On the limits of highest-occupied molecular orbital driven reactions: the frontier effective-for-reaction molecular orbital concept

We carried out Hartree-Fock (HF) and density functional theory calculations for 61 compounds, the conjugated bases of carboxylic acids, phenols, and alcohols, and analyzed their acid-base behavior using molecular orbital (MO) energies and their dependence on solvent effects. Despite the well-known correlation between highest-occupied MO (HOMO) energies and pKa, we observed that HOMO energies are inadequate to describe the acid-base behavior of these compounds. Therefore, we established a criterion to identify the best frontier MO for describing pKa values and also to understand why the HOMO approach fails. The MO that fits our criterion provided very good correlations with pKa values, much better than those obtained by HOMO energies. Since they are the frontier molecular orbitals that drive the acid-base reactions in each compound, they were called frontier effective-for-reaction MOs, or FERMOs. By use of the FERMO concept, the reactions that are HOMO driven, and those that are not, can be better explained, independently from the calculation method used, as both HF and Kohn-Sham methodologies lead to the same FERMO.     

Ab initio and DFT studies on the mechanism of the 1,3-dipolar cycloaddition reaction between nitrone and sulfonylethene chloride

The molecular mechanism for the 1,3-dipolar cycloaddition of nitrone with sulfonylethene chlorides has been studied using ab initio and DFT methods at the HF, MP2 and B3LYP levels together with the 6-31G* basis set. Relative rates, stereo and regioselectivity, have been analysed and discussed. For this cycloaddition four reactive channels associated with the formation of two pairs of diastereoisomeric regioisomers have been characterized. Analysis of the geometries of the corresponding transition structures shows that the cycloaddition takes place along a concerted but asynchronous mechanism. Activation energies as asynchronicity are dependent on the computation level. Thus, while HF calculations gave large barriers, MP2 calculations tend to underestimate them. DFT calculations gave reasonable values. These 1,3-dipolar cycloadditions present an endo stereoselectivity while the meta regioselectivity depends on the computational level. Thus, while HF and DFT calculations predict meta path, in agreement with the experimental results, MP2 calculation predict ortho regioselectivity. The frontier molecular orbitals analysis shows that the reaction is controlled by the (HOMO_dipole–LUMO_{dipolarophile}) interaction in agreement with the charge transfer analysis carried out at the transition structures. Inclusion of diffuse functions at the B3LYP/6-31+G* level increases the energy barriers about 4 kcal/mol, giving a similar endo/meta selectivity. Solvent effects have been taken into account, by means of self-consistent reaction field.     

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.     

Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

Understanding the 1,3-Dipolar Cycloadditions of Allenes

We have quantum chemically studied the reactivity, site-, and regioselectivity of the 1,3-dipolar cycloaddition between methyl azide and various allenes, including the archetypal allene propadiene, heteroallenes, and cyclic allenes, by using density functional theory (DFT). The 1,3-dipolar cycloaddition reactivity of linear (hetero)allenes decreases as the number of heteroatoms in the allene increases, and formation of the 1,5-adduct is, in all cases, favored over the 1,4-adduct. Both effects find their origin in the strength of the primary orbital interactions. The cycloaddition reactivity of cyclic allenes was also investigated, and the increased predistortion of allenes, that results upon cyclization, leads to systematically lower activation barriers not due to the expected variations in the strain energy, but instead from the differences in the interaction energy. The geometric predistortion of cyclic allenes enhances the reactivity compared to linear allenes through a unique mechanism that involves a smaller HOMO–LUMO gap, which manifests as more stabilizing orbital interactions.     

1,3-Dipolar cycloadditions of nonstabilized azomethine ylides to planar chalcones via regio- and stereoselective route: A three-component strategy

