Accurate Ionization Potentials Research Articles

Resonance ionization spectroscopy of neodymium for determining a highly efficient two-step ionization scheme

Two-color two-step resonance ionization spectroscopy of neodymium (Nd) was performed to identify more than 120 even-parity autoionizing levels and their candidate J-values. The analysis of the observed autoionizing Rydberg series yielded a value of 44,560.11 (43)stat (2)sys cm−1 as a more accurate ionization potential of Nd. The saturation method was used to measure the transition cross-sections for some intense ionization transitions. From the measured cross-sections, the ionization efficiencies of some two-step ionization schemes were evaluated using the scheme cross-section formula to obtain several promising schemes.

Relativistic Fully Self-Consistent GW for Molecules: Total Energies and Ionization Potentials.

The fully self-consistent GW (scGW) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior results compared to G0W0 with PBE reference and comparable results to G0W0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with the experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d-shell orbitals. Additionally, using the well-conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of a few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra, and total energies in finite systems with heavy elements with a reasonable computational scaling.

Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models.

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.

Exploiting a derivative discontinuity estimate for accurate G0W0 ionization potentials and electron affinities

The GW approximation has become an important tool for predicting charged excitations of isolated molecules and condensed systems. Its popularity can be attributed to many factors, including a favorable scaling and relatively good accuracy. In practical applications, the GW is often performed as a one-shot perturbation known as G0W0 . Unfortunately, G0W0 suffers from a strong starting point dependence and is often not as accurate as one would need. Self-consistent GW methodologies alleviate these problems but come with a marked increase in computational cost. In this manuscript, we propose the use of an estimate of the exchange-correlation derivative discontinuity to provide a remarkably good starting point for G0W0 calculations, yielding ionization potentials and electron affinities with eigenvalue self-consistent GW quality at no additional cost. We assess the quality of the resulting methodology with the GW100 benchmark set and compare its advantages over other similar methods.

Connections and performances of Green's function methods for charged and neutral excitations.

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established GW approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe-Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the GW approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic.

Accurate Ionization Potentials, Electron Affinities, and Band Gaps from the ωLH22t Range-Separated Local Hybrid Functional: No Tuning Required.

The optimal tuning (OT) of range-separated hybrid (RSH) functionals has been proposed as the currently most accurate DFT-based way to compute the relevant quantities required for charge-transfer processes in organic chromophores used in organic photovoltaics and related fields. The main drawback of OT-RSHs is that the system-specific tuning of the range-separation parameter is not size-consistent. It therefore also lacks transferability, e.g., when considering processes involving orbitals not involved in the tuning or for reactions between different chromophores. Here we show that the recently reported ωLH22t range-separated local hybrid functional provides ionization energies, electron affinities, and fundamental gaps on par with OT-RSH treatments, approaching the quality of GW results, without any need for system-specific tuning. This holds from relevant organic chromophores of varying sizes all the way to atomic electron affinities. ωLH22t also gives excellent outer-valence quasiparticle spectra and is a generally accurate functional for both main-group and transition-metal energetics, as well as for a variety of excitation types. Range-separated local hybrid functionals are suggested as promising new quantum-chemical tools in molecular electronics.

Investigation of Ionization Potential in Quantum Dots Using the Stratified Stochastic Enumeration of Molecular Orbitals Method.

The overarching goal of this work is to investigate the size-dependent characteristics of the ionization potential of PbS and CdS quantum dots. The ionization potentials of quantum dots provide critical information about the energies of occupied states, which can then be used to quantify the electron-removal characteristics of quantum dots. The energy of the highest-occupied molecular orbital is used to understand electron-transfer processes when invesigating the energy-level alignment between quantum dots and electron-accepting ligands. Ionization potential is also important for investigating and interpreting electron-detachment processes induced by light (photoelectron spectra), external voltage (chemiresistance), and collision with other electrons (impact ionization). Accurate first-principles calculations of ionization potential continue to be challenging because of the computational cost associated with the construction of the frequency-dependent self-energy operator and the numerical solution of the associated Dyson equation. The computational cost becomes prohibitive as the system size increases because of the large number of 2particle-1hole (2p1h) and 1particle-2hole (1p2h) terms needed for the calculation. In this work, we present the Stratified Stochastic Enumeration of Molecular Orbitals (SSE-MO) method for efficient construction of the self-energy operator. The SSE-MO method is a real-space method and the central strategy of this method is to use stochastically enumerated sampling of molecular orbitals and molecular-orbital indices for the construction of the 2p1h and 1p2h terms. This is achieved by first constructing a composite MO-index Cartesian coordinate space followed by transformation of the frequency-dependent self-energy operator to this composite space. The evaluation of both the real and imaginary components of the self-energy operator is performed using a stratified Monte Carlo technique. The SSE-MO method was used to calculate the ionization potentials and the frequency-dependent spectral functions for a series of PbS and CdS quantum dots by solving the Dyson equation using both single-shot and iterative procedures. The ionization potentials for both PbS and CdS quantum dots were found to decrease with increasing dot size. Analysis of the frequency-dependent spectral functions revealed that for PbS quantum dots the intermediate dot size exhibited a longer relative lifetime whereas in CdS the smallest dot size had the longest relative lifetime. The results from these calculations demonstrate the efficacy of the SSE-MO method for calculating accurate ionization potentials and spectral functions of chemical systems.

