Assessment of n-Electron Valence State Perturbation Theory for Vertical Excitation Energies

Spinless formulation of linearized adiabatic connection approximation and its comparison with the second order N-electron valence state perturbation theory

The adiabatic connection (AC) approximation, along with its linearized variant AC0, was introduced as a method of obtaining dynamic correlation energy. When using a complete active space self-consistent field (CASSCF) wave function as a reference, the AC0 approximation is considered one of the most efficient multi-reference perturbation theories. It only involves the use of 1st- and 2nd-order reduced density matrices. However, some numerical results have indicated that the excitation energies predicted by AC0 are not as reliable as those from the second-order N-electron valence state perturbation theory (NEVPT2). In this study, we develop a spinless formulation of AC0 based on the Dyall Hamiltonian and provide a detailed comparison between AC0 and NEVPT2 approaches. We demonstrate the components within the correlation energy expressions that are common to both methods and those unique to either AC0 or NEVPT2. We investigate the role of the terms exclusive to NEVPT2 and explore the possibility of enhancing AC0's performance in this regard.

Symmetry Breaking in a Triferrous Extended Metal Atom Chain

Semilocal and random phase approximation (RPA) density functional theory (DFT) and complete active space (CASSCF + NEVPT2) methodologies were applied to investigate a new class of extended metal atom chain (EMAC) complexes. A novel triferrous complex has been synthesized recently that does not utilize the usual 2,2'-dipyridylamine (dpa) ligand framework, which essentially always results in a tetragonal coordination environment and general formula M3(dpa)4X2, where X is an anion. Instead, the triferrous complex utilizes a dianionic, 2,6-bis(trimethylsilylamido)pyridine ligand (L2-) resulting in the formation of trigonal complexes with general formula Fe3L3. To better understand the electronic structure of this complex, calculations were utilized to explore the experimentally isolated Fe3L3, and a smaller theoretical complex, in order to compare and contrast with the traditional dpa-based EMACs. Due to the absence of anionic, axial ligands, the sigma nonbonding orbitals formed from the metal d orbitals are lower in energy than in the dpa complexes, and compete with the pi bonding orbitals for occupation in the Fe3L3 complex. While the idealized geometry of these complexes is D3h, a helical distortion of the ligands and subsequent electronic symmetry breaking due to Jahn-Teller distortions are predicted utilizing both semilocal and RPA DFT methods, ending in a C2 structure that closely matches the reported crystal structure. Predicted Mössbauer isomer shifts and ultraviolet/visible (UV/vis) spectra also agree with the experimental data available in the literature. Magnetic coupling constants also indicate ferromagnetic coupling between nearest neighbor irons. Two-dimensional (2D) potential energy surfaces were calculated for a range of fixed Fe-Fe bond lengths, revealing a flat potential energy surface over a wide range of Fe-Fe bond lengths and verifying the ability of RPA to act as a higher-level check on semilocal DFT results. In order to verify the predicted high-spin ground state, CASSCF + NEVPT2 was applied to selected molecular configurations and confirmed the predictions made by DFT. These calculations shed light on the physical ground state electron configuration of Fe3L3 and correlate this electronic configuration with the available experimental data.

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

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

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

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.

State-Specific Coupled-Cluster Methods for Excited States

We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.

Multireference Correlated Oscillator Strengths from Adiabatic Connection Approaches Based on Extended Random Phase Approximation

We show that accurate oscillator strengths can be obtained from adiabatic connection (AC) approaches based on the extended random phase approximation (ERPA) combined with multireference (complete active space, CAS) wave functions. The oscillator strengths calculated using the perturbation-corrected ERPA transition density matrices, proposed in this work, and the excitation energies calculated with recently introduced AC correlation energy methods, AC0 and AC0D, compete with accuracy in the perturbational CASPT2 approach and require less computational effort. AC0 and AC0D methods scale more favorably with the number of active orbitals than multiconfigurational perturbation approaches like CASPT2 and NEVPT2 thanks to their dependence on reduced density matrices up to the order of 2. Importantly, the newly developed approach for computing correlated transition dipole moments does not entail any additional costs, as all intermediate quantities become available when AC0 energies are being computed. We also test the performance of the recently proposed AC method corrected for the negative-transition contributions to the correlation energy, AC0D, for triplet excitation energies. Similarly, as for the singlet excitations, the correction improves the performance of the AC0 method, particularly for the low-lying excited states.

