Multireference Electronic Structure Research Articles

Nonadiabatic Molecular Dynamics by Multiconfiguration Pair-Density Functional Theory.

We present the first implementation of multiconfiguration pair-density functional theory (MC-PDFT) ab initio molecular dynamics. MC-PDFT is a multireference electronic structure method that in many cases has a similar accuracy (or even better accuracy) the complete active space second-order perturbation theory (CASPT2) at a significantly lower computational cost. In this study, we introduced MC-PDFT analytical gradients into the SHARC molecular dynamics program for ab initio, nonadiabatic molecular dynamics simulations. We verify our implementation by examining the intersystem crossing dynamics of thioformaldehyde, and we observe excellent agreement with recent CASPT2 and experimental findings. Moreover, with MC-PDFT, we could perform dynamics simulations with the 12 electron in 10 orbitals active space that was computationally too expensive for direct dynamics with CASPT2.

SiS Formation in the Interstellar Medium through Si+SH Gas-phase Reactions

Abstract Silicon monosulfide is an important silicon-bearing molecule detected in circumstellar envelopes and star-forming regions. Its formation and destruction routes are not well understood, partially due to the lack of detailed knowledge on the involved reactions and their rate coefficients. In this work we have calculated and modeled the potential energy surface (PES) of the HSiS system employing highly accurate multireference electronic structure methods. After obtaining an accurate analytic representation of the PES, which includes long-range energy terms in a realistic way via the DMBE method, we have calculated rate coefficients for the Si+SH → SiS+H reaction over the temperature range of 25–1000 K. This reaction is predicted to be fast, with a rate coefficient of ∼1 × 10−10 cm3 s−1 at 200 K, which substantially increases for lower temperatures (the temperature dependence can be described by a modified Arrhenius equation with α = 0.770 × 10−10 cm3 s−1, β = −0.756, and γ = 9.873 K). An astrochemical gas-grain model of a shock region similar to L1157-B1 shows that the inclusion of the Si+SH reaction increases the SiS gas-phase abundance relative to H2 from 5 × 10−10 to 1.4 × 10−8, which perfectly matches the observed abundance of ∼2 × 10−8.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiffbase C5H6NH2.

Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2 +, a model of the rhodopsinchromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2 +, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.

High-Lying 31Ag Dark-State-Mediated Singlet Fission.

Singlet fission (SF), the conversion of one high-energy singlet to two low-energy triplets, provides the potential to increase the efficiency of photovoltaic devices. In the SF chromophores with C2h symmetry, exemplified by polyenes, singlet-to-triplet conversion generally involves a low-lying 21Ag dark state, which serves as either a multiexciton (ME) intermediate to promote the SF process or a parasitic trap state to shunt excited-state populations via internal conversion. This controversial behavior calls for a deep understanding of dark-state-related photophysics involving the higher-lying singlet state. However, the optical "dark" and "transient" nature of these dark states and strong correlation feature of double exciton species make their characterization and interpretation challenging from both experimental and computational perspectives. In the present work combining transient spectroscopy and multireference electronic structure calculations (XDW-CASPT2), we addressed a new photophysical model, i.e., a high-lying 31Ag dark-state-mediated ultrafast SF process in the benzodipyrrolidone (BDPP) skeleton. Such a 31Ag dark state with distinctive double excitation character, described as the ME state, could be populated from the initial 11Bu bright state on an ultrafast time scale given the quasi-degeneracy and intersection of the two electronic states. Furthermore, the suitable optical band gap and triplet energy, high triplet yield, and excellent photostability render BDPP a promising SF candidate for photovoltaic devices. These results not only enrich the arsenal of SF materials but also shed new insights into the understanding of dark-state-related photophysics, which could promote the development of new SF-active materials.

Potential energy surface for high-energy N + N2 collisions.

