a stronger bonding orbital between a 4f orbital of Nd and a pz orbital of oxygen atoms. We compared three multireference methods, namely, extended multistate complete active space second-order perturbation theory (XMS-CASPT2), extended multistate pair-density functional theory (XMS-PDFT), and compressed multistate pair-density functional theory (CMS-PDFT), for calculating the spin-orbit-free energies of various isomers of both molecules. We found that although XMS-PDFT and CMS-PDFT are at the same cost level as SA-CASSCF, they give results with the same accuracy as given for the much more demanding XMS-CASPT2 calculation. Between the two multistate PDFT methods, CMS-PDFT is better at giving good degeneracies for states that should be degenerate.

Tuning functionalized hexagonal boron nitride quantum dots for full visible-light fluorescence emission.

Tunable photoluminescence has been observed in hexagonal boron nitride quantum dots (BNQDs), but the underlying luminescence mechanism remains elusive. In this study, we examine excited-state properties of several functionalized BNQDs models using density functional theory (DFT), time-dependent DFT, and multistate complete active space second-order perturbation theory (MS-CASPT2) methods. Unlike reported graphene quantum dots, photoluminescence of BNQDs is not affected by their sizes (<2.5 nm). Instead, the embedded single sp3 carbon atom connecting different functional groups can tune emission colors of BNQDs, whose emission wavelength cover full range of visible light and even extend toward near-infrared region. Further analysis reveals that both exciton self-trapping and electron-hole separation decrease HOMO-LUMO energy gaps, leading to large Stokes shifts. Moreover, uneven and even hybridizations induce blue- and red-shifted emission spectra. These findings provide novel insights into full-spectrum emission of BNQDs modified with functional groups.

Thermally activated delayed fluorescence of a Ir(III) complex: absorption and emission properties, nonradiative rates, and mechanism.

One recent experimental study reported a Ir(III) complex with thermally activated delayed fluorescence (TADF) phenomenon in solution, but its luminescent mechanism is elusive. In this work, we combined density functional theory (DFT), time-dependent DFT (TDDFT) and multi-state complete active space second-order perturbation theory (MS-CASPT2) methods to investigate excited-state properties, photophysics, and emission mechanism of this Ir(III) complex. Two main absorption bands observed in experiments can be attributed to the electronic transition from the S0 state to the S1 and S2 states; while, the fluorescence and phosphorescence are generated from the S1 and T1 states, respectively. Both the S1 and T1 states have clear metal-to-ligand charge transfer (MLCT) character. The present computational results reveal a three-state model including the S0, S1 and T1 states to rationalize the TADF behavior. The small energy gap between the S1 and T1 states benefits the forward and reverse intersystem crossing (ISC and rISC) processes. At 300 K, the rISC rate is five orders of magnitude larger than the phosphorescence rate therefore enabling TADF. At 77 K, the rISC rate is sharply decreased but remains close to the phosphorescence rate; therefore, in addition to the phosphorescence, the delayed fluorescence could also contribute to the experimental emission. The estimated TADF lifetime agrees well with experiments, 9.80 vs. 6.67 μs, which further verifies this three-state model.

On the photorelease of nitric oxide by nitrobenzene derivatives: A CASPT2//CASSCF model.

Nitroaromatic compounds can photorelease nitric oxide after UV absorption. The efficiency of the photoreaction depends on the molecular structure, and two features have been pointed out as particularly important for the yield of the process: the presence of methyl groups at the ortho position with respect to the nitro group and the degree of conjugation of the molecule. In this paper, we provide a theoretical characterization at the CASPT2//CASSCF (complete active space second-order perturbation theory//complete active space self-consistent field) level of theory of the photorelease of NO for four molecules derived from nitrobenzene through the addition of ortho methyl groups and/or the elongation of the conjugation. Our previously described mechanism obtained for the photorelease of NO in nitrobenzene has been adopted as a model for the process. According to this model, the process proceeds through a reactive singlet-triplet crossing (STC) region that the system can reach from the triplet 3(πOπ*) minimum. The energy barrier that must be surmounted in order to populate the reactive STC can be associated with the efficiency of the photoreaction. Here, the obtained results display clear differences in the efficiency of the photoreaction in the studied systems and can be correlated with experimental results. Thus, the model proves its ability to highlight the differences in the photoreaction efficiency for the nitroaromatic compounds studied here.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits.

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet–triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn–Sham density functional theory for singlet–triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates.

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Resolving Ultrafast Photoinitiated Dynamics of the Hachimoji 5-aza-7-deazaguanine Nucleobase: Impact of Synthetically Expanding the Genetic Alphabet†.

The guanine derivative, 5-aza-7-deazaguanine (5N7C G) has recently been proposed as one of four unnatural bases, termed Hachimoji (8-letter) to expand the genetic code. We apply steady-state and time-resolved spectroscopy to investigate its electronic relaxation mechanism and probe the effect of atom substitution on the relaxation mechanism in polar protic and polar aprotic solvents. Mapping of the excited state potential energy surfaces is performed, from which the critical points are optimized by using the state-of-art extended multi-state complete active space second-order perturbation theory. It is demonstrated that excitation to the lowest energy 1 ππ* state of 5N7C G results in complex dynamics leading to ca. 10- to 30-fold slower relaxation (depending on solvent) compared with guanine. A significant conformational change occurs at the S1 minimum, resulting in a 10-fold greater fluorescence quantum yield compared with guanine. The fluorescence quantum yield and S1 decay lifetime increase going from water to acetonitrile to propanol. The solvent-dependent results are supported by the quantum chemical calculations showing an increase in the energy barrier between the S1 minimum and the S1 /S0 conical intersection going from water to propanol. The longer lifetimes might make 5N7C G more photochemically active to adjacent nucleobases than guanine or other nucleobases within DNA.