N-electron Valence State Perturbation Theory Research Articles

Auxiliary Atomic Relay Center Facilitates Enhanced Magnetic Couplings in Blatter's Radical.

The recent accomplishments in obtaining strong ferromagnetic exchange interactions in organic diradicals have made the field quite fascinating and even more promising toward its technological applications. In this context, herein, we report a unique combination of remarkably strong ferromagnetic exchange interactions coupled with molecular rigidity, utilizing superstable Blatter's radical as a spin source. The planar analogues of the parent Blatter's radical obtained by annulation with a chalcogen coupled to nitronyl nitroxide (NN) are investigated using density functional theory along with the wave function-based multiconfigurational self-consistent field methods, for example, complete active space self-consistent field (CASSCF)-N-electron valence state perturbation theory (NEVPT2). The calculations reveal phenomenal modulation in exchange couplings upon annulation such that remarkably strong ferromagnetic interactions are realized especially for a certain class of the Blatter-NN diradicals. The modulation of spin-spin interactions is rationalized by variation in spin density distribution and molecular torsional angles. We demonstrate that annulation in OMMs opens an additional coupling pathway via auxiliary X-atom acting as the atomic relay center which strongly manipulates the magnitude of exchange couplings.

Excited states in the adiabatic connection fluctuation-dissipation theory: Recovering missing correlation energy from the negative part of the density response spectrum.

The adiabatic connection (AC) theory offers an alternative to the perturbation theory methods for computing correlation energy in the multireference wavefunction framework. We show that the AC correlation energy formula can be expressed in terms of the density linear response function as a sum of components related to positive and negative parts of the transition energy spectrum. Consequently, generalization of the adiabatic connection fluctuation-dissipation theory to electronically excited states is obtained. The component of the linear response function related to the negative-transition energy enters the correlation energy expression with an opposite sign to that of the positive-transition part and is non-negligible in the description of excited states. To illustrate this, we analyze the approximate AC model in which the linear response function is obtained in the extended random phase approximation (ERPA). We demonstrate that AC can be successfully combined with the ERPA for excited states, provided that the negative-excitation component of the response function is rigorously accounted for. The resulting AC0D model, an extension of the AC0 scheme introduced in our earlier works, is applied to a benchmark set of singlet excitation energies of organic molecules. AC0D constitutes a significant improvement over AC0 by bringing the excitation energies of the lowest excited states to a satisfactory agreement with theoretical best estimates, which parallels or even exceeds the accuracy of the n-electron valence state perturbation theory method. For higher excitations, AC0D is less reliable due to the gradual deterioration of the underlying ERPA linear response.

Optoelectronic properties of diketopyrrolopyrrole homopolymers compared to donor-acceptor copolymers.

Diketopyrrolopyrrole (DPP) is a component of a large number of materials used for optoelectronic applications. As it is exclusively used in combination with aromatic donors, the properties of its homopolymers are unknown. Because donor-acceptor character has been shown for other systems to reduce bandwidths, DPP homopolymers should have even larger conduction bands and better n-type conductivity than the thiophene-flanked systems, which have exceptional n-type conductivity and ambipolar character. Therefore, a theoretical study was carried out to elucidate the properties of the unknown DPP homopolymer. Calculations were done with density functional theory and with the complete active space self-consistent field method plus n-electron valence state perturbation theory for the dynamic correlation. Poly-DPP is predicted to have radical character and an extremely wide low-lying conduction band. If it were possible to produce this material, it should have unprecedented n-type conductivity and might be a synthetic metal. A comparison with various unknown donor-acceptor systems containing vinyl groups and thienyl rings with a higher concentration of DPP than the known copolymers reveals how donor-acceptor substitution reduces bandwidths and decreases electron affinities.

A Molecular Crystal Shows Multiple Correlated Magnetic and Ferroelectric Switchings

Simultaneous control of the magnetic and electric properties of materials is crucial for their application in next-generation memory and sensor devices. Herein, we report a single-crystal Co(II) co...

Efficient multireference perturbation theory without high-order reduced density matrices.