Simple and efficient strategies toward the synthesis of trisubstituted pyrrolizidines and disubstituted oxazolidine systems by 1,3-dipolar cycloaddition reactions using arylaldehydes and α-amino acids have been developed, followed by a one-pot, three-component strategy. Electron-deficient dipolarophiles, chalcones, were reacted with nonstabilized azomethine ylides derived from arylaldehyde and L-proline in dry dimethyl formamide, leading to substituted pyrrolizidines. The route to substituted oxazolidines involved cycloaddition to the C?O bond of a second molecule of the aldehyde. The structures and stereochemistry of the cycloadducts were established by infrared (IR), NMR spectroscopy, and single-crystal x-ray crystallographic analyses. Condensed Fukui functions and local electrophilicity indices have been computed to characterize the reactive sites and predict the preferred interactions of azomethine ylides to planar chalcones. The softness-matching indices have been evaluated to determine the regioselectivity of the cycloaddition reactions. The theoretical predictions were found to be in complete agreement with the experimental results, implying that the density functional theory (DFT)-based reactivity indices correctly predict the regioselectivities of 1,3-dipolar cycloadditions of azomethine ylides to planar chalcones. The frontier molecular orbital (FMO) energies, electronic chemical potentials, chemical hardness, chemical softness, and global electrophilicity indices of azomethine ylides have been calculated at the DFT/B3LYP/6-31 + G (d, p) level of theory.     

Oxidative Copolymerisation of para‐Functionalized Phenols Catalyzed by Horseradish peroxidase and Thermocrosslinking via Diels‐Alder and (1+3) Cycloaddition

The horseradish peroxidase‐ (HRP‐) catalyzed polyrecombination of N‐(4‐hydroxyphenyl)‐2‐furamide ( 2 ) and 4‐hydroxyphenylmaleimide ( 1 ) is described. The resulting copolymer was used to build crosslinked materials via Diels‐Alder and cycloaddition reactions. We followed the enzymatic copolymerization process of an equimolar mixture of 1 and 2 using high pressure liquid chromatography (HPLC), size‐exclusion chromatography (SEC) and by matrix assisted laser desorption/ionization‐time of flight mass spectroscopy (MALDI‐TOF MS) analysis and found that the polymerization of 2 , which has a significant higher highest occupied molecular orbital (HOMO) energy, proceeds much faster. The HOMO energies of 1 and 2 were calculated using a differential Fourier transform (DFT) method. Furthermore, we tested copolymers consisting of the monomer units 4‐hydoxybenzaldehyde‐methylnitrone ( 3 ) and N‐methacryloyl‐11‐aminoundecanoyl‐4‐hydroxyanilide ( 4 ) on their ability to form networks via 1,3‐dipolaric cycloaddition reactions upon heating. The crosslinking of all copolymers was proven by Fourier transform infrared (FT‐IR) spectroscopy.     

Theoretical studies on molecular structure and vibrational spectra of 8-hydroxyquinolinium picrate

Quantum chemical calculations of geometrical structure and vibrational wavenumbers of 8-hydroxyquinolinium picrate (8-HQP) were carried out by ab initio HF and density functional (DFT/B3LYP) method with 6-31++G(dp) basis set. The calculated geometric parameters of 8-HQP are presented. A detailed interpretation of the infrared spectra of 8-hydroxyquinolinium picrate (8-HQP) are also reported. Theoretical molecular frontier orbital energies of the title compound have been calculated using the method mentioned above in order to understand this phenomenon in the context of molecular orbital picture. The molecular HOMOs and LUMOs generated via HF and B3LYP method have been outlined.     

Pi* orbital system of alternating phenyl and ethynyl groups: measurements and calculations

The temporary anion states of a series of alternating phenyl-ethynyl compounds are studied by means of electron transmission spectroscopy. Calculations of the virtual orbital energies of these compounds are computed with ab initio HF methods as well as DFT, and excellent correlations with the experimental vertical attachment energies are obtained. Scaled orbital energies for long-chain molecules are used to predict the vertical attachment energies of these compounds. In the absence of scaling, HOMO-LUMO gaps computed by DFT are found to be in substantial disagreement with gas-phase data. Such discrepancies may cause significant errors in theoretical studies of molecular conductance.     

Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies

The reactivities of 2-butyne, cycloheptyne, cyclooctyne, and cyclononyne in the 1,3-dipolar cycloaddition reaction with methyl azide were evaluated through DFT calculations at the M06-2X/6-311++G(d)//M06-2X/6-31+G(d) level of theory. Computed activation free energies for the cycloadditions of cycloalkynes are 16.5–22.0 kcal mol⁻¹ lower in energy than that of the acyclic 2-butyne. The strained or predistorted nature of cycloalkynes is often solely used to rationalize this significant rate enhancement. Our distortion/interaction–activation strain analysis has been revealed that the degree of geometrical predistortion of the cycloalkyne ground-state geometries acts to enhance reactivity compared with that of acyclic alkynes through three distinct mechanisms, not only due to (i) a reduced strain or distortion energy, but also to (ii) a smaller HOMO–LUMO gap, and (iii) an enhanced orbital overlap, which both contribute to more stabilizing orbital interactions.     

