DFT study of ionization potentials and electron affinities of formamide and its methylation derivatives

The ionization potentials (IPs) and electron affinities (EAs) of formamide in the gas phase have been calculated using density functional theory (DFT), ab initio HF and Møller-Plesset perturbational theory (MP) at 6-311++G** basis set. The results indicate that the IPs of formamide obtained with DFT and MP are in agreement with the results obtained from experiment. And B3LYP has been confirmed to be the most accurate method in calculating the AIPs and VIPs of formamide through our work. IPs and EAs of formamide in solution are not known experimentally, therefore IPs and EAs of formamide in chloroform, acetone, and dimethylsulfoxide have been calculated using polarized continuum model (PCM) with B3LYP/6-311++G** level and have been compared with the values in the gas phase. The AIPs and VIPs of formamide have been compared with those of its methylation derivatives. All EAs of methylation derivatives of formamide are bigger than those of formamide conformers in the gas phase with BLYP, B3LYP, and B3P86 methods at 6-311++G** basis set. All these indicate that all anions of methylation derivatives of formamide are more stable than anions of formamide with respect to electron detachment adiabatically and vertically in the gas phase.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Limitations of Global Hybrids in Predicting the Geometries and Torsional Energy Barriers of Dimeric Systems and the Role of Hartree Fock and DFT Exchange

Prediction of accurate geometries is a prerequisite for accurate prediction of molecular properties. Impact of Hartree Fock (HF) exchange (a₀) on geometry in the framework of DFT is investigated by monitoring dihedral angles, bond length alternations, and torsional energy barriers of 10 dimeric systems against CCSD (ADZ/ATZ) benchmarks. A strong correlation is observed between the fraction of HF exchange, equilibrium dihedral angles, and the potential energy barriers in global hybrids. Full HF exchange is critical to accurately predict the nonplanarity. Lower fractions of (a₀)/larger DFT exchange (1-a₀) results in overestimation of torsional energy barriers at 90⁰ and underestimation at 0⁰. Large contributions of (1-a₀) in global hybrid functionals tend to overestimate torsional energy barriers (90⁰) and are biased toward planar geometries. However, inclusion of larger fractions of (a₀)/lower (1-a₀) also overestimate the torsional energy barriers in syn-conformations due to the localization errors associated with HF exchange in global hybrids. Hence, irrespective of the fraction of HF/DFT exchange incorporated, global hybrids fail to accurately predict torsional energy barriers at 0⁰ and 90⁰ simultaneously. Long-range corrected (LC) functionals, which employ full HF exchange at longer regions, outperform global hybrid functionals in predicting geometries and torsional energy barriers of the dimeric molecules. The distance dependence of (a₀) thus provides a balanced fraction of HF exchange as the dihedral torsion varies. Impact of range separation parameter on geometries is marginal in altering the planarity/nonplanarity. However, range separation parameter within 0.20–0.40 bohr⁻¹ predicts more reliable torsional energies and geometries. © 2019 Wiley Periodicals, Inc.     

Design of low band gap polymers employing density functional theory—hybrid functionals ameliorate band gap problem

Band gaps in solids and excitation energies in finite systems are underestimated significantly if estimated from differences between eigenvalues obtained within the local spin density approximation (LSDA). In this article we present results on 20 small- and medium-sized π-systems which show that HOMO–LUMO energy differences obtained with the B3LYP, B3P86, and B3PW91 functionals are in good agreement with vertical excitation energies from UV-absorption spectra. The improvement is a result of the use of the exact Hartree–Fock exchange with hybrid methods. Negative HOMO energies and negative LUMO energies do not provide good estimates for IPs and EAs. In contrast to Hartree–Fock theory, where IPs are approximated well and EAs are given poorly, DFT hybrid methods underestimate IPs and EAs by about the same amount. LSDA yields reasonable EAs but poor IPs. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1943–1953, 1997     