Potential energy surface calculations yield physical insight into the structure of intermediates and the dynamics of molecular collisions, and they are the first step toward molecular simulations that provide physical insight into energy transfer, reaction, and dissociation probabilities. The potential energy surface for high-energy collisions of N2 with N can be used for modeling chemical dynamics and energy transfer in atmospheric shock waves. Here we present an analytic ground-state. (4A'') potential energy surface for N3 that governs electronically adiabatic collisions of N2(1Σ+g) with N(4S). The fitted surface consists of a pairwise potential based on an accurate diatomic potential energy curve plus a connected permutationally invariant polynomial (PIP) in mixed-exponential-Gaussian bond order variables (MEGs) for the three-body part. The three-body fit is based on multireference complete active space second order perturbation theory (CASPT2) calculations. The quality of the quartet N3 fit is comparable to that for a previous fit of the NO2 potential. We characterize two local minima of N3, two tight transition structures, two van der Waals geometries, and the noncollinear reaction path for the symmetric exchange reaction. The nonreactive approach of an N atom to N2 along the perpendicular bisector is more repulsive than the collinear reproach, but plots of the force on the bond versus the potential energy at the distance of closest approach allow us to infer that vibrational energy transfer should occur much more readily in high-energy collinear collisions than in high-energy perpendicular-bisector collisions.

Conformational Control of the Photodynamics of a Bilirubin Dipyrrinone Subunit: Femtosecond Spectroscopy Combined with Nonadiabatic Simulations.

The photochemistry of bilirubin has been extensively studied due to its importance in the phototherapy of hyperbilirubinemia. In the present work, we investigated the ultrafast photodynamics of a bilirubin dipyrrinone subunit, vinylneoxanthobilirubic acid methyl ester. The photoisomerization and photocyclization reactions of its (E) and (Z) isomers were studied using femtosecond transient absorption spectroscopy and by multireference electronic structure theory, where the nonadiabatic dynamics was modeled with a Landau-Zener surface hopping technique. The following picture has emerged from the combined theoretical and experimental approach. Upon excitation, dipyrrinone undergoes a very fast vibrational relaxation, followed by an internal conversion on a picosecond time scale. The internal conversion leads either to photoisomerization or regeneration of the starting material. Further relaxation dynamics on the order of tens of picoseconds was observed in the ground state. The nonadiabatic simulations revealed a strong conformational control of the photodynamics. The ultrafast formation of a cyclic photochemical product from a less-populated conformer of the studied subunit was predicted by our calculations. We discuss the relevance of the present finding for the photochemistry of native bilirubin. The work has also pointed to the limits of semiclassical nonadiabatic simulations for simulating longer photochemical processes, probably due to the zero-point leakage issue.

Multireference Description of Nickel-Aryl Homolytic Bond Dissociation Processes in Photoredox Catalysis.

Multireference electronic structure calculations consistent with known experimental data have elucidated a novel mechanism for photo-triggered Ni(II)-C homolytic bond dissociation in Ni 2,2'-bipyridine (bpy) photoredox catalysts. Previously, a thermally assisted dissociation from the lowest energy triplet ligand field excited state was proposed and supported by density functional theory (DFT) calculations that reveal a barrier of ∼30 kcal mol-1. In contrast, multireference ab initio calculations suggest that this process is disfavored, with barrier heights of ∼70 kcal mol-1, and highlight important ligand noninnocent and multiconfigurational contributions to excited state relaxation and bond dissociation processes that are not captured with DFT. In the multireference description, photo-triggered Ni(II)-C homolytic bond dissociation occurs via initial population of a singlet Ni(II)-to-bpy metal-to-ligand charge transfer (1MLCT) excited state, followed by intersystem crossing and aryl-to-Ni(III) charge transfer, overall a formal two-electron transfer process driven by a single photon. This results in repulsive triplet excited states from which spontaneous homolytic bond dissociation can occur, effectively competing with relaxation to the lowest energy nondissociative triplet Ni(II) ligand field excited state. These findings guide important electronic structure considerations for the experimental and computational elucidation of the mechanisms of ground and excited state cross-coupling catalysis mediated by Ni heteroaromatic complexes.