We present a stochastic approach to perform strongly contracted n-electron valence state perturbation theory (SC-NEVPT), which only requires one- and two-body reduced density matrices, without introducing approximations. We use this method to perform SC-NEVPT2 for complete active space self-consistent field wave functions obtained from selected configuration interaction, although the approach is applicable to a larger class of wave functions, including those from orbital-space variational Monte Carlo. The accuracy of this approach is demonstrated for small test systems, and the scaling is investigated with the number of virtual orbitals and the molecule size. We also find the SC-NEVPT2 energy to be relatively insensitive to the quality of the reference wave function. Finally, the method is applied to the Fe(II)-porphyrin system with a (32e, 29o) active space and to the isomerization of [Cu2O2]2+ in a (28e, 32o) active space.

Probing ultrafast reaction mechanisms of photo-excited dithizone through transient absorption spectroscopy and computational CASSCF studies

Dithizone, with its derivatives and complexes, is characterized by seven classes of chromic reactions, which make it a remarkable candidate for diverse sensor applications. We now present dithizone’s chromic response to experimental photoexcitation as studied by ultrafast laser spectroscopy, density functional theory (DFT), and complete active space self-consistent field (CASSCF) calculations. After vertical excitation to the first excited state, within 240 fs the reaction proceeds towards an intersystem crossing (ISC) that is coupled with a conical intercept (CI), while the second path proceeds via a second CI. The ISC leads to excited state tautomerization within 1.6 ps to form a triplet excited state product that takes a longer time to return back to reactant ( ∼ 5 n s ), while the first and second CIs both lead to the ground state within 1.6 ps and 12 ps, respectively. Additionally, dynamics through both CIs allow for efficient repopulation of the reactant ground state. Theoretical calculations using minimum energy path analysis and CASSCF calculation (including n-electron valence state perturbation theory multireference perturbation theory correction) gave additional insight into ground and excited state conformational changes that are observed by means of experimental femtosecond laser pulse excitations of dithizone.

DFT, DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine.

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T1 and T2 diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.

Model Dimeric Manganese(IV) Complexes Featuring Terminal Tris-hydroxotetraazaadamantane and Various Bridging Ligands.

A series of model dinuclear manganese(IV) complexes of the general formula [(H3COH)(L')MnIV(μ-L)2MnIV(L')(HOCH3)] is presented. These compounds feature capping 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands derived from a polydentate oxime compound (L'). The bridging ligands L include azide (1), methoxide (2), and oxalate (3) anions. The magnetic properties and high-field (HF) EPR spectra of 1-3 were studied in detail and revealed varying weak antiferromagnetic coupling and modest zero-field splitting (ZFS) of the local quartet spin sites. Our HF EPR studies provide insight into the dimer ZFS, including determination of the corresponding parameters by giant spin approach for methoxido-bridged complex 2. Furthermore, the physicochemical properties of 1-3 were studied using IR, UV-vis, and electrochemical (cyclic voltammetry) methods. Theoretical exchange coupling constants were obtained using broken-symmetry (BS) density functional theory (DFT). Computational estimates of the local quartet ground spins state ZFSs of 1-3 were obtained using coupled-perturbed (CP) DFT and complete active space self-consistent field (CASSCF) calculations with n-electron valence state perturbation theory (NEVPT2) corrections. We found that the CP DFT calculations which used the B3LYP functional and models derived experimental structures performed best in reproducing both the magnitude and the sign of the experimental D values. Moreover, our computational investigation of 1-3 suggests that we observe metals sites which have an increased +3 character and are supported by redox noninnocent 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands. The latter conclusion is further corroborated by the observation that the free ligand can be readily oxidized to yield a NO-based radical.

Electronically Asynchronous Transition States for C-N Bond Formation by Electrophilic [CoIII(TAML)]-Nitrene Radical Complexes Involving Substrate-to-Ligand Single-Electron Transfer and a Cobalt-Centered Spin Shuttle.

