Equations of Motion Theory for Electron Affinities

Response of a Molecule to Adding or Removing an Electron

Chapter 17 - Equations of motion methods for computing electron affinities and ionization potentials

Theab initiocalculation of molecular electron affinities (EA) is a difficult task because the energy of interest is a very small fraction of the total electronic energy of the parent neutral. That is, EAs typically lie in the 0.01–10 eV range, but the total electronic energy of even a small molecule is usually several orders of magnitude larger. Moreover, because the EA is an intensive quantity but the total energy is an extensive quantity, the difficulty in evaluating EAs to within a fixed specified (e.g., ±0.1 eV) accuracy becomes more and more difficult as the size and number of electrons in the molecule grows. The situation becomes especially problematic when studying extended systems such as solids, polymers, or surfaces for which the EA is an infinitesimal fraction of the total energy. The equations of motion (EOM) methods offer a route to calculating the intensive EAs directly as eigenvalues of a set of working equations. A history of the development of the EOM theories as applied to EAs, their numerous practical implementations, and their relations to Green's function or propagator theories are covered in this contribution. EOM methods based upon Møller–Plesset, multiconfiguration self‐consistent field, and coupled‐cluster reference wave functions are included in the discussion as is the application of EOM methods to metastable resonance states of anions.

We present implementation of second- and third-order algebraic diagrammatic construction (ADC) theory for efficient and accurate computations of molecular electron affinities (EA), ionization potentials (IP), and densities of states [EA-/IP-ADC(n), n = 2, 3]. Our work utilizes the non-Dyson formulation of ADC for the single-particle propagator and reports working equations and benchmark results for the EA-ADC(2) and EA-ADC(3) approximations. We describe two algorithms for solving EA-/IP-ADC equations: (i) conventional algorithm that uses iterative diagonalization techniques to compute low-energy EA, IP, and density of states and (ii) Green's function algorithm (GF-ADC) that solves a system of linear equations to compute density of states directly for a specified spectral region. To assess the accuracy of EA-ADC(2) and EA-ADC(3), we benchmark their performance for a set of atoms, small molecules, and five DNA/RNA nucleobases. As our next step, we demonstrate the efficiency of our GF-ADC implementation by computing core-level K-, L-, and M-shell ionization energies of a zinc atom without introducing the core-valence separation approximation. Finally, we use EA- and IP-ADC methods to compute the bandgaps of equally spaced hydrogen chains Hn with n up to 150, providing their estimates near thermodynamic limit. Our results demonstrate that EA-/IP-ADC(n) (n = 2, 3) methods are efficient and accurate alternatives to widely used electronic structure methods for simulations of electron attachment and ionization properties.

DFT methods are used to calculate the ionization energy (IE) and electron affinity (EA) trends in a series of pincer ligated d(8)-Ir((tBu4)PXCXP) complexes (1-X), where C is a 2,6-disubstituted phenyl ring with X = O, NH, CH2, BH, S, PH, SiH2, and GeH2. Both C2v and C2 geometries are considered. Two distinct σ-type ((2)A1 or (2)A) and π-type ((2)B1 or (2)B) electronic states are calculated for each of the free radical cation and anion. The results exhibit complex trends, but can be satisfactorily accounted for by invoking a combination of electronegativity and specific π-orbital effects. The calculations are also used to study the effects of varying X on the thermodynamics of oxidative H2 addition to 1-X. Two closed shell singlet states differentiated in the C2 point group by the d(6)-electon configuration are investigated for the five-coordinate Ir(III) dihydride product. One electronic state has a d(6)-(a)(2)(b)(2)(b)(2) configuration and a square pyramidal geometry, the other a d(6)-(a)(2)(b)(2)(a)(2) configuration with a distorted-Y trigonal bipyramidal geometry. No simple correlations are found between the computed reaction energies of H2 addition and either the IEs or EAs. To better understand the origin of the computed trends, the thermodynamics of H2 addition are analyzed using a cycle of hydride and proton addition steps. The analysis highlights the importance of the electron and hydride affinities, which are not commonly used in rationalizing trends of oxidative addition reactions. Thus, different complexes such as 1-O and 1-CH2 can have very similar reaction energies for H2 addition arising from opposing hydride and proton affinity effects. Additional calculations on methane C-H bond addition to 1-X afford reaction and activation energy trends that correlate with the reaction energies of H2 addition leading to the Y-product.

Further developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP) and electron affinities (EA) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty‐seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N+, as in pyridine, N+2, as in pyrrole, and O+2, as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical‐adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values.The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.

