The extended Koopmans’ theorem and its exactness

Numerical analysis of the complete active-space extended Koopmans's theorem

We investigate the numerical accuracy of the extended Koopmans's theorem (EKT) in reproducing the full configuration interaction (FCI) and complete active-space configuration interaction (CAS-CI) ionization energies (IEs) of atomic and molecular systems calculated as the difference between the energies of N and (N - 1) electron states. In particular, we study the convergence of the EKT IEs to their exact values as the basis set and the active space sizes vary. We find that the first FCI EKT IEs approach their exact counterparts as the basis set size increases. However, increasing the basis set or the active space sizes does not always lead to more accurate CAS-CI EKT IEs. Our investigation supports the observation of Davidson et al. [J. Chem. Phys. 155, 051102 (2021)] that the FCI EKT IEs can be systematically improved with arbitrary numerical accuracy by supplementing the basis set with diffuse functions of appropriate symmetry, which allow the detached electron to travel far away from the reference system. By changing the exponent and the center of the diffuse functions, our results delineate a complex pattern for the CAS-CI EKT IE of LiH, which can be important for the spectroscopic studies of small molecules.

The role of ETFS amino acids on the stability and inhibition of p53-MDM2 complex of anticancer p53-derivatives peptides: Density functional theory and molecular docking studies

Cancer is one of the leading causes of mortality in the world. Despite the existence of diverse antineoplastic treatments, these do not possess the expected efficacy in many cases. Knowledge of the molecular mechanisms involved in tumor processes allows the identification of a greater number of therapeutic targets employed in the study of new anticancer drugs. In the last decades, peptide-based therapy design using computational chemistry has gained importance in the field of oncology therapeutics. This work aims to evaluate the electronic structure, physicochemical properties, stability, and inhibition of ETFS amino acids and peptides derived from the p53-MDM2 binding domain with action in cancer cells; by means of chemical descriptors at the DFT-BHandHLYP level in an aqueous solution, and its intermolecular interactions through molecular docking studies. The results show that The ETFS fragment plays a critical role in the intermolecular interactions. Thus, the amino acids E17, T18 and S20 increase intermolecular interactions through hydrogen bonds and enhance structural stability. F19, W23 and V25 enhance the formation of the alpha-helix. The hydrogen bonds formed by the backbone atoms for PNC-27, PNC-27-B and PNC-28 stabilize the α-helices more than hydrogen bonds formed by the side chains atoms. Also, molecular docking indicated that the PNC27B-MDM2, PNC28B-MDM2, PNC27-MDM2 and PNC28A-MDM2 complexes show the best binding energy. Therefore, DFT and molecular docking studies showed that the proposed peptides: PNC-28B, PNC-27B and PNC-28A could inhibit the binding of MDM2 to the p53 protein, decreasing the translocation and degradation of p53 native protein.

ERRORS IN APPROXIMATE IONIZATION ENERGIES DUE TO THE ONE-ELECTRON SPACE TRUNCATION OF THE EKT EIGENPROBLEM

Unless the approximate wavefunction of the parent system is expressed in terms of explicitly correlated basis functions, the finite size of the generalized Fock matrix is unlikely to be the leading source of the truncation error in the ionization energy E produced by the EKT (extended Koopmans' theorem) formalism. This conclusion is drawn from a rigorous analysis that involves error partitioning into the parent- and ionized-system contributions, the former being governed by asymptotic power laws when the underlying wavefunction is assembled from a large number of spinorbitals and the latter arising from the truncation of the infinite-dimensional matrix V whose elements involve the 1-, 2- and 3-matrices of the parent system. Quite surprisingly, the decay of the second contribution with the number $n$ of the natural spinorbitals (NOs) employed in the construction of the truncated V turns out to be strongly system-dependent even in the simplest case of the 1S states of two-electron systems, following the n-5 power law for the helium atom while exhibiting an erratic behavior for the H- anion. This phenomenon, which stems from the presence of the so-called solitonic natural spinorbitals among the NOs, renders the extrapolation of the EKT approximates of E to the complete-basis-set limit generally unfeasible. However, attaining that limit is not contingent upon attempted reproduction of the ill-defined one-electron function known as 'the removal orbital', which does not have to be invoked in the derivation of EKT and whose expansion in terms of the NOs diverges.