The oxidation state of the redox noninnocent tetra-amido macrocyclic ligand (TAML) scaffold was recently shown to affect the formation of nitrene radical species on cobalt(III) upon reaction with PhI=NNs [van LeestN. P.; J. Am. Chem. Soc.2020, 142, 552−56331846578]. For the neutral [CoIII(TAMLsq)] complex, this leads to the doublet (S = 1/2) mono-nitrene radical species [CoIII(TAMLq)(N•Ns)(Y)] (bearing an unidentified sixth ligand Y in at least the frozen state), while a triplet (S = 1) bis-nitrene radical species [CoIII(TAMLq)(N•Ns)2]– is generated from the anionic [CoIII(TAMLred)]– complex. The one-electron-reduced Fischer-type nitrene radicals (N•Ns–) are formed through single (mono-nitrene) or double (bis-nitrene) ligand-to-substrate single-electron transfer (SET). In this work, we describe the reactivity and mechanisms of these nitrene radical complexes in catalytic aziridination. We report that [CoIII(TAMLsq)] and [CoIII(TAMLred)]– are both effective catalysts for chemoselective (C=C versus C–H bonds) and diastereoselective aziridination of styrene derivatives, cyclohexane, and 1-hexene under mild and even aerobic (for [CoIII(TAMLred)]–) conditions. Experimental (Hammett plots; [CoIII(TAML)]-nitrene radical formation and quantification under catalytic conditions; single-turnover experiments; and tests regarding catalyst decomposition, radical inhibition, and radical trapping) in combination with computational (density functional theory (DFT), N-electron valence state perturbation theory corrected complete active space self-consistent field (NEVPT2-CASSCF)) studies reveal that [CoIII(TAMLq)(N•Ns)(Y)], [CoIII(TAMLq)(N•Ns)2]–, and [CoIII(TAMLsq)(N•Ns)]– are key electrophilic intermediates in aziridination reactions. Surprisingly, the electrophilic one-electron-reduced Fischer-type nitrene radicals do not react as would be expected for nitrene radicals (i.e., via radical addition and radical rebound). Instead, nitrene transfer proceeds through unusual electronically asynchronous transition states, in which the (partial) styrene substrate to TAML ligand (single-) electron transfer precedes C–N coupling. The actual C–N bond formation processes are best described as involving a nucleophilic attack of the nitrene (radical) lone pair at the thus (partially) formed styrene radical cation. These processes are coupled to TAML-to-cobalt and cobalt-to-nitrene single-electron transfer, effectively leading to the formation of an amido-γ-benzyl radical (NsN––CH2–•CH–Ph) bound to an intermediate spin (S = 1) cobalt(III) center. Hence, the TAML moiety can be regarded to act as a transient electron acceptor, the cobalt center behaves as a spin shuttle, and the nitrene radical acts as a nucleophile. Such a mechanism was hitherto unknown for cobalt-catalyzed hypovalent group transfer and the more general transition-metal-catalyzed nitrene transfer to alkenes but is now shown to complement the known concerted and stepwise mechanisms for N-group transfer.

Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment-A case study on V(IV)/V(III) complexes.

In this work, we present a combined experimental and theoretical study on the V L2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of VIVO(acac)2 and VIII(acac)3 prototype complexes. The recorded V L2,3-edge XAS and XMCD spectra are richly featured in both V L3 and L2 spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L2,3-edge XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin-orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S' = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.

Electronic Excited States and UV-Vis Absorption Spectra of the Dihydropyrene/Cyclophanediene Photochromic Couple: a Theoretical Investigation.

Dihydropyrene (DHP)/cyclophanediene (CPD) is a fascinating photoswitchable organic system displaying negative photochromism. Upon irradiation in the visible region, the colored DHP can be converted to its open-ring CPD colorless isomer, which can be converted back to DHP by UV light. DHP and CPD thus possess very different absorption spectra whose absorption bands have never been assigned in detail so far. In this work, we characterize the vertical electronic transitions of the first six and seven excited states of DHP and CPD, respectively, aiming for a realistic comparison with experiment. We used state-of-the-art electronic structure methods [e.g., complete active space second-order perturbation theory (CASPT2), n-electron valence-state perturbation theory (NEVPT2), extended multiconfigurational quasi-degenerate perturbation theory (XMCQDPT2), and third-order algebraic diagrammatic construction ADC(3)] capable of describing differential electron correlation. Vertical transition energies were also computed with time-dependent density functional theory (TD-DFT) and compared to these accurate methods. After the reliability of TD-DFT was validated for the main optical transitions, this efficient method was used to simulate the absorption spectra of DHP and CPD in the framework of the Franck-Condon Herzberg-Teller approximation and also using the nuclear ensemble approach. Overall, for both methods, the simulated absorption spectra reproduce nicely the main spectral features of the DHP and CPD isomers, that is, the main four absorption bands of increasing intensity of DHP and the absorption rise below 300 nm for CPD.

Improvement of Ab Initio Ligand Field Theory by Means of Multistate Perturbation Theory.