We present an approximate approach for the calculation of ionization potential (IP) and electron affinity (EA) by exploiting the complementary energy non-linearity errors for a species M and its one-electron-ionized counterpart (M+). Reasonable IPs and EAs are thus obtained by averaging the orbital energies of M and M+, even with a low-level method such as BLYP/6-31G(d). By combining the corrected IPs and EAs, we can further obtain reasonable excitation energies. The errors in uncorrected valence IPs and uncorrected virtual-orbital energies show systematic trends. These characteristics provide a convenient and computationally efficient avenue for qualitative estimation of these properties with single corrections for multiple IPs and excitation energies.

Molecular doping is a charge-transfer process intended to improve the electrical properties of organic semiconductors and the efficiency of organic electronic devices, by incorporation of a complex-forming, strong molecular electron acceptor or donor. Using density functional theory methods with dispersion corrections, we seek to monitor charge transfer and estimate its amount via calculations of experimental observables. With 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ) as a p-dopant (electron acceptor) and an array of π-conjugated molecules as hole-transport materials (donors), the amount of charge transfer is seen to be a non-monotonic function of the offset defined by the donor ionization potential (IP) and the acceptor electron affinity (EA), IP – |EA|. Interestingly, a well-defined, linear relationship between the amount of charge transfer and IP – |EA| is obtained when the IP and EA values are adjusted to reflect intramolecular geometric changes in the final form of the complex. This study offers a straightforward way to match donor–acceptor pairs with desired doping effects and to estimate the resulting charge density in organic semiconductors.

The Multiconfigurational Spin-Tensor Electron Propagator Method (MCSTEP)

Pseudopotentials are an essential ingredient in diffusion quantum Monte Carlo (DMC) calculations to increase efficiency substantially. A new generation of effective core potentials (ccECP) has been recently developed for DMC calculations. In this paper, performance of DMC using ccECP potentials on total energies, ionization potentials (IPs) and electron affinities (EAs) of some second- and third-row atoms and molecules is investigated systematically with different types of trial wave functions. DMC results are compared with those of high-level coupled-cluster methods extrapolated to complete basis set limit (CC-CBS). Error of ccECP potentials on IPs and EAs is also evaluated through a comparison with those from all-electron calculations. Our results show that mean errors in DMC energies with the ccECP potentials are smaller than those with the pseudopotentials developed by Burkatzki, Filippi, and Dolg (BFD), when the same type of trial wave functions is adopted. Mean absolute deviations (MADs) on IPs of DMC compared with those of CC-CBS are about 1.6 kcal/mol with single-determinant-Jastrow trial wave functions, and 1 kcal/mol with multideterminant-Jastrow trial wave functions using either ccECP or BFD potentials. MADs on EAs with DMC using the ccECP potentials are about 1 kcal/mol and slightly larger than those with the BFD potentials. Our results show that ccECP potentials are able to provide reliable IPs and EAs in DMC calculations. Accuracy of IPs and EAs from DMC calculations using ccECP potentials is similar to that with the BFD potentials, although mean error in total DMC energies with ccECP potentials is smaller. Furthermore, error of ccECP potentials in DMC calculations on IPs and EAs is smaller than that of BFD potentials compared with all-electron results.

Calculation of electron affinity, ionization potential, transport gap, optical band gap and exciton binding energy of organic solids using ‘solvation’ model and DFT

Molecular doping of charge carriers in organic semiconductors is a complex process influenced by both single-molecule energetics and multiscale morphology. Here, we employ atomistic molecular dynamics simulations and density functional theory (DFT) calculations of disordered P3HT:F4TCNQ morphologies to understand how conformational disorder influences doping efficiency. We find that conformational variations in P3HT:F4TCNQ dimers can modulate the amount of ground-state charge transfer between P3HT and F4TCNQ by more than 0.5 C. The amount of charge transfer in P3HT:F4TCNQ dimers exhibits a linear correlation with the difference between the ionization potential (IP) of P3HT and the electron affinity (EA) of F4TCNQ, when using geometries extracted from DFT-optimized dimer aggregates. We find that most variation in IP - |EA| that governs the amount of ground-state charge transfer is due to conformational variations of P3HT's IP (∼0.35 eV) compared with F4TCNQ's EA (∼0.15 eV). Finally, we show that the free energy of charge generation (ΔGrxn) of the dimer, when treated as the sum of IP - |EA| and electrostatic energies derived from atomic partial charges, correlates linearly with the amount of charge transfer in the dimer. These findings shed light on the energetics of the molecular doping process, justifying simple approximations employed in recent reactive Monte Carlo methods for molecular doping and providing an avenue for systematic DFT parametrization of multiscale doping methods.

Electronic structure and spectroscopic properties of (2S,3S)-2,3-diphenyl-5,6-diheteroaryl-2,3-dihydropyrazines and their model oligomers

The self-consistent determination of the ion and neutral molecule wavefunctions in a theory of electron affinities and ionization potentials

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.