Engineering Clock Transitions in Molecular Lanthanide Complexes

Molecular lanthanide (Ln) complexes are promising candidates for the development of next-generation quantum technologies. High-symmetry structures incorporating integer spin Ln ions can give rise to well-isolated crystal field quasi-doublet ground states, i.e., quantum two-level systems that may serve as the basis for magnetic qubits. Recent work has shown that symmetry lowering of the coordination environment around the Ln ion can produce an avoided crossing or clock transition within the ground doublet, leading to significantly enhanced coherence. Here, we employ single-crystal high-frequency electron paramagnetic resonance spectroscopy and high-level ab initio calculations to carry out a detailed investigation of the nine-coordinate complexes, [HoIIIL1L2], where L1 = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane and L2 = F- (1) or [MeCN]0 (2). The pseudo-4-fold symmetry imposed by the neutral organic ligand scaffold (L1) and the apical anionic fluoride ion generates a strong axial anisotropy with an mJ = ±8 ground-state quasi-doublet in 1, where mJ denotes the projection of the J = 8 spin-orbital moment onto the ∼C4 axis. Meanwhile, off-diagonal crystal field interactions give rise to a giant 116.4 ± 1.0 GHz clock transition within this doublet. We then demonstrate targeted crystal field engineering of the clock transition by replacing F- with neutral MeCN (2), resulting in an increase in the clock transition frequency by a factor of 2.2. The experimental results are in broad agreement with quantum chemical calculations. This tunability is highly desirable because decoherence caused by second-order sensitivity to magnetic noise scales inversely with the clock transition frequency.

Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory

The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

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.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)₄, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)₄ molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the ⁵³Cr nuclear spin and to the ¹³C and ¹H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with ¹H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20-40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

Reference Energies for Cyclobutadiene: Automerization and Excited States

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D_4h square geometry but also in the D_2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D_2h and D_4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

Combined Experimental and Computational Kinetics Studies for the Atmospherically Important BrHg Radical Reacting with NO and O2

We report on the first experimental determination of the absolute rate constant of the reaction of BrHg + NO in N₂ bath gas using a laser photolysis-laser-induced fluorescence (LP-LIF) system. The rate constant of the reaction of BrHg + NO is determined to be 7.0_-0.9^+1.3 × 10^-12 cm³ molecule^-1 s^-1 over 50-700 Torr and 315-353 K. The absence of a pressure or temperature dependence suggests that this reaction leads mainly to mercury reduction (Hg + BrNO) rather than mercury oxidation (BrHgNO). Our theoretical calculations using NEVPT2 energies on density functional theory (DFT) geometries are consistent with a barrierless reaction to form Hg + BrNO. The equilibrium constants and the rate constants of the reaction BrHg + O₂ ⇌ BrHgOO are computed theoretically because they are too low to be measured in the LP-LIF system. Molecular oxygen quenches the LIF signal of BrHg with a large rate constant of (1.7 ± 0.1) × 10^-10 cm³ molecule^-1 s^-1. Thus, different techniques that capture the absolute [BrHg(X̃)] would be advantageous for kinetics studies of BrHg reactions in the presence of O₂. The computed equilibrium constant suggests a non-negligible upper limit of the fraction of BrHg stored as BrHgOO (up to 0.5) at low-temperature conditions, e.g., in the upper troposphere and in polar winters at ground level. Preliminary results indicate that BrHgOO behaves like HOO or organic peroxy radicals in reactions with atmospheric radicals.

Benchmarking CASPT3 Vertical Excitation Energies

Based on 280 reference vertical transition energies of various natures (singlet, triplet, valence, Rydberg, n → π∗, π → π∗, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. When one applies the disputable ionization- potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction of the mean absolute error to 0.09 eV when the IPEA shift is switched off.

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals

Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC_n method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, AC_n is more efficient than existing ab initio multireference dynamic correlation methods. AC_n affords excellent results for singlet-triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.