Over the last few years, ab initio ligand field theory (AILFT) has evolved into an important tool for the extraction of ligand field models from ab initio calculations. The inclusion of dynamic correlation on top of complete active space self-consistent field (CASSCF) reference functions, which is important for accurate results, was so far realized at the level of second-order N-electron valence state perturbation theory (NEVPT2). In this work, we introduce two alternative methods for the inclusion of dynamic correlation into AILFT calculations, the second-order dynamic correlation dressed complete active space method (DCD-CAS(2)) and the Hermitian quasi-degenerate NEVPT2 (HQD-NEVPT2). These methods belong to the class of multistate perturbation theory approaches, which allow for the mixing of CASSCF states under the effect of dynamic correlation (state-mixing). The two new versions of AILFT were tested for a diverse set of transition-metal complexes. It was found that the multistate methods have, compared to NEVPT2, an AILFT fit with smaller root mean square deviations (rmsds) between ab initio and AILFT energies. A comparison of AILFT excitation energies with the experiment shows that for some systems, the agreement gets better at the multistate level because of the smaller rmsds. However, for some systems, the agreement gets worse, which could be attributed to a cancellation of errors at the NEVPT2 level that is partly removed at the multistate level. An investigation of trends in the extracted ligand field parameters shows that at the multistate level, the ligand field splitting Δ gets larger, whereas the Racah parameters B and C get smaller and larger, respectively. An investigation of the reasons for the observed improvement for octahedral CrIII halide complexes shows that the possibility of state-mixing relaxes constraints that are present at the NEVPT2 level and that keep Δ and B from following their individual preferences.

The combination of multipartitioning of the Hamiltonian with canonical Van Vleck perturbation theory leads to a Hermitian variant of quasidegenerate N-electron valence perturbation theory.

Many recent developments in the area of multistate multireference perturbation theories focused on methods that use a state-averaged 0th order Hamiltonian. We recently found that the dynamic correlation dressed complete active space method fails in describing ligand field and charge transfer states in a balanced way precisely because it uses a state-averaged 0th order Hamiltonian [L. Lang and F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioning idea allows the use of state-specific 0th order Hamiltonians in a multistate framework and could therefore alleviate the mentioned problem. However, the effective Hamiltonian is non-Hermitian in the traditional formulation of multipartitioning, which can lead to unphysical behavior, especially for nearly degenerate states. In order to achieve a more balanced treatment of states with different physical character and at the same time have a Hermitian effective Hamiltonian, we combine in this work multipartitioning with canonical Van Vleck perturbation theory. At the 2nd order, the result is a Hermitian variant of multipartitioning quasidegenerate N-electron valence state perturbation theory. The effect of model space noninvariance of the method is discussed and the benefit of a Hermitian formulation is highlighted with numerical examples. The method is shown to give good results for the calculation of electronic transitions of the [CuCl4]2 -complex and for the calculation of electron paramagnetic resonance parameters, which are two examples where the balance between ligand field and charge transfer configurations is of utmost importance.

Analytical Gradient Theory for Quasidegenerate N-Electron Valence State Perturbation Theory (QD-NEVPT2).

Analytical nuclear gradient and derivative coupling theories for the quasidegenerate N-electron valence state perturbation theory using state-averaged orbitals and density matrices are formulated and implemented. In our implementation, the Lagrangian formalism is employed to derive the working expressions. By implementing a direct algorithm for the four-particle reduced density matrix derivatives, large active spaces up to (12e,12o) are routinely tractable. The applicability of the current algorithm is tested for optimizing the minimal energy conical intersections of the representative photochemical systems: ethylene, a retinal protonated Schiff base (penta-2,4-dieniminium cation, PSB3) model, and a green fluorescent protein chromophore (para-hydroxybenzilideneimidazolin-5-one, pHBI) model. For ethylene, we show that the optimized geometries reasonably agree with the previous geometries using the (extended) multistate second-order complete active space perturbation theory and the multireference configuration interaction with the singles and doubles method. For PSB3, we investigate the effect of the basis set selections, ranging from cc-pVDZ to cc-pV5Z, and the effect of noninvariance in describing conical intersections. For pHBI, we test two active spaces, (4e,3o) and (12e,11o), and survey the active-space dependence. We also discuss the computational cost, the parallel efficiency, and the future applicability of the current algorithm.

Experimental and Multireference ab Initio Investigations of Hydrogen-Atom-Transfer Reactivity of a Mononuclear MnIV-oxo Complex.