Ultraviolet photodissociation of gas-phase transition metal complexes: dicarbonylcyclopentadienyliodoiron(II)

The ultraviolet photodissociation of the prototypical organometallic half-sandwich compound dicarbonylcyclopentadienyliodoiron(II) [η 5-CpFe(CO)2I] has been studied in the gas phase across the wavelength range 260 ≤ λ ≤ 310 nm using multi-mass velocity-map ion imaging with photoproducts detected using both resonance enhanced multiphoton and vacuum ultraviolet (λ = 118.2 nm) single photon ionisation methods. Ion images recorded for the atomic iodine and the cyclopentadienyl photoproducts reveal fast, anisotropic components to their recoil velocity distributions. The experimental work is supported by multi-reference (spin–orbit averaged) electronic structure calculations that suffice to illustrate the high electronic state density in such transition metal complexes and provide insights into the rival fragmentation dynamics. The ground state parent molecule has singlet spin multiplicity, but the product energy disposal measured following Fe–Cp bond fission shows the involvement of nominally spin-forbidden transitions. The Fe–I and Fe–Cp bond fissions should both be viewed as homolytic and occurring on excited state potentials that are dissociative in the relevant ligand elimination coordinate.

Describing Strong Correlation with Block-Correlated Coupled Cluster Theory.

A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide satisfactory descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single C-C bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all C-C bonds.

Extending the ASS1ST Active Space Selection Scheme to Large Molecules and Excited States

Multireference electronic structure methods based on the CAS (complete active space) Ansatz are well established as means to provide reliable predictions of physical properties of strongly correlated systems. A critical aspect of every CAS calculation is the selection of an adequate active space, in particular as the boundaries for tractable active spaces have been shifted significantly with the emergence of efficient approximations to the Full-CI problem like the Density Matrix Renormalization Group and Full-CI Quantum Monte Carlo. Recently, we proposed an Active Space Selection based on 1st order perturbation theory (ASS1ST) that yields satisfactory results for the electronic ground state of a variety strongly correlated systems. In this work we present a state-averaged extension of ASS1ST (SA-ASS1ST) that determines suitable active spaces when electronically excited state are targeted. Furthermore, the computational cost of the single state and state-averaged variants are significantly reduced by a simple approximation that avoids the most expensive step of the original method, the evaluation of active space four-electron reduced density matrices, altogether. After the applicability of the approximation is established test calculations on a biomimetic \ce{Mn4O4} cluster demonstrate the enhanced range of ASS1ST in terms of system size and complexity. Furthermore, calculations on \ce{[VOCl4]2-}, \ce{MeMn(CO)3}-$\alpha$-diimine and anthracene show that SA-ASS1ST suggests well-suited active spaces to describe d$\rightarrow$d and charge-transfer excitations in transition metal complexes as well as $\pi\rightarrow\pi^*$ excitations in aryl compounds. Finally the application of ASS1ST on multiple points of the potential energy surface of Cr 2 illustrates the applicability of the method even when extremely complicated bonding patterns are met. More importantly, however, it highlights the necessity to use special strategies when different points of a potential energy surface are investigated, e.g. during chemical reactions.

Understanding the Role of Aromaticity and Conformational Changes in Bond Dissociation Processes of Photo-Protecting Groups.

Photoremovable protecting groups (PPGs) provide spatial and temporal control over the release of various chemicals. Using surface hopping studies with multireference electronic structure methods we have unravelled the nuclear and the electronic events at play. Furthermore, the electronic changes along the reaction path were probed using excited state aromaticity quantifiers and orbital analysis. We find that upon irradiation with light of appropriate wavelength on the substituted coumarin system a π-π* electronic excitation occurs which is followed by an electron loss from the aromatic ring on gaining proper alignment between the π* and the C-LG (LG = leaving group) σ*. This alignment is brought about by a critical dihedral angle change in the molecule, which subsequently triggers C-LG bond cleavage. The sequence of events is indicative of an intramolecular electron catalyzed process which is established through investigations of changes in aromaticity of the phenyl ring which acts as an electron reservoir.

Reaction Profiles and Kinetics for Radical-Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory.

Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H2+ Be, H + NH2 → H2 + NH, CH3 + C2H5 → CH4 + C2H4, H + C2H5 → H2 + C2H4, and H + HCO → H2 + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH2, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH3 + C2H5, H + C2H5, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.

Two-layer Gaussian-based MCTDH study of the S1 ← S vibronic absorption spectrum of formaldehyde using multiplicative neural network potentials

The absorption spectrum of the vibronically allowed S1(1A2) ← S0(1A1) transition of formaldehyde is computed by combining multiplicative neural network (NN) potential surface fits, based on multireference electronic structure data, with the two-layer Gaussian-based multiconfiguration time-dependent Hartree (2L-GMCTDH) method. The NN potential surface fit avoids the local harmonic approximation for the evaluation of the potential energy matrix elements. Importantly, the NN surface can be constructed so as to be physically well-behaved outside the domain spanned by the ab initio data points. A comparison with experimental results shows spectroscopic accuracy of the converged surface and 2L-GMCTDH quantum dynamics.