有机半导体的电子电离能、亲和势和极化能的密度泛函理论研究

准确预测有机半导体的能级(如电子电离能和亲和势等)对设计新型有机半导体材料和理解相关机理至关重要。从理论计算的角度看,主要挑战来自于缺少一种不仅能够在定性上合理而且在定量上精确预测,同时并不显著增加计算成本的理论方法。本文中,我们证明了通过结合极化连续介质模型(PCM)和"最优调控"区间分离密度泛函方法能够准确预测一系列有机半导体的电子电离能(IP)、亲和势(EA)和极化能,其预测结果与实验数据吻合得很好。重要的是,经过调控后分子的前线分子轨道能量(即-~εHOMO和-~εLUMO)与对应的IP和EA计算值很接近。调控方法的成功可以进一步归因于其能够根据不同分子体系或同种分子所处的不同状态(气态和固态)"最优"地平衡泛函中分别用于描述电子局域化和离域化的作用。相比而言,其它常见的密度泛函方法由于包含的HF%比例过低(如PBE)或过高(如M06HF和未调控的区间分离泛函),均不能给予合理的预测。因此,我们相信这种PCM-调控的方法能够为研究其它更加复杂的有机体系的能级问题提供一种更加可靠和便捷的理论工具。     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

Atomic ionization potentials and electron affinities with relativistic and mass corrections

Relativistic corrections to ionization potentials (IPs) and electron affinities (EAs) of atoms with an atomic number Z≤54 are examined based on the first-order perturbation theory with an approximate Schr?dinger form of the Dirac-Coulomb-Breit Hamiltonian. Using a Hartree-Fock (HF) wave function from the numerical HF method as the unperturbed function, both the LS-non-splitting and fine-structure corrections are evaluated together with the normal and specific mass corrections. The LS-non-splitting corrections are found to be important for IPs and EAs of transition metal atoms. The fine-structure corrections are generally larger in magnitude than the LS-non-splitting corrections for the atoms of groups 13–18 with Z≥31, and can never be neglected. Comparison of the IPs and EAs presented here and experimental IPs and EAs gives an estimation of the electron correlation correction for these properties. For some light atoms, the estimated values agree with the results directly obtained from correlated calculations. Received: 28 January 1997 / Accepted: 4 March 1997     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

Calculation of electron affinities of polycyclic aromatic hydrocarbons and solvation energies of their radical anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.     

BFW: a density functional for transition metal clusters

Ionization potentials (IPs) or electron affinities (EAs) for transition metal clusters are an important property that can be used to identify and differentiate between clusters. Accurate calculation of these values is therefore vital. Previous attempts using a variety of DFT models have correctly predicted trends, but have relied on the use of scaling factors to compare to experimental IPs. In this paper, we introduce a new density functional (BFW) that is explicitly designed to yield accurate, absolute IPs for transition metal clusters. This paper presents the numerical results for a selection of transition metal clusters and their carbides, nitrides, and oxides for which experimental IPs are known. When tested on transition metal clusters, the BFW functional is found to be significantly more accurate than B3LYP and B3PW91.     

Computational Study of Vertical Ionization Potentials Using Density Functional Theory and Green's Function Methods

Over one hundred vertical ionization potentials (VIPs) were computed using density functional theory (DFT) and Green's function (GF) based methods. The DFT approaches include the unrestricted transition state (uTS) and unrestricted diffuse ionization (uDI) approximations using the Becke88‐Perdew86 exchange‐correlation functional. Green's function methods include the outer‐valence GF (OVGF) approach, the parametrized GF2 (pGF2), and the parametrized GF2 times screened interaction (pGW2) approximations. DFT computations of IPs using the uTS approximation was found to be nearly as accurate as those predicted using the elaborate OVGF method. The much more computationally efficient uDI approximation provides predictions of moderate accuracy and is recommended for computing IPs for larger molecules. We have observed that the average absolute deviations from a uDI calculation using poorer basis set (DZVP) and poorer geometry (AM1 optimization) is only slightly larger.     