A molecularly enhanced proof of concept for targeting cocrystals at molecular scale in continuous pharmaceuticals cocrystallization

It is impossible to optimize a process for a target drug product with the desired profile without a proper understanding of the interplay among the material attributes, the process parameters, and the attributes of the drug product. There is a particular need to bridge the micro- and mesoscale events that occur during this process. Here, we propose а molecular engineering methodology for the continuous cocrystallization process, based on Raman spectra measured experimentally with a probe and from quantum mechanical calculations. Using molecular dynamics simulations, the theoretical Raman spectra were calculated from first principles for local mixture structures under an external shear force at various temperatures. A proof of concept is developed to build the process design space from the computed data. We show that the determined process design space provides valuable insight for optimizing the cocrystallization process at the nanoscale, where experimental measurements are difficult and/or inapplicable. The results suggest that our method may be used to target cocrystallization processes at the molecular scale for improved pharmaceutical synthesis.

Electron Impact Ionization of Metastable States of Diatomic Molecules

The Binary-Encounter Bethe approach was applied to the estimation of total ionization induced by electron impact in metastable states of diatomic molecules. The cross sections recently obtained for N2 and CO are reviewed and the new results for H2 are presented, discussing their reliability through the comparison with other theoretical methods.

State-Of-The-Art Computations of Vertical Electron Affinities with the Extended Koopmans' Theorem Integrated with the CCSD(T) Method

Accurate computation of electron affinities (EAs), within 0.10 eV, is one of the most challenging problems in modern computational quantum chemistry. The extended Koopmans' theorem (EKT) enables direct computations of electron affinities (EAs) from any level of the theory. In this research, the EKT approach based on the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is applied to computations of EAs for the first time. For efficiency, the density-fitting (DF) technique is used for two-electron integrals. Further, the EKT-CCSD(T) method is applied to three test sets of atoms and closed- and open-shell molecules, denoted A16, C10, and O33, respectively, for comparison with the experimental electron affinities. For the A16, C10, and O33 sets, the EKT-CCSD(T) approach, along with the aug-cc-pV5Z basis set, provide mean absolute errors (MAEs) of 0.05, 0.08, and 0.09 eV, respectively. Hence, our results demonstrate that high-accuracy computations of EAs can be achieved with the EKT-CCSD(T) approach. Further, when the EKT-CCSD(T) approach is not computationally affordable, the EKT-MP2.5, EKT-LCCD, and EKT-CCSD methods can be considered, and their results are also reasonably accurate. The huge advantage of the EKT method for the computation of IPs is that it comes for free in an analytic gradient computation. Hence, one needs neither separate computations for neutral and ionic species, as in the case of common approaches, nor additional efforts to obtain IPs, as in the case of equation-of-motion approaches. Overall, we believe that the present research may open new avenues in EA computations.

Complete-active-space extended Koopmans theorem method

The complete-active-space (CAS) extended Koopmans theorem (EKT) method is defined as a special case of the EKT in which the reference state is a CAS configuration interaction (CI) expansion and the electron removal operator acts only on the active orbitals. With these restrictions, the EKT is equivalent to the CI procedure involving all hole-state configurations derived from the active space of the reference wavefunction and has properties analogous to those of the original Koopmans theorem. The equivalence is used to demonstrate in a transparent manner that the first ionization energy predicted by the EKT is in general not exact, i.e., not equal to the difference between the full CI energies of the neutral and the ion, but can approach the full CI result with arbitrary precision even within a finite basis set. The findings also reconcile various statements about the EKT found in the literature.

Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans' Theorem Approach

We explore the extended Koopmans' theorem (EKT) within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method. The EKT allows for the direct calculation of electron addition and removal spectral functions using reduced density matrices of the N-particle system and avoids the need for analytic continuation. The lowest level of EKT with AFQMC, called EKT1-AFQMC, is benchmarked using atoms, small molecules, 14-electron and 54-electron uniform electron gas supercells, and a minimal unit cell model of diamond at the Γ-point. Via comparison with numerically exact results (when possible) and coupled-cluster methods, we find that EKT1-AFQMC can reproduce the qualitative features of spectral functions for Koopmans-like charge excitations with errors in peak locations of less than 0.25 eV in a finite basis. We also note the numerical difficulties that arise in the EKT1-AFQMC eigenvalue problem, especially when back-propagated quantities are very noisy. We show how a systematic higher-order EKT approach can correct errors in EKT1-based theories with respect to the satellite region of the spectral function. Our work will be of use for the study of low-energy charge excitations and spectral functions in correlated molecules and solids where AFQMC can be reliably performed for both energy and back propagation.