CF2BrCl分子近域轨道的电子动量谱学研究

The frontier molecular orbitals (HOMO and NHOMO) of CF2BrCl molecule have been firstly investigated by (e,2e) electron momentum spectroscopy. The experimental momentum profiles are compared with the theoretical profiles employing Hartree-Fock and density functional theory with 6-31G and 6-311+G(d) basis sets. Both HF and DFT calculations using 6-311+G(d) basis set can well describe the experiment, whereas those calculated using 6-31G basis set largely underestimate the experiment at the low momentum region. Furthermore, orbital electron density images show that HOMO and NHOMO have a mixed character of the bromine and chlorine lone pairs.     

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     

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity

Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital energy differences, Deltavarepsilon, between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), using the same potential for both. They are combined with accurate vertical ionization potentials, I(0), and electron affinities, A(0), to determine accurate "average" orbital energies. These are the orbital energies associated with an exchange-correlation potential that averages over a constant jump in the accurate potential, of magnitude Delta(XC)=(I(0)-A(0))-Deltavarepsilon, as given by the discontinuity analysis. Local functional HOMO energies are shown to be almost an order of magnitude closer to these average values than to -I(0), with typical discrepancies of just 0.02 a.u. For systems that do not bind an excess electron, this level of agreement is only achieved when A(0) is set equal to the negative experimental affinity from electron transmission spectroscopy (ETS); it degrades notably when the zero ground state affinity is instead used. Analogous observations are made for the local functional LUMO energies, although the need to use the ETS affinities is less pronounced for systems where the ETS values are very negative. The application of an asymptotic correction recovers the preference, leading to positive LUMO energies (but bound orbitals) for these systems, consistent with the behavior of the average energies. The asymptotically corrected LUMO energies typically agree with the average values to within 0.02 a.u., comparable to that observed with the HOMOs. The study provides numerical support for the view that local functionals exhibit a near-average behavior based on a constant jump of magnitude Delta(XC). It illustrates why a recently proposed DFT expression involving local functional frontier orbital energies and ionization potential yields reasonable estimates of negative ETS affinities and is consistent with earlier work on the failure of DFT for charge-transfer excited states. The near-average behavior of the exchange-correlation potential is explicitly illustrated for selected systems. The nature of hybrid functional orbital energies is also mentioned, and the results of the study are discussed in terms of the variation in electronic energy as a function of electron number. The nature of DFT orbital energies is of great importance in chemistry; this study contributes to the understanding of these quantities.     

Experimental and theoretical electron momentum spectroscopic study of the valence electronic structure of tetrahydrofuran under pseudorotation

The most populated structure of tetrahydrofuran (THF) has been investigated in our previous study using electron momentum spectroscopy (EMS). Because of the relatively low impact energy (600 eV) and low energy resolution (DeltaE = 1.20 eV) in the previous experiment, only the highest occupied molecular orbital (HOMO) of THF was investigated. The present study reports the most recent high-resolution EMS of THF in the valence space for the first time. The binding energy spectra of THF are measured at 1200 and 2400 eV plus the binding energies, respectively, for a series of azimuthal angles. The experimentally obtained binding energy spectra and orbital momentum distributions (MDs) are employed to study the orbital responses of the pseudorotation motion of THF. The outer valence Greens function (OVGF), the OVGF/6-311++G** model, and density function theory (DFT)-based SAOP/et-pVQZ model are employed to simulate the binding energy spectra. The orbital momentum distributions (MDs) are produced using the DFT-based B3LYP/aug-cc-pVTZ model, incorporating thermodynamic population analysis. Good agreement between theory and experiment is achieved. Orbital MDs of valence orbitals exhibit only slight differences with respect to the impact energies at 1200 and 2400 eV, indicating validation of the plane wave impulse approximation (PWIA). The present study has further discovered that the orbital MDs of the HOMO in the low-momentum region (p < 0.70 a.u) change significantly with the pseudorotation angle, phi, giving a v-shaped cross section, whereas the innermost valence orbital of THF does not vary with pseudorotation, revealing a very different bonding mechanism from the HOMO. The present study explores an innovative approach to study pseudorotation of sugar puckering, which sheds a light to study other biological systems with low energy barriers among ring-puckering conformations.     