Theoretical approach to modeling the early nonadiabatic events of ESIPT originating from three-state conical intersection in quinophthalone

We explore the excited-state intramolecular proton transfer process of quinophthalone theoretically. This molecule possesses three low-lying singlet excited states ([Formula: see text] and [Formula: see text]) in a narrow energy gap of less than the N-H stretching frequency. Dynamics simulations show nonadiabatic wavepacket transfer to [Formula: see text] and [Formula: see text] upon initiating the wavepacket on [Formula: see text]. Multiple accessible conical intersections that lie in the Franck-Condon region facilitate the nonadiabatic wavepacket transfer. Nuclear densities associated with the proton transfer promoting vibrations would start accumulating on [Formula: see text] and [Formula: see text] within a few tens of femtoseconds, validating the involvement of these vibrations in the nonadiabatic events that occur before the proton transfer process. Our findings emphasize the necessity of refined kinetic models for assigning the time constants of ultrafast transient spectroscopy measurements due to the simultaneous evolution of nonadiabatic events and proton transfer kinetics in quinophthalone.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

The Adsorption of Small Molecules on the Copper Paddle-Wheel: Influence of the Multi-Reference Ground State

We report a theoretical study of the adsorption of a set of small molecules (C2H2, CO, CO2, O2, H2O, CH3OH, C2H5OH) on the metal centers of the "copper paddle-wheel"-a key structural motif of many MOFs. A systematic comparison between DFT of different rungs, single-reference post-HF methods (MP2, SOS-MP2, MP3, DLPNO-CCSD(T)), and multi-reference approaches (CASSCF, DCD-CAS(2), NEVPT2) is performed in order to find a methodology that correctly describes the complicated electronic structure of paddle-wheel structure together with a reasonable description of non-covalent interactions. Apart from comparison with literature data (experimental values wherever possible), benchmark calculations with DLPNO-MR-CCSD were also performed. Despite tested methods show qualitative agreement in the majority of cases, we showed and discussed reasons for quantitative differences as well as more fundamental problems of specific cases.

Reactive quenching of NO (A2Σ+) with H2O leads to HONO: a theoretical analysis of the reactive and nonreactive electronic quenching mechanisms

In this study, we develop a mechanistic understanding of the pathways for nonreactive and reactive electronic quenching of NO (A2Σ+) with H2O. In doing so, we identify a photochemical mechanism for HONO production in the upper atmosphere.

Effect of Substituent on C-H Activation Catalysed by a nonheme Fe(IV)O Complex: A Computational Investigation of Reactivity and Hydrogen Tunneling

A density functional theory investigation has been presented here to address the C-H activation reactivity and the influence of quantum mechanical tunneling catalyzed by a non-heme iron(IV)-Oxo complex viz. [FeIVOdpaq-X]+...

Multireference Perturbation Theory Combined with PCM and RISM Solvation Models: A Benchmark Study for Chemical Energetics

The polarizable continuum model (PCM) has been one of the most widely used approaches to take into account the solvation effect in quantum chemical calculations. In this paper, we performed a series of benchmark calculations to assess the accuracy of the PCM scheme combined with the second-order complete-active-space perturbation theory (CASPT2) for molecular systems in polar solvents. For solute molecules with extensive conjugated π orbitals, exemplified by elongated conjugated arylcarbenes, we have incorporated the ab initio density matrix renormalization group algorithm into the PCM-CASPT2 method. In the previous work, we presented a combination of the DMRG-CASPT2 method with the reference interaction site model (RISM) theory for describing the solvation effect using the radial distribution function and compared its performance to the widely used density-functional approaches (PCM-TD-DFT). The work here allows us to further show a more thorough assessment of the RISM model compared to the PCM with an equal level of the wave function treatment, the (DMRG-)CASPT2 theory, toward a high-accuracy electronic structure calculations for solvated chemical systems. With the exception that the PCM models are not capable of properly describing the hydrogen bondings, accuracy of the PCM-CASPT2 model is in most cases quite comparable to the RISM counterpart.

