Ionization Potential Electron Affinity Research Articles

Strategies to Improve the Quantum Computation Accuracy for Electrochemical Windows of Ionic Liquids.

Rational design of ionic liquids (ILs) with wide electrochemical windows (ECWs) for high-voltage cathodes is essential to elevating the energy density of current rechargeable batteries. It is significant to determine appropriate strategies for accurately predicting the ECWs of ILs. In this study, we compare the calculated ECWs based on three quantum methods, including the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) method, the ionization potential-electron affinity (IP-EA) method, and the thermodynamic method, under four unique combinations of simulation environments, and assess the discrepancies between the calculated and the experimental results of ECWs. For the three quantum methods, although HOMO-LUMO and IP-EA methods show limited prediction accuracy compared to the experimental values, they can qualitatively rank the anodic limits of anions and the cathodic limits of cations. For the thermodynamic method, we demonstrate that the highest accuracy can be achieved by considering the most rational redox reaction process. By varying the calculation environments, the calculated ECWs tend to be underestimated by considering separate cations and anions of ILs under gas phase, whereas they always exhibit overestimated results when calculating based on the cation-anion pairs. When the computation considers isolated ions with the solvent model plus proper thermodynamic corrections, we observe improved consistency with the experimental results. Though all methods have limitations to achieving perfect predictions of ECWs, we believe rational selection of calculation methods based on application-oriented scenarios can balance the efficiency and accuracy of the results for the development of a high-throughput and accurate database of ECWs for ILs.

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.

Benchmarking CASPT3 vertical excitation energies.

Based on 280 reference vertical transition energies of various excited states (singlet, triplet, valence, Rydberg, n → π*, π → π*, and double excitations) extracted from the QUEST database, we assess the accuracy of complete-active-space third-order 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 0.11eV. 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 in the mean absolute error to 0.09eV when the IPEA shift is switched off.

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.

Electronic structure of isomeric graphene nanoflakes

A comparative theoretical study of graphene nanoflakes (NFs) and isomeric NFs based on two different graphene allotropes has been carried out using hybrid density functional theory and complete active space calculations. Two graphene allotropes H1 and H2 consisted of fused azulene rings were found to be less stable compared to isomeric graphene NFs at all theoretical levels. H1 and H2 have closed shell singlet ground state independently on their size and strong bond length alternation. For all types of NFs, the evolution of the ionization potential (IP), electron affinity (EA) and band gap (Eg) with size is similar. IP and Eg drop and EA increases with NF size. H1 and H2 show lower IPs and Egs and higher EAs compared to the corresponding graphene NF of the same size. However, IPs, Egs and EAs converge with size for all three types of the NF becoming nearly identical for the largest representatives of H1, H2 and graphene NF. H1 and H2 types of NF have a non-uniform distribution of the electron density across the NF, unlike graphene systems, which makes them promising candidates for regioselective chemical modification.

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S0 →S1 and S0 →S2 energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc.

Excitation Energies of Canonical Nucleobases Computed by Multiconfigurational Perturbation Theories.

In this computational work, we assessed the performance of abinitio multireference (MR) methods for the calculation of vertical excitation energies of five nucleobases: adenine, guanine, cytosine, thymine and uracil. In total, we have studied 38 singlet and 30 triplet excited states. Where possible we used the multireference configuration interaction (MRCI) method as a reference for various flavors of multireference perturbation theory to second order. In particular, we have benchmarked CASPT2, NEVPT2 and XMCQDPT2. For CASPT2, we have analyzed the single-state, multistate (MS) and extended MS variants. In addition, we have assessed the effect of the ionization potential electron affinity (IPEA) shift. For NEVPT2, we have used the partially and the strongly contracted variants. Further, we have tested the commonly used RI-CC2, RI-ADC2 and EOM-CCSD methods. Generally, we observe the following trends for singlet excited states: NEVPT2 is the closest MR method to MRCISD+Q, closely followed by CASPT2 with the default IPEA shift. The same trend is observed for triplet states, although NEVPT2 and CASPT2-IPEA are getting closer. Interestingly, the n, π* singlet excited states were described more accurately than π, π* excited states, while for triplet states the trend is inverted except for NEVPT2. This work is an important benchmark for future photochemical investigations.

