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.     

Role of s-p orbital mixing in the bonding and properties of second-period diatomic molecules

Qualitative molecular orbital theory is widely used as a conceptual tool to understand chemical bonding. Symmetry-allowed orbital mixing between atomic or fragment orbitals of different energies can greatly complicate such qualitative interpretations of chemical bonding. We use high-level Amsterdam Density Functional calculations to examine the issue of whether orbital mixing for some familiar second-row homonuclear and heteronuclear diatomic molecules results in net bonding or antibonding character for a given molecular orbital. Our results support the use of slopes of molecular orbital energy versus bond distance plots (designated radial orbital-energy slope: ROS) as the most useful criterion for making this determination. Calculated atomic charges and frontier orbital properties of these molecules allow their acid-base chemistry, including their reactivities as ligands in coordination chemistry, to be better understood within the context of the Klopman interpretation of hard and soft acid-base theory. Such an approach can be extended to any molecular species.     

Effects of different basis sets and donor‐acceptor groups on linear and second‐order nonlinear optical properties and molecular frontier orbital energies

The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Studies on the 1,4-oxazepine ring formation reaction using the molecular orbital method

1,4-Oxazepine formation reactions of 1,8-naphthyridine derivatives (1-4) with peroxy acid have been studied using a semiempirical MO method (AM1) and an ab initio molecular orbital method (Gaussian 94). The energies of molecules involved in the reaction paths were calculated and the transition states related to experimental products were obtained. For the reactions of 1-3, the calculated energies of the transition states predicted the previously obtained products. However, the calculated values for the reaction of 4 suggested a different type of oxazepine compound, which was verified in further experiments.     

Orbital phase in Suzuki–Miyaura cross-coupling reactions

We investigated the electronic structures of the transition states of the oxidative addition, transmetalation, and reductive elimination steps in the catalytic cycle of the title reaction. The frontier orbital theory was surprisingly found to be applicable whereas any d orbitals of transition metals can be a main component of frontier orbitals because of their close energies. Visualizing the actually calculated HOMO and LUMO of the two parts of the transition structure of each step clearly demonstrated their orbital phase matching in favor of overlapping. The HOMO for the transmetalation step suggests that electron-donating ability of the carbon–metal bond of organometallic compounds (RMX) could control the reactivities of related cross-coupling reactions. The energies of the molecular orbitals having large amplitudes of the C–M bonding orbitals of RMX explain why the Suzuki–Miyaura cross-coupling reaction needs a base while the Kumada–Tamao and Negishi reactions take place without any bases.     

Basis set effects on frontier molecular orbital energies and energy gaps: a comparative study between plane waves and localized basis functions in molecular systems

In order to study the Kohn-Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximation exchange-correlation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the plane-waves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the plane-wave expansion have been appropriately calibrated.     

Linear-scaling molecular orbital calculations for the pKa values of ionizable residues in proteins

In this report, we present a computational methodology for the pKa prediction of proteins, based on linear-scaling molecular orbital calculations for their solution-conformations obtained from NMR measurements. The method is used to predict the pKa values of five carboxylic acids (Asp7, Glu10, Glu19, Asp27, and Glu43) in turkey ovomucoid third domain (OMTKY3), and six aspartates residues (Asp 22, Asp 44, Asp 54, Asp 75, Asp 83, and Asp 93) in barnase. For OMTKY3, all the predicted pKa values are within 1 pH units from the available experimental ones, except for the case of Glu 43. For barnase, the root-mean-square deviation from experiment is 1.46 pH units. As a result, the proposed pKa calculation method correctly reproduces the relative order of the pKa values among the carboxylic acids located in different sites of the proteins. The calculated pKa values are decomposed into the contributions of short- and long-range structural difference effects. The results indicate that in both proteins the pKa value of the given carboxylic acid is partially influenced by long-range interactions with distant charged residues, which significantly contribute to determining the relative order of the pKa values. The current methodology based on LSMO provides us useful information about the titration behavior in a protein.     

Long‐range corrected functionals satisfy Koopmans' theorem: Calculation of correlation and relaxation energies

In this article, we show that the long‐range‐corrected (LC) density functionals LC‐BOP and LCgau‐BOP reproduce frontier orbital energies and highest‐occupied molecular orbital (HOMO)—lowest‐unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6‐311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO‐LUMO gaps of LC‐BOP and LCgau‐BOP are better than those of recently proposed ωM05‐D (Lin et al., J. Chem. Phys. 2012, 136 , 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree–Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr^?1 for the above test set molecules with LC‐BOP functional and found our parameter value, 0.47 bohr^?1, is usefully applicable to our tested systems. © 2013 Wiley Periodicals, Inc.     

Variable ζ calculation for self-consistent screening parameters in ab initio molecular theory

A resolution of Roothaan's HF–SCF–LCAO–MO equations is proposed in which atomic orbital exponents (ζ) are made dependent on the molecular charge distribution and included in the self-consistent scheme. Screening parameters so obtained are self-consistent with the molecular orbital coefficients and compare closely to optimum orbital exponents found by other methods. The technique is applied to the ground, lowest positive, and lowest negative ion states of the hydride series LiH, BH, and HF. Calculated potential curves are used to define purely theoretical values for the vertical and adiabatic ionization energies and electron affinities. Predictions are compared to experimental values where available.     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

On the position of the highest occupied molecular orbital in aqueous solutions of simple ions.

