EOMIP-CCSD(2)*: An Efficient Method for the Calculation of Ionization Potentials

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

Pair Natural Orbital Equation-of-Motion Coupled-Cluster Method for Core Binding Energies: Theory, Implementation, and Benchmark

We present the theory and implementation of a lower scaling core-valence separated equation-of-motion coupled-cluster approach based on domain-based local pair natural orbitals for core binding energies. The accuracy of the new method has been compared with that of the standard equation-of-motion coupled-cluster method and experimentally measured results. The use of pair natural orbitals significantly reduces the computation cost and can be applied to large molecules.

A Core-Valence Separated Similarity Transformed EOM-CCSD Method for Core-Excitation Spectra

We present the theory and implementation of a core-valence separated similarity transformed EOM-CCSD (STEOM-CCSD) method for K-edge core excitation spectra. The method can select an appropriate active space using CIS natural orbitals and near "black box" to use. The second similarity transformed Hamiltonian is diagonalized in the space of single excitation. Therefore, the final diagonalization step is free from the convergence problem arising due to the coupling of the core-excited states with the continuum of doubly excited states. Convergence trouble can appear for the preceding core-ionized state calculation in STEOM-CCSD. A core-valence separation (CVS) scheme compatible with the natural orbital based active space selection (CVS-STEOM-CCSD-NO) is implemented to overcome the problem. The CVS-STEOM-CCSD-NO has a similar accuracy to that of the standard CVS-EOM-CCSD method but comes with a lower computational cost. The modification required in the CVS scheme to make use of the CIS natural orbital is highlighted. The suitability of the CVS-STEOM-CCSD-NO method for chemical application is demonstrated by simulating the K-edge spectra of glycine and thymine.

Perturbation theory made efficient and effective for predictions of ionization potential and electron affinity

Ionization potential and electron affinity are essential molecular properties. The most straightforward method is to calculate them by taking the total energy differences of the initial and final states according to the definition. However, it often suffers from a serious convergence problem due to the requirement of the self-consistent field (SCF) calculations for the ionic states with non-Aufbau choices of occupations. In the present work, we have constructed a theoretical framework in view of perturbation theory to bypass the SCF calculations of the ionic states. To address the imbalance issue that arises from the precisely treated neutral ground state followed by the truncated perturbative treatment of the ionic states, an accurate yet effective method has been developed here, which adds back some terms from the higher order perturbations into the lower order to cancel out the most computationally cost terms in the truncated expansion, thus reaching a better convergence with less computation. The validity of the present methodology has been tested out by applying it to the Hartree-Fock (HF) method in combination with the correlation effect described at the second-order Møller-Plesset level in a frozen-orbital approximation. All the derivations in this work are given in a general framework, which are applicable not only to HF but also to a wide range of density functional theory methods from semi-local functionals to hybrid and doubly hybrid functionals.

Probing the ionization potentials of the formaldehyde dimer

In this work, we present a computational investigation on the ionization potentials (IPs) of the formaldehyde dimer, (H₂CO)₂. Twelve lowest lying IPs (corresponding to the entire valence orbitals) for both C_2h and C_s symmetry conformers have been computed at the coupled cluster level of theory using large correlation consistent basis sets with extrapolation to the complete basis set limit and consideration of core electron correlation effects. Specifically, the equation-of-motion ionization potential coupled-cluster with single and double (EOMIP-CCSD) excitations method with the aug-cc-pVXZ and aug-cc-pCVXZ (X = T, Q, and 5) basis sets combined with the Feller-Peterson-Dixon approach was employed, as well as CCSD with perturbative triples [CCSD(T)] with the aug-cc-pVTZ basis sets. In general, excellent agreement was observed from the comparison between the results obtained through the use of these approaches. In addition, the IPs for the formaldehyde monomer were also obtained using such methodologies and the results compared with existing experimental data; excellent agreement was also observed in this case. To the best of our knowledge, this work represents the first of its kind to determine the IPs for all these systems using a high level theory approach and is presented to motivate experimental investigations, e.g., studies involving photoionization, particularly for the formaldehyde dimer. The equilibrium binding energy of the C_2h dimer is calculated in this work at the CCSD(T)/aug-cc-pVTZ level of theory to be -4.71 kcal/mol. At this same level of theory, the equilibrium isomerization energy between C_2h and C_s conformers is 0.76 kcal/mol (C_s conformer being more stable).

A correlation–relaxation-balanced direct method at the second order perturbation theory for accurate ionization potential predictions

With almost no extra computational cost after a normal MP2 procedure, the CRB-MP2 method proposed here yields high quality valence and core IPs for a wide range of species.

A simple scheme for calculating approximate transition moments within the equation of motion expectation value formalism

A simple scheme for calculating approximate transition moments within the framework of the equation of motion coupled cluster method is proposed. It relies on a matrix inversion technique to calculate the excited state left eigenvectors and requires no additional cost over that of the excitation energy calculation. The new approximation gives almost identical UV-Vis spectra to that obtained using the standard equation of motion coupled cluster method with single and double excitations for molecules in a standard test set.

Electron Detachment and Subsequent Structural Changes of Water Clusters

A cost-effective equation of motion coupled cluster method, EOMIP-CCSD(2), is used to investigate vertical and adiabatic ionization potential as well as ionization-induced structural changes of water clusters and compared with CCSD(T), CASPT2, and MP2 methods. The moderate N(5) scaling and low storage requirement yields EOMIP-CCSD(2) calculation feasible even for reasonably large molecules and clusters with accuracy comparable to CCSD(T) method at much cheaper computational cost. Our calculations shed light on the authenticity of EOMIP-CCSD(2) results and establish a reliable method to study of ionization energy of molecular clusters. We have further investigated the performance of several classes of DFT functionals for ionization energies of water clusters to benchmark the results and to get a reliable functionals for the same.