Vibrational spectroscopy (FT-IR and FT-Raman) investigation, and hybrid computational (HF and DFT) analysis on the structure of 2,3-naphthalenediol

The FT-IR and FT-Raman vibrational spectra of 2,3-naphthalenediol (C(10)H(8)O(2)) have been recorded using Bruker IFS 66V spectrometer in the range of 4000-100 cm(-1) in solid phase. A detailed vibrational spectral analysis has been carried out and the assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The optimized molecular geometry and vibrational frequencies in the ground state are calculated by using the ab initio Hartree-Fock (HF) and DFT (LSDA and B3LYP) methods with 6-31+G(d,p) and 6-311+G(d,p) basis sets. There are three conformers, C1, C2 and C3 for this molecule. The computational results diagnose the most stable conformer of title molecule as the C1 form. The isotropic computational analysis showed good agreement with the experimental observations. Comparison of the fundamental vibrational frequencies with calculated results by HF and DFT methods. Comparison of the simulated spectra provides important information about the capability of computational method to describe the vibrational modes. 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 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. On the basis of the thermodynamic properties of the title compound at different temperatures have been calculated. The statistical thermodynamic properties (standard heat capacities, standard entropies, and standard enthalpy changes) and their correlations with temperature have been obtained from the theoretical vibrations.     

Investigation of the correlation between the energy of the highest occupied molecular orbital (HOMO) and the logarithm of the OH rate constant of hydrofluorocarbons and hydrofluoroethers

A regression based model was developed to determine whether highest occupied molecular orbital (HOMO) energies, calculated using Kohn-Sham orbital density functional theory (DFT), could be used to estimate the OH rate constants of hydrofluorocarbons (HFCs) and hydrofluoroethers (HFEs), proposed substitutes for stratospheric O₃ depleting chlorofluorocarbons. The goodness of fit of the DFT model was compared with a second regression model, derived using recently reported HOMO energies obtained from Hartree Fock theory (HFT). Both models were employed to predict OH rate constants for a number of HFCs and HFEs whose OH rate constants have not been measured, thus providing data on the types of chemical structures that may increase the OH reactivity of the substitute and hence decrease its contribution to global warming. The estimated percent standard errors in the OH rate constant HFT and DFT regression models were 72% and 78%, respectively. The goodness of fits were such that the models can differentiate between two rate constants only when their ratio exceeds about a factor of four. Model results suggest that (1) only a limited number of HFEs will have OH rate constants that are more than an order of magnitude greater than the value for their corresponding HFCs and (2) the strategy of introducing an ether linkage into an HFC to dramatically enhance its reactivity will be most effective for the least fluorinated HFCs. © 1994 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Molecular structure, vibrational spectra and HOMO, LUMO analysis of yohimbine hydrochloride by density functional theory and ab initio Hartree-Fock calculations

Yohimbine hydrochloride (YHCl) is an aphrodisiac and promoted for erectile dysfunction, weight loss and depression. The optimized geometry, total energy, potential energy surface and vibrational wavenumbers of yohimbine hydrochloride have been determined using ab initio, Hartree–Fock (HF) and density functional theory (DFT/B3LYP) method with 6-311++G(d,p) basis set. A complete vibrational assignment is provided for the observed Raman and IR spectra of YHCl. The UV absorption spectrum was examined in ethanol solvent and compared with the calculated one in gas phase as well as in solvent environment (polarizable continuum model, PCM) using TD-DFT/6-31G basis set. These methods are proposed as a tool to be applied in the structural characterization of YHCl. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with frontier orbital gap are presented.     

Novel bipolar bathophenanthroline containing hosts for highly efficient phosphorescent OLEDs

The electronic structures of eight bathophenanthroline derivatives were elucidated by DFT calculations, and four representatives of which CZBP, m-CZBP, m-TPAP, and BPABP were synthesized and employed as the hosts to afford highly efficient phosphorescent OLEDs. The calculated molecular orbital energies agree well with the experimental results, which further demonstrates that the localization of HOMO and LUMO at the respective hole- and electron-transporting moieties is desirable in bipolar molecular designs.     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.