Multidimensional insights involving electrochemical andin silicoinvestigation into the corrosion inhibition of newly synthesized pyrazolotriazole derivatives on carbon steel in a HCl solution

Herein, the anti-corrosion of carbon steel in 1 M HCl by two newly synthesized pyrazolotriazole derivatives, namely, 6-methyl-1H-pyrazolo[5,1-c][1,2,4]triazole-7-carbonitrile (CPT) and 1-acetyl-6-methyl-1H-pyrazolo[5,1-c][1,2,4]triazole-7-carbothioamide (MPT), was studied using electrochemical, density functional theory (DFT), and molecular dynamics (MD) simulation techniques. The experimental results showed that the concentrations of inhibitors had a significant influence on their inhibition efficiencies. Potentiodynamic polarization curves indicated that the two pyrazolotriazoles were mixed-type inhibitors. DFT calculations were employed to explore the molecular activity, and MD simulations were performed to obtain the interaction energy between the inhibitor molecules and the iron surface. The findings obtained using the theoretical calculation techniques were consistent with those obtained via experiments.

Anti-corrosion of carbon steel in 1 M HCl by 6-methyl-1H-pyrazolo[5,1-c][1,2,4]triazole-7-carbonitrile and 1-acetyl-6-methyl-1H-pyrazolo[5,1-c][1,2,4]triazole-7-carbothioamide, was studied using electrochemical, DFT and molecular dynamics simulation techniques.

An electronic time scale in chemistry

Ultrafast, subfemtosecond charge migration in small peptides is discussed on the basis of computational studies and compared with the selective bond dissociation after ionization as observed by Schlag and Weinkauf. The reported relaxation could be probed in real time if the removal of an electron could be achieved on the attosecond time scale. Then the mean field seen by an electron would be changing rapidly enough to initiate the migration. Tyrosine-terminated tetrapeptides have a particularly fast charge migration where in <1 fs the charge arrives at the other end. A femtosecond pulse can be used to observe the somewhat slower relaxation induced by correlation between electrons of different spins. A slower relaxation also is indicated when removing a deeper-lying valence electron. When a chromophoric amino acid is at one end of the peptide, the charge can migrate all along the peptide backbone up to the N end, but site-selective ionization is probably easier to detect for tryptophan than for tyrosine.

A Case Study of State-Specific and State-Averaged Brueckner Equation-of-Motion Coupled-Cluster Theory: The Ionic-Covalent Avoided Crossing in Lithium Fluoride

State-specific Brueckner equation-of-motion coupled-cluster theory (SS-B-EOMCC) is summarized, which can be considered an internally contracted version of a state-selective multireference coupled-cluster theory, which, however, is not entirely size-consistent. The method is applicable to general multireference problems, adheres to the space and spin symmetries of the molecular system, is straightforwardly extended to a state-averaged version, and has an associated perturbative variant which yields results close to the full coupled-cluster treatment. A key strength is that Brueckner orbitals are used, such that orbitals are optimized in the presence of dynamic correlation. A number of variations on the theme of SS-EOMCC is applied to study the ionic-covalent avoided crossing in LiF in a 6-311++G(3df,3pd) basis set. While reasonable results are obtained at the state-averaged level, the iterative solution process does not consistently converge for SS-EOMCC, due to the non-Hermiticity of the transformed Hamiltonian which may yield complex eigenvalues upon truncated diagonalization. This leads to an irrevocable breakdown of the state-specific EOMCC approach. We indicate some future directions that can resolve some of the problems with the SS-EOMCC methodology, as revealed by the demanding test case of the LiF potential energy curves.

Independent particle theory with electron correlation

We formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equation-of-motion coupled-cluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupled-cluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.