The energies of the highest occupied molecular orbital (HOMO) of four simple microsolvated aqua ion clusters (Na+, Ag+, Cl-, CN-) are computed for varying numbers of water molecules. Extrapolating to infinite hydration numbers we find that these energies approach a value of -6 eV. This limiting one-electron energy is within a margin of +/-1 eV independent of the character of the ion and is 4 eV lower compared to the estimate obtained for the HOMO energy of the ions in aqueous solution under periodic boundary conditions. We argue that this discrepancy must the attributed to a shift in the reference of the one-electron potential of the periodic solvent model.     

Implications of molecular orbital symmetries and energies for the electron delocalization of inorganic clusters.

Isostructural clusters exhibit contrasting magnetic properties when the number of electrons differs. Surprisingly, the same is true even for isoelectronic cages (e.g. O(h) B6H6(2-) is diatropic, whereas O(h) Si6(2-) is paratropic) or for those with different substitutents (e.g. T(d) B4H4 is paratropic, whereas T(d) B4F4 is diatropic). Indeed, the total nucleus-independent chemical shift (NICS) values, based on shieldings computed at cluster centers, may range considerably in magnitude and even change from diatropic (up-field shifted) to paratropic (down-field shifted). Similarly, individual dissected canonical molecular orbital contributions to the total NICS values computed at the "gauge-including atomic orbitals" (GIAO) level vary greatly. This contrasting behavior arises from molecular orbital energy differences, from the extent of orbital overlap, as well as from symmetry-based selection rules derived from group theory. Differences in magnetic properties may originate from the symmetry of the orbitals; specifically from the forbidden nature of the highest occupied molecular orbital --> lowest unoccupied molecular orbital (HOMO --> LUMO) electronic excitation weighted by the occupied-unoccupied orbital energy difference. Thus, HOMO-NICS values are generally highly paratropic if the HOMO --> LUMO rotational transition is allowed by symmetry selection rules.     

Theoretical study of a conjugated aromatic molecular wire

In this study, an organic conjugated molecule, 4,4′-[ethane-1,2-diylidenedi(nitrilo)] dibenzenthiol designed and is proposed as a molecular wire. Structural and electronic responses of this aromatic molecular wire to the static electric field with intensities −1.6 × 10⁻² to +1.6 × 10⁻² a.u., are studied using the DFT-B3LYP/6-31G* level of theory. Natural bond orbital atomic charge analysis shows that the imposition of static external electric field induces polarization—localization of charge on the two ends of molecule, especially on considered terminal contact sulfur atoms. The frontier molecular orbitals (MOs) energy levels including the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) and the HOMO–LUMO gap (HLG) values are modified by the static electric field as well. The electric dipole moment and polarizability of the proposed molecular wire under the studied electric field strengths are considerably increased. The current–voltage characteristic curve is estimated for the proposed molecular wire.     

Experimental (FT-IR, FT-Raman) and theoretical (HF and DFT) investigation and HOMO and LUMO analysis on the structure of p-fluoronitrobenzene

FT-IR and FT-Raman spectra of p-fluoronitrobenzene (FNO(2)C(6)H(4)) have been recorded in the region 4000-100 cm(-1). In this work, the experimental and theoretical spectra of p-fluoronitrobenzene (p-FNBz) are studied. The molecular geometry and vibrational frequencies are calculated in the ground state of molecule using ab initio Hartree-Fock (HF) and DFT (B3LYP and LSDA) methods with 6-31++G(d,p) and 6-311++G(d,p) basis sets. The computed values of frequencies are scaled to yield good coherence with observed values by using suitable factor. The complete assignments are performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The observed and calculated frequencies are found to be in very good agreement. The alteration of vibration bands due to the substitutions at the first and fourth position of the skeletal ring is also investigated from their characteristic region of linked spectrum. A study on the electronic properties, such as absorption wavelengths, excitation energy, dipole moment and frontier molecular orbital energies, are performed by time dependent DFT (TD-DFT) approach. The electronic structure and the assignment of the absorption bands in the electronic spectra of steady compounds are discussed. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. The thermodynamic properties of the title compound at different temperatures have been calculated in gas phase, revealing the correlations between standard heat capacities (C) standard entropies (S), standard enthalpy changes (H) and temperatures.     

Synthesis and characterization of three novel perfluoro-oligothiophenes ranging in length from the trimer to the pentamer

In this Article, we report on the synthesis and full characterization of three perfluorinated oligothiophenes, ranging in length from the trimer to the pentamer (PF-nT, with n = 3, 4, or 5). The differential pulse voltammetry (DPV) analysis of the compounds showed that they can be both oxidized and reduced (i.e., they display a dual or amphoteric electrochemical behavior), with the reduction peaks positively shifted relative to those of the corresponding unsubstituted oligothiophenes. The electrochemically determined energy gaps are in agreement with those measured from the UV-vis-NIR absorption spectra in solution. The conjugational properties have been investigated by means of FT-Raman spectroscopy, both as pure solids and as dilute solutes in CH(2)Cl(2), revealing that: (i) pi-conjugation does not still reach saturation with chain length for the longest oligomer, and (ii) conformational distortions from a nearly coplanar arrangement of the successive thiophene units upon solution are not too large. DFT and TDDFT quantum chemical calculations have been performed, at the B3LYP/6-31G level, to assess information about the optimized molecular structure, equilibrium atomic charges distribution, energies and topologies of the frontier molecular orbitals (MO) around the gap, vibrational normal modes associated with the most outstanding Raman scatterings, and vertical one-electron excitations that give rise to the main optical absorptions.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

Selected valence electron split-shell molecular orbital calculations on the diatomic interhalogen molecules

Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.