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.     

Atomic spectral methods for molecular electronic structure calculations

Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectral-product representation. Calculations of the lowest-lying singlet and triplet electronic states of the covalent electron pair bond (H(2)) illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectral-product development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.     

阿魏酸分子结构和振动光谱的理论研究

阿魏酸是一种有效的天然油脂抗氧化剂.采用密度泛函理论(DFT) B3LYP方法和从头算HF两种方法,在6-311++G**基组水平上对阿魏酸分子的几何结构进行全优化,得到其几何结构参数,进一步计算得到阿魏酸的红外和拉曼振动光谱.计算结果表明,采用B3LYP和HF 2种方法优化得到的几何结构及频率值是一致的,对在B3LYP方法下计算得到的红外和拉曼振动频率进行合理的理论归属并与SDBS数据库实验数据进行比较,发现计算得到的红外和拉曼振动频率与实验测定结果符合较好.阿魏酸分子结构和振动光谱的研究,为研究阿魏酸及其衍生物的化学结构与生理活性之间的构效关系提供依据.     

Ab initio and DFT calculations for the structure and vibrational spectra of cyclopentene and its isotopomers

Ab initio calculations using the MP2/cc-pVTZ basis set do an excellent job of predicting the inversion barrier (247 vs. 232 cm⁻¹) and dihedral angle (26°) of cyclopentene. DFT calculations also do an excellent job of predicting the vibrational frequencies of the d₀, d₁, d₄, and d₈ isotopomers. They have also allowed the reassignments of several of the vibrational frequencies.     

Combination of solid-state NMR,molecular mechanics and DFT calculations for the molecular structure determination of methyl glycoside benzoates

Structural Chemistry - A reliable method for molecular structure determination, excluding single-crystal X-ray diffraction (SCXRD), has been applied to six methyl glycoside tetrabenzoates. The...     

Molecular structure and vibrational spectra analysis of diethylsilanediol by IR and Raman spectroscopies and DFT calculations

A thorough theoretical analysis (DFT/B3LYP) of the potential energy surface of diethylsilanediol (DESD) allowed finding ten stable conformations of the molecule, differing on the relative arrangement of both ethyl and hydroxyl groups. The Boltzmann??s population analysis allowed establishing their stability order that was justified in terms of the anomeric effect analyzed by means of the Natural Bond Orbitals methodology. Besides, DESD was synthesized and characterized using FT-IR and Raman spectroscopies data, firstly reported in this work, combined with DFT calculations (B3LYP/aug-ccpVTZ). Finally some of the main structural and vibrational features of this and other closely related alkylsilanediols, i. e. DMSD and EMSD, have been put together in order to establish some trends that can allow a better understanding of the chemistry of these compounds.     

DFT calculations of vibrational spectra and nonlinear optical properties for MgO nanotube clusters

The IR and Raman spectra, nonlinear optical properties of MgO nanotube clusters are studied by density-functional theory at B3LYP/6-31G(d) level. The IR spectra are match closely to those in the corresponding MgO cluster and bulk materials. The strongest peaks of the IR spectra are located in the range from 650 to 750 cm⁻¹. The Raman spectra are very sensitive to structural variations in MgO clusters, and redshift of vibrational frequency is observed in Raman spectra as increasing cluster length. The motion of the strongest peaks in spectra is discussed. The total dipole moment and the first hyperpolarizabilities oscillate between zero and a constant when the layer is grown for the layer dependence of symmetry in MgO nanotube clusters.     

Comparison of the molecular structure and spectra of benzene and borazine

Ab initio SCF MO and CI calculations for two different gaussian basis sets are carried out for the isoelectronic molecules benzene C₆H₆ and borazine B₃N₃H₃ in order to investigate the effect of increasing the flexibility in the representation of their respective systems. In the process it is found from comparison of orbital charge density contour diagrams and inner shell orbital energies of borazine with analogous data for other systems that the BN bonds of this compound are considerably less polar (B⁺N^–) than that of ammonia borane BNH₆ (B^–N⁺). CI calculations employing the larger basis set produce generally better agreement with the experimental transition energies of benzene than do those using the smaller basis. In both treatments ¹ E _2g is predicted to lie lower than ¹ E _1u , in contrast to single excitation results; an analogous inversion in the calculated order of states is not observed in the study of borazine but the effect of double and triple excitation configurations is also found to be quite important for this system. For both benzene and borazine the CI calculations suggest in addition that transitions to ^* states occur at relatively low energy, perhaps within 0.5 eV of the strongest ^* absorption in each case.