Electronic structure of NdO via slow photoelectron velocity-map imaging spectroscopy of NdO--

Electronically excited NdO is a possible product of the chemistry associated with the release of Nd into the ionosphere, and emission from these states may contribute to the observations following such experiments. To better characterize the energetics and spectroscopy of NdO, we report a combined experimental and theoretical study using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled NdO^- anions (cryo-SEVI) supplemented by wave function-based quantum-chemical calculations. Using cryo-SEVI, we measure the electron affinity of NdO to be 1.0091(7) eV and resolve numerous transitions to low-lying electronic and vibrational states of NdO that are assigned with the aid of the electronic structure calculations. Additionally, temperature-dependent data suggest contributions from the (2)4.5 state of NdO^- residing 2350 cm^-1 above the ground anion state. Photodetachment to higher-lying excited states of NdO is also reported, which may help to clarify observations from prior release experiments.

Comparison of different approaches to derive classical bonded force-field parameters for a transition metal cofactor: a case study for non-heme iron site of ectoine synthase

Computational investigations into the structure and function of metalloenzymes with transition metal cofactors require proper preparation of the model, which requires obtaining reliable force field parameters for the cofactor. Here, we present a test case where several methods were used to derive amber force field parameters for a bonded model of the Fe(II) cofactor of ectoine synthase. Moreover, the spin of the ground state of the cofactor was probed by DFT and post-HF methods, which consistently indicated the quintet state is lowest in energy and well separated from triplet and singlet. The performance of the obtained force field parameter sets, derived for the quintet spin state, was scrutinized and compared taking into account metrics focused on geometric features of the models as well as their energetics. The main conclusion of this study is that Hessian-based methods yield parameters which represent the geometry around the metal ion, but poorly reproduce energy variance with geometrical changes. On the other hand, the energy-based method yields parameters accurately reproducing energy-structure relationships, but with bad performance in geometry optimization. Preliminary tests show that admixing geometrical criteria to energy-based methods may allow to derive parameters with acceptable performance for both energy and geometry.

Intersystem crossing pathways in [5]-, [7]-, and [9]cycloparaphenylenes

We analyze the energetics and internal conversion dynamics of singlet and triplet manifolds to identify the possible intersystem crossing pathways in odd-numbered [n]cycloparaphenylenes ([n]CPPs, n = 5, 7, and 9). Quantum wavepacket propagation calculations within the linear vibronic coupling framework suggest that both [5]- and [7]CPPs rapidly relax to S₂ upon populating "bright" higher singlet excited states. The S₂-S₁ energy decreases with the increase in CPP size, and hence, [9]CPP exhibits a faster S₂ → S₁ internal conversion decay. Higher triplet states act as receiver states for the intersystem crossing happening either via S₁ or S₂. The wavepacket evolving on the receiver triplet state would decay to lower states via multiple conical intersections and reach T₁. The estimated size-dependent fluorescence and emission energies are in good accord with the experiment.

Single-Ion Anisotropy and Intramolecular Interactions in CeIII and NdIII Dimers

This article reports the syntheses, characterization, structural description, together with magnetic and spectroscopic properties of two isostructural molecular magnets based on the chiral ligand N,N'-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-(R,R/S,S)-ethane-1,2-diamine), L1, of general formula [Ln2(RR-L1)2(Cl6)]·MeOH·1.5H2O, (Ln = Ce (1) or Nd (2)). Multifrequency electron paramagnetic resonance (EPR), cantilever torque magnetometry (CTM) measurements, and ab initio calculations allowed us to determine single-ion magnetic anisotropy and intramolecular magnetic interactions in both compounds, evidencing a more important role of the anisotropic exchange for the NdIII derivative. The comparison of experimental and theoretical data indicates that, in the case of largely rhombic lanthanide ions, ab initio calculations can fail in determining the orientation of the weakest components, while being reliable in determining their principal values. However, they remain of paramount importance to set the analysis of EPR and CTM on sound basis, thus obtaining a very precise picture of the magnetic interactions in these systems. Finally, the electronic structure of the two complexes, as obtained by this approach, is consistent with the absence of zero-field slow relaxation observed in ac susceptibility.