A combined experimental-computational study of hydrocarbon oxidation by the MnIV-oxo complex of the neutral, pentadentate N4py ligand [N,N-bis(2-pyridylmethyl)-N-bis(2-pyridyl)methylamine] offers support for a complex reaction coordinate involving multiple electronic states. Variable-temperature kinetic investigations of ethylbenzene oxidation by [MnIV(O)(N4py)]2+ yield experimental activation parameters that were used to evaluate computationally predicted energy barriers. Both density functional theory (DFT) and multireference complete-active-space self-consistent-field (CASSCF) computations with n-electron valence state perturbation theory (NEVPT2) corrections were employed to investigate the hydrogen-atom-transfer reaction barriers for the 4B1 and 4E states. The 4B1 state is the ground state in the absence of substrate, and the 4E state is related to the ground state by a one-electron MnIV e(dxz,3dyz) to MnIV b1(dx2-y2) excitation. A comparison of the DFT, CASSCF/NEVPT2, and experimental results shows that the B3LYP-D3 method underestimates the activation barriers of both electronic states by ca. 10 kcal mol-1. In contrast, the enthalpic barrier predicted for the 4E state by the CASSCF/NEVPT2 method is within 2 kcal mol-1 of the experimental value. The 4E state is early, with dominant structural distortions in the Mn-Nequatorial distances and perturbations to Mn═O bonding that lead to strong electronic stabilization of interactions between the MnIV-oxo unit and substrate C-H bond. While previous DFT studies were qualitatively correct in their ordering of the 4B1 and 4E transition states, this combined use of experimental and CASSCF/NEVPT2 methods provides an ideal means of assessing the two-state reactivity model of MnIV-oxo complexes.

Analytical Gradient Theory for Strongly Contracted (SC) and Partially Contracted (PC) N-Electron Valence State Perturbation Theory (NEVPT2).

An analytical gradient theory for single-state N-electron valence state perturbation theory (NEVPT2), using both strongly contracted (SC) and partially contracted (PC) internal contraction schemes, is developed. We demonstrate the utility of the developed algorithm in the optimization of the single-state molecular geometry of acrolein, benzyne, benzene, the retinal chromophore PSB3, the GFP chromophore pHBI, and porphine, with the cc-pVTZ basis sets. The SC-NEVPT2 analytical gradients exhibit numerical instability due to the lack of invariance with respect to the rotations among the inactive orbitals. On the other hand, PC-NEVPT2 gives molecular geometries comparable to the second-order complete active space perturbation theory in any tested cases. We discuss possible future developments that will make the NEVPT2 gradient algorithm a powerful tool for optimizing molecular geometries and conducting molecular dynamics simulations of correlated systems.

UV-Vis Absorption Spectroscopy of Polonium(IV) Chloride Complexes: An Electronic Structure Theory Study.

More than a hundred years after its discovery, the chemistry of the polonium radioelement is still largely unknown. However, it is quite clear that the properties of this heavy element ( Z = 84) may be affected by relativistic effects, in particular scalar relativistic effects and the so-called spin-orbit coupling (SOC). In this Article, we revisit the interpretation of UV-vis absorption spectra of polonium(IV) complexes in HCl medium, reported decades ago. From the data, two complexes were hypothesized, complex I with a maximum of absorption at 344 nm (at low HCl concentration) and complex II with a maximum at 418 nm (the only visible peak for HCl concentrations above 0.5 M). By monitoring the absorbance at 344 and 418 nm as a function of both the HCl concentration and the pH, complex I was formulated as [Po(OH)Cl x]3- x while complex II was formulated as [PoCl2+ x]2- x. In this work, we study the ground-state geometries of the [Po(OH)Cl x]3- x and [PoCl2+ x]2- x complexes for x = 4-2, i.e. for the most probable complexes, with density functional theory (DFT), demonstrating that solvation can remarkably change the geometries of such systems. The electronic excitation energies are then computed with time-dependent DFT (TD-DFT), second-order N-electron valence state perturbation theory (NEVPT2), and contracted spin-orbit configuration interaction (c-SOCI), showing (i) that the SOC must be at play to obtain excitation energies in the right energy domain and (ii) that the quantum chemical calculations point toward x = 4, i.e., toward the [Po(OH)Cl4]- and [PoCl6]2- complexes.

Spin-dependent properties in the framework of the dynamic correlation dressed complete active space method.