DFT calculations of the ionization potentials and electron affinities of serinamide

Adiabatic and vertical ionization potentials (IPs) and valence electron affinities (EAs) of serinamide in the gas phase have been determined using density functional theory (DFT) B3LYP, B3P86, and B3PW91 methods with the 6‐311++G** and 6‐311G** basis sets, respectively. IPs and EAs of serinamide in solution have been calculated with the B3LYP method using the 6‐311++G** and 6‐311G** basis sets. Eight possible conformers of serinamide and its charged states in the gas phase have been optimized employing the DFT B3LYP method with 6‐311++G** and 6‐311G** basis sets, respectively. All the adiabatic and vertical ionization potentials (AIPs and VIPs) of eight serinamide conformers in our work are positive values, whether in the gas phase or in solutions; the IPs in solutions are smaller than the results in the gas phase and decrease with increased dielectric constants in solutions. This finding indicates that the cationic states in solutions are more stable than those in the gas phase. All EAs of eight serinamide conformers are negative values in the gas phase, indicating that the anionic states are unstable with respect to electron autodetachment, both adiabatically and vertically. In contrast, all other adiabatic electron affinities (AEAs) are negative values in solutions except for 6S in water; 7S in chloroform, acetone, and water; and 8S in acetone and water, and increase with increasing of dielectric constants in solutions. All vertical electron affinities (VEAs) are negative values in solutions; however, no good rule has been found for these values in solutions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

QSPR Studies on lgK_(ow) and lgK_(oc) of Fluorobenzenes and Property Parameters Based on HF and DFT Calculations

1 INTRODUCTION Quantitative structure-activity relationship (QSAR) equation could be employed to predict the biological activities of unknown compounds, which is signifi- cant for initial screening and evaluation of toxic compounds[1]. Soil sorption coeff…     

Addition by subtraction in coupled cluster theory. II. Equation-of-motion coupled cluster method for excited, ionized, and electron-attached states based on the nCC ground state wave function

New iterative double and triple excitation corrections to the equation-of-motion coupled cluster (EOM-CC) based upon the recently developed nCC methods [Bartlett and Musia?, J. Chem. Phys. 125, 204105-1 (2006)] are applied to excitation energies (EEs), ionization potentials (IPs), and electron affinities (EAs). The methods have been tested by the evaluation of the vertical EEs, IPs, and EAs for Ne, BH, CH(2), H(2)O, N(2), C(2), CH(+), CO, and C(2)H(4) compared to full configuration interaction, EOM-CCSD, EOM-CCSDT, and experimental data.     

Ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and ionic radii of element Uus (Z = 117) and astatine

Multiconfiguration Dirac-Fock (MCDF) method was employed to calculate the first five ionization potentials, electron affinities, resonance excitation energies, oscillator strengths, and radii for the element Uus and its homologue At. Main valence correlation effects were taken into account. The Breit interaction and QED effects were also estimated. The uncertainties of calculated IPs, EAs, and IR for Uus and At were reduced through an extrapolation procedure. The good consistency with available experimental and other theoretical values demonstrates the validity of the present results. These theoretical data therefore can be used to predict some unknown physicochemical properties of element Uus, Astatine, and their compounds.     

Structural,electronic, and optical properties of phenol‐pyridyl boron complexes for light‐emitting diodes

The coordination chemistry of polydentate chelating ligands that contain mixed pyridinephenol donor sets has been a sought‐after target of study and is a possible extension to the chemistry of polypyridines. In this article, seven compounds, which are the four‐coordinate boron complexes containing the mixed phenol‐pyridyl group, have been studied by theoretical calculation. They can function as charge transport materials and emitters, with high efficiency and stability. To reveal the relationship between the structures and properties of these bifunctional or multifunctional electroluminescent materials, the ground and excited state geometries were optimized at the B3LYP/6‐31G(d), HF/6‐31G(d), and CIS/6‐31G(d) levels, respectively. The ionization potentials (IPs) and electron affinities (EAs) were computed. The mobilities of hole and electron in these compounds were studied computationally based on the Marcus electron transfer theory. The lowest excitation energies, and the maximum absorption and emission wavelengths of these compounds were calculated by time‐dependent density functional theory method. As a result of these calculations, the values of HOMO, LUMO, energy gaps, IPs, EAs, and the balance between the hole‐ and electron‐transfer are greatly improved with the substitution of carbazole in compound 6 . The calculated emission spectra of the seven studied molecules can almost cover the full UV‐vis range (from 447.4 to 649.3 nm). Also, the Stokes shifts are unexpectedly large, ranging from 139.4 to 335.1 nm. This will result in the relatively long fluorescence lifetimes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009