Scaled σ-functionals for the Kohn-Sham correlation energy with scaling functions from the homogeneous electron gas.

The recently introduced σ-functionals constitute a new type of functionals for the Kohn-Sham (KS) correlation energy. σ-Functionals are based on the adiabatic-connection fluctuation-dissipation theorem, are computationally closely related to the well-known direct random phase approximation (dRPA), and are formally rooted in many-body perturbation theory along the adiabatic connection. In σ-functionals, the function of the eigenvalues σ of the Kohn-Sham response matrix that enters the coupling constant and frequency integration in the dRPA is replaced by another function optimized with the help of reference sets of atomization, reaction, transition state, and non-covalent interaction energies. σ-Functionals are highly accurate and yield chemical accuracy of 1 kcal/mol in reaction or transition state energies, in main group chemistry. A shortcoming of σ-functionals is their inability to accurately describe processes involving a change of the electron number, such as ionizations or electron attachments. This problem is attributed to unphysical self-interactions caused by the neglect of the exchange kernel in the dRPA and σ-functionals. Here, we tackle this problem by introducing a frequency- and σ-dependent scaling of the eigenvalues σ of the KS response function that models the effect of the exchange kernel. The scaling factors are determined with the help of the homogeneous electron gas. The resulting scaled σ-functionals retain the accuracy of their unscaled parent functionals but in addition yield very accurate ionization potentials and electron affinities. Moreover, atomization and total energies are found to be exceptionally accurate. Scaled σ-functionals are computationally highly efficient like their unscaled counterparts.

Ionization potentials for the H2CO trimer.

In this work, a computational study on the ionization potentials (IPs) of the formaldehyde trimer, (H2CO)3, is presented. Twelve lowest-lying vertical IPs were determined through the use of the coupled-cluster level of theory using 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 excitations method with the aug-cc-pVnZ and aug-cc-pCVnZ (n = D and T) basis sets was used. The Feller-Peterson-Dixon (FPD) composite approach was employed to provide accurate IPs, and eight conformations of (H2CO)3 were considered. The FPD IPs determined for (H2CO)3 were found to be systematically lower than those computed for the dimer and monomer of H2CO in the pattern IP(monomer) > IP(dimer) > IP(trimer) for a given IP. In addition, the IPs calculated when considering only the more stable conformation (C0) are in good agreement with those obtained using the eight conformations of the H2CO trimer, and thus, the actual conformation played only a minor role in determining such properties in the present case. By providing first accurate IP results for the H2CO trimer, we hope to motivate future experimental and computational investigations (e.g., studies involving photoionization) that rely on such quantities.

Symmetry-adapted formulation of the hybrid treatment resulting from the G-particle-hole Hypervirial equation and equations of motion methods: a procedure for modeling solids

Highly accurate electron affinities and ionization potentials of chemical systems were described by means of the procedure called GHV-EOM (Valdemoro et al, in Int J Quantum Chem 112:2965, 2012), which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al, in Int J Quantum Chem 109:3178, 2009) and that of the equations-of-motion (EOM), by Simons and Smith (Simons and Smith, in J Chem Phys 58:4899, 1973). The present work improves that hybrid method by introducing the point group symmetry within its framework, providing a higher computational efficiency. We report results which show the achievements attained by using the symmetry-adapted methodology. The new formulation turns out to be particularly suitable for characterizing solid models, as cyclic one-dimensional chains.