Methodological CASPT2 study of the valence excited states of an iron-porphyrin complex.

The singlet valence excited states of an iron-porphyrin-pyrazine-carbonyl complex are investigated up to the Soret band (about 3 eV) using multi-state complete active space with perturbation at the second order (MS-CASPT2). This complex is a model for the active site of carboxy-hemoglobin/myoglobin. The spectrum of the excited states is rather dense, comprising states of different nature: d→π* transitions, d→d states, π→π* excitations of the porphyrin, and doubly excited states involving simultaneous intra-porphyrin π→π* and d→d transitions. Specific features of the MS-CASPT2 method are investigated. The effect of varying the number of roots in the state average calculation is quantified as well as the consequence of targeted modifications of the active space. The effect of inclusion of standard ionization potential-electron affinity (IPEA) shift in the perturbation treatment is also investigated.

Accurate Spin-State Energetics of Transition Metal Complexes. 1. CCSD(T), CASPT2, and DFT Study of [M(NCH)6](2+) (M = Fe, Co).

Highly accurate estimates of the high-spin/low-spin energy difference ΔEHLel in the high-spin complexes [Fe(NCH)6]2+ and [Co(NCH)6]2+ have been obtained from the results of CCSD(T) calculations extrapolated to the complete basis set limit. These estimates are shown to be strongly influenced by scalar relativistic effects. They have been used to assess the performances of the CASPT2 method and 30 density functionals of the GGA, meta-GGA, global hybrid, RSH, and double-hybrid types. For the CASPT2 method, the results of the assessment support the proposal [Kepenekian, M.; Robert, V.; Le Guennic, B. J. Chem. Phys. 2009, 131, 114702] that the ionization potential–electron affinity (IPEA) shift defining the zeroth-order Hamiltonian be raised from its standard value of 0.25 au to 0.50–0.70 au for the determination of ΔEHLel in Fe(II) complexes with a [FeN6] core. At the DFT level, some of the assessed functionals proved to perform within chemical accuracy (±350 cm–1) for the spin-state energetics of [Fe(NCH)6]2+, others for that of [Co(NCH)6]2+, but none of them simultaneously for both complexes. As demonstrated through a reparametrization of the CAM-PBE0 range-separated hybrid, which led to a functional that performs within chemical accuracy for the spin-state energetics of both complexes, performing density functionals of broad applicability may be devised by including in their training sets highly accurate data like those reported here for [Fe(NCH)6]2+ and [Co(NCH)6]2+.

Complete vs Restricted Active Space Perturbation Theory Calculation of the Cr2 Potential Energy Surface

In this paper, we calculate the potential energy surface (PES) and the spectroscopic constants of the chromium dimer using the recently developed restricted active space second-order perturbation (RASPT2) method. This approach is benchmarked against available experimental measurements and the complete active space second-order perturbation theory (CASPT2), which is nowadays established as one of the most accurate theoretical models available. Dissociation energies, vibrational frequencies, and bond distances are computed at the RASPT2 level using several reference spaces. The major advantage of the RASPT2 method is that with a limited number of configuration state functions, it can reproduce well the equilibrium bond length and the vibrational frequency of the Cr dimer. On the other hand, the PES is well described only at short distances, while at large distances, it compares very poorly with the CASPT2. The dissociation energy is also ill-behaved, but its value can be largely improved using a simple workaround that we explain in the text. In the paper, we also address the effect of the Ionization Potential Electron Affinity (IPEA) shift (a parameter introduced in the zeroth-order Hamiltonian in the CASPT2 method to include the effect of two-electron terms) and show how its default value of 0.25 is not suitable for a proper description of the PES and of the spectroscopic parameters and must be changed to a more sound value of 0.45.