Photoinduced Formation of H-Bonded Ion Pair in HCFC-133a.

High-level multireference electronic structure calculations have been performed to study the Cl- yield from photoexcited CF3CH2Cl (HCFC-133a). The analysis of this process tells that it relates to an electron transfer from the carbon to the Cl atom, forming a highly polar contact ion-pair complex, CF3HCH+···Cl-, in the excited (S3) state. This complex has a strong binding energy of 3.53 eV, from which 0.47 eV is due to an underlying hydrogen bond. Through comparison with the results obtained for the prototype CH3Cl system, where a similar ion-pair state associated with Cl- formation has also been observed, it is suggested that photodissociation of HCFC-133a can also yield Cl- through an analogous process. This hypothesis is further supported by nonadiabatic dynamics simulations, which shows formation of the ion-pair complex in the subpicosecond time scale.

Electron-Coupled Double Proton Transfer in the Slr1694 BLUF Photoreceptor: A Multireference Electronic Structure Study.

Photoreceptor proteins control vital cellular responses to light. The photocycle of the Slr1694 blue light using flavin photoreceptor is initiated by photoexcitation to a locally excited state within the flavin, followed by electron transfer from Tyr8 to the flavin and a proton relay from Tyr8 to the flavin via an intervening glutamine. Herein, the two-dimensional excited state potential energy surfaces associated with this double proton-transfer reaction are computed using the complete active space self-consistent-field method and multiconfigurational perturbation theory, including the protein and solvent environment with electrostatic embedding. The double proton-transfer reaction was found to be energetically unfavorable in the ground state and locally excited state but energetically favorable in the charge-transfer state corresponding to electron transfer from Tyr8 to the flavin. These results indicate that the proton-coupled electron transfer process is sequential, with electron transfer preceding double proton transfer, and that the double proton-transfer reaction is also sequential, with proton transfer from Tyr8 to Gln50 followed by proton transfer from Gln50 to the flavin. The barrier is lower for the first proton-transfer reaction, and both barriers are significantly influenced by geometrical changes within the active site, particularly the proton donor-acceptor distance as well as the protein environment. These calculations provide insight into the impact of protein reorganization and electrostatics on the excited electronic states prior to and during the double proton-transfer reaction. This interplay between excited states and the environment has implications for other photoreceptor proteins.

A comprehensive benchmark of the XMS-CASPT2 method for the photochemistry of a retinal chromophore model

ABSTRACTThe performance of the extended multi-state (XMS)-complete active space second-order perturbation theory (CASPT2) method has been assessed for the benchmark of a truncated retinal model, the penta-2,4-dieniminium cation (PSB3). This benchmark presents a challenge for multireference electronic structure methods because the wave function character is changing considerably. The assessment comprises ground and excited state pathways of the isomerisation, including transition states and conical intersection (CI) points. It also includes circular paths centred around different CIs, and 2D potential energy scans located in the branching planes. In this work, we compare the performance of the previous formulations of CASPT2, the single-state and the multi-state, with the recently developed XMS-CASPT2. Besides, we have also tested two variants of internal contraction in XMS-CASPT2, namely, the single-state single reference (SS-SR) and multi-state multireference (MS-MR) schemes. In our study, we find that XMS-CASPT2 corrects the artefacts and discontinuities present in other CASPT2 variants. The investigation of a circular loop and 2D potential energy surfaces around the surface crossing point shows that XMS-CASPT2 exhibits a smooth topology at the CI with the correct degeneracy. It also agrees better with the reference method MRCISD+Q in regions of the potential energy surfaces further away from CIs. Another observation is the close agreement between the results from the SS-SR contraction scheme and the more demanding MS-MR scheme.

Photochemistry of CF3Cl: Quenching of Charged Fragments Is Caused by Nonadiabatic Effects.