Experimental and theoretical study on p-chlorofluorobenzene in the S, S1 and D states

The geometric structures and vibration frequencies of para-chlorofluorobenzene (p-ClFPh) in the first excited state of neutral and ground state of cation were investigated by resonance-enhanced multiphoton ionization and slow electron velocity-map imaging. The infrared spectrum of S0 state and absorption spectrum for S1 ← S0 transition in p-ClFPh were also recorded. Based on the one-color resonant two-photon ionization spectrum and two-color resonant two-photon ionization spectrum, we obtained the adiabatic excited-state energy of p-ClFPh as 36302±4 cm−1. In the two-color resonant two-photon ionization slow electron velocity-map imagin spectra, the accurate adiabatic ionization potential of p-ClFPh was extrapolated as 72937±8 cm−1 via threshold ionization measurement. In addition, Franck-Condon simulation was performed to help us confidently ascertain the main vibrational modes in the S1 and D0 states. Furthermore, the mixing of vibrational modes between S0 → S1 and S1 → D0 has been analyzed.

From simple molecules to nanotubes. Reliable predictions of ionization potentials from the ΔMP2-SCS methods

The vertical ionization potentials for systems of various sizes, ranging from simple molecules, DNA/RNA bases, donor and acceptor organic molecular systems as well as nanotubes are calculated using the ΔMP2-SCS family of methods [Śmiga et al 2018 J. Chem. Theory Comput. 14 4780–90]. We have shown that for all investigated cases, the ΔMP2-SCS methods, being almost cost free single-step post-Hartree–Fock calculation, provide very accurate vertical ionization potentials comparable in quality with state-of-art outer valence Green’s function methods. Moreover, we show that a combination of the ΔMP2-SCS methods with the resolution of identity technique is effective and reliable an alternative to the semi-empirical density functional theory methods and Green’s function-based calculations of ionization potentials for large molecular systems such as silicon-based or organic-based solar cells, for which the IP-EOM-CCSD calculations are too expensive for routine calculations.

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

The development of a quasi-particle approach for an accurate yet efficient prediction of a complete ionization potential (IP) spectrum, from valence down to core electrons for the system of interest, is a long-cherished goal in quantum chemistry. Based on the physical understanding of the electron correlation and relaxation effects at the second order perturbation theory, we present here a correlation-relaxation-balanced direct method, dubbed CRB-MP2, via a parameter scaled scheme of the 2ph (two-particle, one-hole summation) and 2hp (two-hole, one-particle summation) terms. With almost no extra computational cost after a normal MP2 procedure, the CRB-MP2 method yields high quality valence and core IPs for a wide range of species. A direct approach for complete IP spectrum calculations with both computational accuracy and efficiency is therefore established.

Explicitly correlated renormalized second-order Green's function for accurate ionization potentials of closed-shell molecules.

We present an energy-dependent explicitly correlated (F12) formalism for the nondiagonal renormalized second-order (NR2) Green's function method of closed-shell molecules. For a test set of 21 small molecules, the mean basis set error in IP computed using NR2-F12 with aug-cc-pVTZ basis is 0.028 eV, compared to 0.044 eV for NR2 with aug-cc-pV5Z basis. Similarly, for a set of 24 medium-sized organic electron acceptor molecules (OAM24), the mean basis set errors are 0.015 eV for NR2-F12 with aug-cc-pVTZ basis compared to 0.067 eV for NR2 with aug-cc-pVQZ basis. Hence, NR2-F12 facilitates accurate calculation of IP at a lower cost compared to the NR2 method. NR2-F12 has O(N6)/O(N5)noniterative/iterative costs with system size. At a small basis, the performance of NR2-F12 for 21 small molecules and OAM24 dataset is comparable to equation-of-motion ionized coupled-cluster singles and doubles, whose cost is iterativeO(N6).

Improved density matrices for accurate molecular ionization potentials

The ionization potential and the other quasiparticle energies of electrons in molecules or solids are often evaluated within the $GW$ approximation. Though this approximation can be considered as a fantastic tradeoff between accuracy and simplicity, there exist ionization potentials of simple molecules that are unacceptably wrong. We derive here a working approximation to the density matrix that we name the $GW$ density matrix. This relatively light approximation improves several physical properties and, in particular, it yields excellent electronic dipoles for the examined molecules. As a direct consequence, the ionization potentials are affected through the change in the electrostatic potential and in the exchange operator. Benchmarking on a set of 34 molecules, we demonstrate that most of the error in the $GW$ ionization potentials is indeed eliminated thanks to this simple addition. This contribution is not a vertex correction, but nevertheless it is crucial when going beyond the standard $GW$.