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). I. Revisiting the NEVPT2 construction

Over the last decade, the second-order N-electron valence state perturbation theory (NEVPT2) has developed into a widely used multireference perturbation method. To apply NEVPT2 to systems with large active spaces, the computational bottleneck is the construction of the fourth-order reduced density matrix. Both its generation and storage become quickly problematic beyond the usual maximum active space of about 15 active orbitals. To reduce the computational cost of handling fourth-order density matrices, the cumulant approximation (CU) has been proposed in several studies. A more conventional strategy to address the higher-order density matrices is the pre-screening approximation (PS), which is the default one in the ORCA program package since 2010. In the present work, the performance of the CU, PS, and extended PS (EPS) approximations for the fourth-order density matrices is compared. Following a pedagogical introduction to NEVPT2, contraction schemes, as well as the approximations to density matrices, and the intruder state problem are discussed. The CU approximation, while potentially leading to large computational savings, virtually always leads to intruder states. With the PS approximation, the computational savings are more modest. However, in conjunction with conservative cutoffs, it produces stable results. The EPS approximation to the fourth-order density matrices can reproduce very accurate NEVPT2 results without any intruder states. However, its computational cost is not much lower than that of the canonical algorithm. Moreover, we found that a good indicator of intrude states problems in any approximation to high order density matrices is the eigenspectra of the Koopmans matrices.

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.

Experimental and Theoretical Evidence for an Unusual Almost Triply Degenerate Electronic Ground State of Ferrous Tetraphenylporphyrin

Iron porphyrins exhibit unrivalled catalytic activity for electrochemical CO₂-to-CO conversion. Despite intensive experimental and computational studies in the last 4 decades, the exact nature of the prototypical square-planar [Fe^II(TPP)] complex (1; TPP^2- = tetraphenylporphyrinate dianion) remained highly debated. Specifically, its intermediate-spin (S = 1) ground state was contradictorily assigned to either a nondegenerate ³A_2g state with a (d_xy)²(d_z²)²(d_xz,yz)² configuration or a degenerate ³E_g^θ state with a (d_xy)²(d_xz,yz)³(d_z²)¹/(d_z²)²(d_xy)¹(d_xz,yz)³ configuration. To address this question, we present herein a comprehensive, spectroscopy-based theoretical and experimental electronic-structure investigation on complex 1. Highly correlated wave-function-based computations predicted that ³A_2g and ³E_g^θ are well-isolated from other triplet states by ca. 4000 cm^-1, whereas their splitting Δ_A-E is on par with the effective spin-orbit coupling (SOC) constant of iron(II) (≈400 cm^-1). Therfore, we invoked an effective Hamiltonian (EH) operating on the nine magnetic sublevels arising from SOC between the ³A_2g and ³E_g^θ states. This approach enabled us to successfully simulate all spectroscopic data of 1 obtained by variable-temperature and variable-field magnetization, applied-field ⁵⁷Fe Mössbauer, and terahertz electron paramagnetic resonance measurements. Remarkably, the EH contains only three adjustable parameters, namely, the energy gap without SOC, Δ_A-E, an angle θ that describes the mixing of (d_xy)²(d_xz,yz)³(d_z²)¹ and (d_z²)²(d_xy)¹(d_xz,yz)³ configurations, and the ⟨r_d^-3⟩ expectation value of the iron d orbitals that is necessary to estimate the ⁵⁷Fe magnetic hyperfine coupling tensor. The EH simulations revealed that the triplet ground state of 1 is genuinely multiconfigurational with substantial parentages of both ³A_2g (<88%) and ³E_g (>12%), owing to their accidental near-triple degeneracy with Δ_A-E = +950 cm^-1. As a consequence of this peculiar electronic structure, 1 exhibits a huge effective magnetic moment (4.2 μB at 300 K), large temperature-independent paramagnetism, a large and positive axial zero-field splitting, strong easy-plane magnetization (g_⊥ ≈ 3 and g_∥ ≈ 1.7) and a large and positive internal field at the ⁵⁷Fe nucleus aligned in the xy plane. Further in-depth analyses suggested that g_⊥ ≫ g_∥ is a general spectroscopic signature of near-triple orbital degeneracy with more than half-filled pseudodegenerate orbital sets. Implications of the unusual electronic structure of 1 for CO₂ reduction are discussed.