For the first time, high-level multireference electronic structure calculations have been performed to study the photochemistry of CF3Cl, allowing a comprehensive interpretation and assignment of experimental data concerning fluorescence, ion-pair formation, and generation of CF3 fragments in several electronic states. All studied dissociation channels correlate either with Cl or Cl- in the ground state. On the other hand, a CF3 fragment can be generated either in the ground or excited state. A rationalization for the nonadiabatic relaxation of CF3Cl, including the formation of an (n4s) stable state and internal conversion at multiple-state intersections, has been provided. Our results explain the anomalous quenching of a charged fragment after low-energy excitation, a fact experimentally observed by separate groups. We show that the CF3+···Cl- ion pair undergoes an internal conversion to the ground state, producing neutral CF3 and Cl fragments. The results also allow understanding as to why CF3Cl is usually a nonemitting species and how UV emission could be induced.

Investigations of the Magnetic and Spectroscopic Properties of V(III) and V(IV) Complexes.

Herein, we utilize a variety of physical methods including magnetometry (SQUID), electron paramagnetic resonance (EPR), and magnetic circular dichroism (MCD), in conjunction with high-level ab initio theory to probe both the ground and ligand-field excited electronic states of a series of V(IV) ( S = 1/2) and V(III) ( S = 1) molecular complexes. The ligand fields of the central metal ions are analyzed with the aid of ab initio ligand-field theory (AILFT), which allows for a chemically meaningful interpretation of multireference electronic structure calculations at the level of the complete-active-space self-consistent field with second-order N-electron valence perturbation theory. Our calculations are in good agreement with all experimentally investigated observables (magnetic properties, EPR, and MCD), making our extracted ligand-field theory parameters realistic. The ligand fields predicted by AILFT are further analyzed with conventional angular overlap parametrization, allowing the ligand field to be decomposed into individual σ- and π-donor contributions from individual ligands. The results demonstrate in VO2+ complexes that while the axial vanadium-oxo interaction dominates both the ground- and excited-state properties of vanadyl complexes, proximal coordination can significantly modulate the vanadyl bond covalency. Similarly, the electronic properties of V(III) complexes are particularly sensitive to the available σ and π interactions with the surrounding ligands. The results of this study demonstrate the power of AILFT-based analysis and provide the groundwork for the future analysis of vanadium centers in homogeneous and heterogeneous catalysts.

Automated Construction of Molecular Active Spaces from Atomic Valence Orbitals.

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multiconfiguration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wave function (such as from a Hartree-Fock or Kohn-Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition-metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not a universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition-metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results.

Ab Initio Ligand-Field Theory Analysis and Covalency Trends in Actinide and Lanthanide Free Ions and Octahedral Complexes.

Actinide chemistry is gaining increased focus in modern research, particularly in the fields of energy research and molecular magnetism. However, the structure-function and structure-property relationships of actinides have still not been studied as intensely as those for transition metals. In this work, we report a detailed ab initio study of the spectroscopic, magnetic, and bonding properties of the trivalent actinide free ions and their associated hexachloride complexes in octahedral symmetry. The electronic structures of these systems are examined using complete active-space self-consistent-field calculations followed by second-order N-electron valence perturbation theory, including both scalar relativistic and spin-orbit-coupling effects. The computed energies and wave functions are further analyzed by means of ab initio ligand-field theory (AILFT) and finally chemically interpreted by means of the angular overlap model (AOM). The derived Slater-Condon and spin-orbit parameters have allowed us to systematically rationalize the spectroscopic and magnetic properties of the investigated free ions and complexes along the entire actinide series. Overall, the AILFT- and AOM-derived parameters accurately reproduce the multireference electronic structure calculations. The small observed discrepancies with respect to experimentally derived ligand-field parameters are essentially due to an underestimation of the electronic correlation, which arises from both the constrained size of the active space (restricted to the f orbitals) and the limit of the perturbation approach to account for dynamical correlation. Our analysis also provides insight into the metal-ligand covalency trends along the series. Consistent with natural population analysis, the nephelauxetic (Slater-Condon parameters) and relativistic nephelauxetic (spin-orbit-coupling) reductions determined for these complexes indicate a decrease in the covalency along the series. These trends also hold, to varying extents, for the corresponding tetravalent derivatives, as well as the lanthanide analogues.