Neutral atoms and ion energies, accurate ionization potential, and electron affinities by polynomial generator coordinate Hartree–Fock method

We have developed accurate Gaussian basis functions obtained with the polynomial generator coordinate Hartree-Fock (p-GCHF) method for H, Zn, and Ga-Kr atoms. These basis sets have been applied in the calculation of nonrelativistic energies for neutral atoms, monovalent cations, monovalent anions, ionization potential (IP), and electron affinity (EA), with the objective of proving the quality of the basis set generated by the p-GCHF method. The total energies calculated for neutral atoms and monovalent cations and respective IP were minimally affected by the addition of polarization functions and their precision was comparable to the values reported in the literature. The relative errors were lower than 6.0 \texttimes\ 10$^{-5}$% and 7.0 \texttimes\ 10$^{-5}$% for neutral atoms and monovalent cations, respectively. The IP results were strictly equal to numerical Hartree-Fock (NHF) calculations and comparable to some experimental values. For monovalent anions, the nonrelativistic total energies were better than the Slater-type functions results and the relative errors were lower than 0.05% when compared to NHF. The EA results were the same as those obtained with NHF calculations reported in the literature for heavier elements. For IP and EA, our results followed the same periodic tendency when compared with experimental data.

Accurate Ionization Potentials, Electron Affinities and Electronegativities of Single-Walled Carbon Nanotubes by State-of-the-Art Local Coupled-Cluster Theory

Abstract Single-walled carbon nanotubes (SWCNTs) possess novel conducting properties and high potential as a building block for molecular electronic devices. In this paper, we report accurate ionization potentials, electron affinities and electronegativities for large SWCNTs using our state-of-the-art implementations of reduced-scaling coupled-cluster method (DLPNO-CCSD(T)) using triple zeta basis set.

Quantitative Structure-Property Relationships for the Electronic Properties of Polycyclic Aromatic Hydrocarbons.

This study presents a development in quantitative structure–property relationships (QSPRs) for research in organic semiconductor materials by introducing a new structural descriptor called “degree of π-orbital overlap” based on two-dimensional structure information of aromatic molecules. Application of this method to predict the electronic properties of polycyclic aromatic hydrocarbon (PAH) molecules, which are known to be the core component of many organic semiconductor materials, is presented. Results demonstrated that QSPRs based on the new descriptor can predict rather accurate band gaps, ionization potentials and electron affinities for a large number of PAHs compared to those explicitly calculated by density functional theory method. This research opens new possibilities for developing QSPRs for other organic semiconductor classes in future.

Range-Separated Double-Hybrid Functional from Nonempirical Constraints.

On the basis of our previous developments in the field of nonempirical double hybrids, we present here a new exchange-correlation functional based on a range-separated model for the exchange part and integrating a nonlocal perturbative correction to the electron correlation contribution. Named RSX-QIDH, the functional is free from any kind of empirical parametrization. Its range-separation parameter is set to recover the total energy of the hydrogen atom, thus eliminating the self-interaction error for this one-electron system. Subsequent tests on some relevant benchmark data sets confirm that the self-interaction error is particularly low for RSX-QIDH. This new functional provides also correct dissociation profiles for charged rare-gas dimers and very accurate ionization potentials directly from Kohn-Sham orbital energies. Above all, these good results are not obtained at the expense of other properties. Indeed, further tests on standard benchmarks show that RSX-QIDH is competitive with the more empirical ωB97X-2 double hybrid and outperforms the parent LC-PBE long-range corrected hybrid, thus underlining the important role of the nonlocal perturbative correlation.

Size-Dependence of Nonempirically Tuned DFT Starting Points for G0W0 Applied to π-Conjugated Molecular Chains.

G0W0 calculations for predicting vertical ionization potentials (IPs) and electron affinities of molecules and clusters are known to show a significant dependence on the density functional theory (DFT) starting point. A number of nonempirical procedures to find an optimal starting point have been proposed, typically based on tuning the amount of HF exchange in the underlying hybrid functional specifically for the system at hand. For the case of π-conjugated molecular chains, these approaches lead to a significantly different amount of HF exchange for different oligomer sizes. In this study, we analyze if and how strongly this size dependence affects the ability of nonempirical tuning approaches to predict accurate IPs for π-conjugated molecular chains of increasing chain length. To this end, we employ three different nonempirical tuning procedures for the G0W0 starting point to calculate the IP of polyene oligomers up to 22 repeat units and compare the results to highly accurate coupled-cluster calculations. We find that, despite its size dependence, using an IP-tuned hybrid functional as a starting point for G0W0 yields excellent agreement with the reference data for all chain lengths.