Zeolites at the Molecular Level: What Can Be Learned from Molecular Modeling

This review puts the development of molecular modeling methods in the context of their applications to zeolitic active sites. We attempt to highlight the utmost necessity of close cooperation between theory and experiment, resulting both in advances in computational methods and in progress in experimental techniques.

Single-Root Multireference Brillouin-Wigner Perturbative Approach to Excitation Energies

The state-specific Brillouin-Wigner multireference perturbation theory [which employs Jeziorski-Monkhorst parametrization of the wave function] using improved virtual orbitals, denoted as IVO-BWMRPT, is applied to calculate excitation energies (EEs) for methylene, ethylene, trimethylenemethane, and benzyne systems exhibiting various degrees of diradical character. In IVO-BWMRPT, all of the parameters appearing in the wave function ansatz are optimized for a specific electronic state. For these systems, the IVO-BWMRPT method provides EEs that are in close agreement with the benchmark results and experiments, where available, indicating that the method does not introduce imbalance in the target-specific treatment of closed- and open-shell states involved. The good performance of the present methodology is primarily related to structural compactness of the formalism. Overall, present findings are encouraging for both further development of the approach and chemical applications on the energy differences of strongly correlated systems.

Role of Skeletal and O-H Vibrational Motions in the Ultrafast Excited-State Relaxation Dynamics of Alizarin

The role of two skeletal (C═C and C═O stretch) and O-H vibrational motions in the internal conversion dynamics associated with the coupled S₁(ππ*, A') -S₂(nπ*, A″) potential energy surfaces of alizarin are investigated theoretically. Quantum wavepacket dynamics simulations reveal a nonadiabatic population transfer from the "bright" S₁(ππ*, A') to "dark" S₂(nπ*, A″) state on a time scale of 10 fs. A detailed analysis of computed structural parameters, energetics, and time-dependent observables suggest that these vibrations promote the nonadiabatic dynamics before initiating the proton transfer process. We also discuss how the simultaneous evolution of multidimensional dynamics involving several vibrational degrees of freedom would increase the complexity, while analyzing the spectral and kinetic data of time-resolved spectroscopy measurements.

Benchmarking Quantum Mechanical Methods for the Description of Charge-Transfer States in π-Stacked Nucleobases

Charge-transfer (CT) states are of special interest in photochemical research because they can facilitate chemical reactions through the rearrangement of electrons and subsequently chemical bonds in a molecular system. Of particular importance to this research is the transfer of electrons between π-stacked nucleobases in DNA because they play an important role in its photophysics and photochemistry. Computational methods are paramount for the study of CT states because of the current inability of experimental methods to easily detect such states. However, many ab-initio wavefunction-based and density functional theory (DFT) methods fail to accurately describe these CT states. Here, we benchmark how 40 different quantum mechanical methods describe the excited states of a guanine-thymine π-stacked nucleobase dimer system, both in 5'-TG-3' and 5'-GT-3' conformations. We find that the distance between the nucleobases plays a major role in the energy of the CT state and in the difference of the dipole moments between the CT and ground state. There is a larger range of values (and errors) for the energies of CT states compared to those of states localized on one nucleobase. Wavefunction-based methods have similar errors for the CT and localized valence states, while DFT methods are very sensitive to the amount of Hartree-Fock exchange. Long-range-corrected functionals with a careful balance of the Hartree-Fock exchange included can predict very accurate CT states and a balanced description with the localized states.

Computational refinement of the puzzling red tetrasulfur chromophore in ultramarine pigments

We investigated the cryptic red chromophore, accompanying the blue S3˙- radical in ultramarine pigments, which usually was tentatively assigned to an unspecified isomer of either neutral S4 or ionic S4˙- species. To reveal its identity, we performed the first systematic density functional studies on periodic and large cluster models of red ultramarines, considering several S4/S4˙- isomers embedded in aluminosilicate cages. For both neutral and charged tetrasulfides the most stable confined isomer is the planar C2v one. The only plausible candidate for the red chromophore among the tetrasulfur species is the planar C2v isomer of the neutral S4 molecule, which, apart from being thermodynamically preferable, strongly absorbs green light and its vibrational modes match very well with the available Raman data. The C2v-S4˙- radical, if present at all in red ultramarines, could be identified by strong absorption in the near infrared region and possibly by the slightly larger isotropic value of the g tensor than that of the S3˙- radical.