We report an extension of the recently proposed 2nd order dynamic correlation dressed complete active space method [S. Pathak et al., J. Chem. Phys. 147, 234109 (2017)] to incorporate spin-dependent relativistic effects into the Hamiltonian. The result is an effective Hamiltonian that contains the effects of static correlation, dynamic correlation, and relativistic effects on an equal footing. All contributions necessary for the description of magnetic phenomena and electron paramagnetic resonance (EPR) spectroscopy, namely, spin-orbit coupling, magnetic hyperfine coupling, Zeeman interaction, and direct electronic spin-spin coupling, are incorporated. We also suggest a novel analysis of g-matrices and A-matrices based on the singular value decomposition, which can provide not only the magnitude but also the sign of the principal components and allows for a transparent decomposition into different physical contributions. The new method was tested for excitation energies of first-row transition metal ions as well as D-tensors and g-shifts of first-row transition metal complexes using minimal active spaces. It was observed that state-mixing effects are usually small in these cases and that the results are comparable to nondegenerate N-electron valence state perturbation theory (NEVPT2) in conjunction with quasi-degenerate perturbation theory (QDPT). Results on EPR parameters of pseudo-square-planar Cu(ii) complexes show that state-mixing with a ligand-to-metal-charge-transfer configuration greatly improves results compared with NEVPT2/QDPT but also demonstrate that future modifications of the 0th order Hamiltonian or more elaborate electron correlation treatments will be necessary in order to achieve better agreement with the experiment.

Ab Initio Wave Function-Based Determination of Element Specific Shifts for the Efficient Calculation of X-ray Absorption Spectra of Main Group Elements and First Row Transition Metals.

In this study, a detailed calibration of the performance of modern ab initio wave function methods in the domain of X-ray absorption spectroscopy (XAS) is presented. It has been known for some time that for a given level of approximation, for example, using time-dependent density functional theory (TD-DFT) in conjunction with a given basis set, there are systematic deviations of the calculated transition energies from their experimental values that depend on the functional, the basis set, and the chosen treatment of scalar relativistic effects. This necessitates a linear correlation for a given element/functional/basis set combination to be established before chemical applications can be performed. This is a laborious undertaking since it involves sourcing trustworthy experimental data, lengthy geometry optimizations, and detailed comparisons between theory and experiment. In this work, reference values for the element-specific shifts of all the first-row transition metal atoms and the main group elements C, N, O, F, Si, P, S, and Cl have been computed by using a protocol that is based on the complete active space configuration interaction in conjunction with second-order N-electron valence state perturbation theory (CASCI/NEVPT2). It is shown that by extrapolating the results to the basis set limit of the method and taking into account scalar relativistic effects via the second-order Douglas-Kroll-Hess (DKH2) corrections, the predicted element shifts are on average less than 0.75 eV across all the absorption edges and a very good agreement between theory and experiment in all the studied XAS cases is observed. The transferability of these errors to molecular systems is thoroughly investigated. The constructed CASCI/NEVPT2 database of element shifts is used to evaluate the performance and to automatically calibrate prior to comparison with the experiment two commonly used methods in X-ray spectroscopy, namely, DFT/Restricted open shell configuration interaction singles (DFT/ROCIS) and TD-DFT methods.

Mechanistic Insights into Photocatalyzed Hydrogen Desorption from Palladium Surfaces Assisted by Localized Surface Plasmon Resonances.

Nanoparticles synthesized from plasmonic metals can absorb low-energy light, producing an oscillation/excitation of their valence electron density that can be utilized in chemical conversions. For example, heterogeneous photocatalysis can be achieved within heterometallic antenna-reactor complexes (HMARCs), by coupling a reactive center at which a chemical reaction occurs to a plasmonic nanoparticle that acts as a light-absorbing antenna. For example, HMARCs composed of aluminum antennae and palladium (Pd) reactive centers have been demonstrated recently to catalyze selective hydrogenation of acetylene to ethylene. Here, we explore within a theoretical framework the rate-limiting step of hydrogen photodesorption from a Pd surface-crucial to achieving partial rather than full hydrogenation of acetylene-to understand the mechanism behind the photodesorption process within the HMARC assembly. To properly describe electronic excited states of the metal-molecule system, we employ embedded complete active space self-consistent field and n-electron valence state perturbation theory to second order within density functional embedding theory. The results of these calculations reveal that the photodesorption mechanism does not create a frequently invoked transient negative ion species but instead enhances population of available excited-state, low-barrier pathways that exhibit negligible charge-transfer character.