Multiple ESIPT pathways originating from three-state conical intersections in tropolone

Internal conversion decay dynamics associated with the potential energy surfaces of three low-lying singlet excited electronic states, S₁ (ππ^*, A'), S₂ (ππ^*, A'), and S₃ (nπ^*, A″), of tropolone are investigated theoretically. Energetic and spatial aspects of conical intersections of these electronic states are explored with the aid of the linear vibronic coupling approach. Symmetry selection rules suggest that non-totally symmetric modes would act as coupling modes between S₁ and S₃ as well as between S₂ and S₃. We found that the S₁-S₂ interstate coupling via totally symmetric modes is very weak. A diabatic vibronic Hamiltonian consisting of 32 vibrational degrees of freedom is constructed to simulate the photoinduced dynamics of S₀ → S₁ and S₀ → S₂ transitions. We observe a direct nonadiabatic population transfer from S₁ to S₃, bypassing S₂, during the initial wavepacket propagation on S₁. On the other hand, the initial wavepacket evolving on S₂ would pass through the S₂-S₃ and S₁-S₃ conical intersections before reaching S₁. The presence of multiple proton transfer channels on the S₁-S₂-S₃ coupled potential energy surfaces of tropolone is analyzed. Our findings necessitate the treatment of proton tunneling dynamics of tropolone beyond the adiabatic symmetric double well potentials.

Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.

Multireference Ground and Excited State Electronic Structures of Free- versus Iron Porphyrin-Carbenes

Iron porphyrin carbenes (IPCs) are important reaction intermediates in engineered carbene transferase enzymes and homogeneous catalysis. However, discrepancies between theory and experiment complicate the understanding of IPC electronic structure. In the literature, this has been framed as whether the ground state is an open- vs closed-shell singlet (OSS vs CSS). Here we investigate the structurally dependent ground and excited spin-state energetics of a free carbene and its IPC analogs with variable trans axial ligands. In particular, for IPCs, multireference ab initio wave function methods are more consistent with experiment and predict a mixed singlet ground state that is dominated by the CSS (Fe(II) ← {:C(X)Y}⁰) configuration (i.e., electrophilic carbene) but that also has a small, non-negligible contribution from an Fe(III)-{C(X)Y}^-• configuration (hole in d(xz), i.e., radical carbene). In the multireference approach, the "OSS-like" excited states are metal-to-ligand charge transfer (MLCT) in nature and are energetically well above the CSS-dominated ground state. The first, lowest energy of these "OSS-like" excited states is predicted to be heavily weighted toward the Fe(III)-{C(X)Y}^-• (hole in d(yz)) configuration. As expected from exchange considerations, this state falls energetically above a triplet of the same configuration. Furthermore, potential energy surfaces (PESs) along the IPC Fe-C(carbene) bond elongation exhibit increasingly strong mixings between CSS/OSS characters, with the Fe(III)-{C(X)Y}^-• configuration (hole in d(xz)) growing in weight in the ground state during bond elongation. The relative degree of electrophilic/radical carbene character along this structurally relevant PES can potentially play a role in reactivity and selectivity patterns in catalysis. Future studies on IPC reaction coordinates should evaluate contributions from ground and excited state multireference character.

Interplay of Electronic and Steric Effects to Yield Low-Temperature CO Oxidation at Metal Single Sites in Defect-Engineered HKUST-1

In contrast to catalytically active metal single atoms deposited on oxide nanoparticles, the crystalline nature of metal-organic frameworks (MOFs) allows for a thorough characterization of reaction mechanisms. Using defect-free HKUST-1 MOF thin films, we demonstrate that Cu+ /Cu2+ dimer defects, created in a controlled fashion by reducing the pristine Cu2+ /Cu2+ pairs of the intact framework, account for the high catalytic activity in low-temperature CO oxidation. Combining advanced IR spectroscopy and density functional theory we propose a new reaction mechanism where the key intermediate is an uncharged O2 species, weakly bound to Cu+ /Cu2+ . Our results reveal a complex interplay between electronic and steric effects at defect sites in MOFs and provide important guidelines for tailoring and exploiting the catalytic activity of single metal atom sites.