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Zusammenfassung Es wurden ab initio SCF-MO- und CI-Berechnungen für die isoelektrischen Moleküle Benzol C₆H₆ und Borazin B₃N₃H₆ durchgeführt; dabei werden zwei verschiedene Gaußfunktions-Basissätze von unterschiedlicher Güte hinsichtlich der Darstellung der entsprechenden -Systeme der Moleküle verwendet, und ihr Einfluß wird diskutiert. Beim Vergleich von Orbital-Elektronendichtediagrammen sowie den Orbitalenergien der inneren Schalen von Borazin mit entsprechenden Daten von anderen Systemen stellt sich heraus, daß die BN-Bindungen in B₃N₃H₆ bedeutend weniger polar (B⁺N^–) sind als die entsprechende Bindung (B^–N⁺) in BNH₆. Die CI-Rechnungen liefern bei Zugrundelegung der flexibleren AO-Basis Werte für die Übergangsenergien in Benzol, welche im allgemeinen in besserer Übereinstimmung mit den experimentellen Daten sind als bei Verwendung der kleineren Basis. In beiden Verfahren liegt der ¹ E _2g -Zustand niedriger als der ¹ E _1u , im Gegensatz zu den Ergebnissen, welche lediglich mit einer einfach angeregten Konfiguration erhalten werden; eine ähnliche Inversion in der berechneten Reihenfolge der Borazin-Zustände wird nicht gefunden, aber der Einfluß von zwei- und dreifach angeregten Konfigurationen stellt sich bei diesem Molekül ebenfalls als sehr wesentlich heraus. Die CI-Rechnungen legen weiterhin nahe, daß in den beiden Molekülen Benzol und Borazin ^*-Übergänge bei verhältnismäßig niedrigen Energien vorkommen, ungefähr 0,5 eV von der stärksten ^*-Absorption entfernt.

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Résumé Calculs ab-initio dans deux bases de gaussiennes, SCF-MO et I.C., pour les molécules isolélectroniques de benzène C₆H₆ et de borazole B₃N₃H₆, aux fins d'étude de la flexibilité de représentation de leurs systèmes . De la comparaison des diagrammes de contour de densité de charge orbitale et des énergies des orbitales des couches internes du borazole avec des données analogues pour d'autres systèmes on déduit que les liaisons B-N de ce composé sont considérablement moins polaires (B⁺N^–) que celles du borure d'ammonium BNH₆ (B^–N⁺). Des calculs d'I.C. utilisant la plus grande base donnent généralement de meilleures énergies de transition pour le benzène que ceux utilisant la plus petite base. Dans les deux cas ¹ E _2g est trouvée en dessous de ¹E_1u contrairement à ce que donne l'approximation monoparticulaire; une inversion analogue de l'ordre des états calculés n'est pas observée dans l'étude du borazole mais l'effet des configurations diet tri-excitées est aussi assez important pour ce système. Pour le benzène comme pour le borazole les calculs d'I.C. suggèrent d'autre part que les transitions ^* se produisent à des énergies relativement basses, à 0,5 eV peut être de la plus forte absorption ^* dans chaque cas.

     

Algebraic methods for molecular rotation-vibration spectra

Algebraic techniques similar to those recently introduced in nuclear physics may be useful in the treatment of molecular Spectra. A spectrum generating algebra appropriate to diatomic molecules is constructed. This algebra, U(4), is the simplest generalization to 3-D of the algebra of the 1-D Morse oscillator and a simplification of the U(6)algebra of nuclear rotation-vibration spectra.     

Structures and EPR spectra of binary sulfur-nitrogen radicals from DFT calculations

The scattered electron paramagnetic resonance (EPR) spectroscopic data for binary sulfur-nitrogen (S,N) radicals have been compiled and critically assessed.Many of these are inorganic rings or cages.For each species, possible equilibrium structures in the gas phase and the EPR hyperfine coupling (hfc) constants have been calculated with DFT using the B3LYP functional and basis sets of triple-ζ (or better) quality.Good agreement is obtained between calculated and measured values for the well characterized [S₃N₂]⁺, a planar π-radical for which the s-component of the orbitals is likely to be reasonably independent of minor geometrical changes between gas-phase and condensed-phase states.The cage compounds [S₄N₄]⁻ and [S₄N₅]⁻², for which reliable experimental EPR spectra have been reported, show larger variation between calculated and measured hfc, as a consequence of the dependence of the s orbital content of the molecular orbitals on small structural changes.The very large disagreements between the DFT calculated and experimentally claimed hfc constants for [NS], [SNS] and [S₄N₄]⁻³ in condensed phases lead us to question their assignment.Among binary S,N radicals, ³³S hfc data has only been reported for [S₃N₂]⁺ (through isotopic enrichment).These values were essential for the correct identification of the EPR spectra of this important radical, which previously was misassigned to other species.Our results suggest that ³³S data will be equally important for the correct identification of the EPR spectra of other binary S,N species, many of which are cyclic systems, e.g.[S₃N₃], [S₄N₃] and[S₄N₅].     

Spectral-product methods for electronic structure calculations

Progress is reported in development, implementation, and application of a spectral method for ab initio studies of the electronic structure of matter. In this approach, antisymmetry restrictions are enforced subsequent to construction of the many-electron Hamiltonian matrix in a complete orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer is seen to enforce the requirements of the Pauli principle ex post facto, and to eliminate the unphysical (non-Pauli) states spanned by the product representation. Results identical with conventional use of prior antisymmetrization of configurational state functions are obtained in applications to many-electron atoms. The development provides certain advantages over conventional methods for polyatomic molecules, and, in particular, facilitates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry. An exact atomic-pair expression is obtained in this way for polyatomic Hamiltonian matrices which avoids the ambiguities of previously described semi-empirical fragment-based methods for electronic structure calculations. Illustrative applications to the well-known low-lying doublet states of the H₃ molecule in a minimal-basis-set demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including the seams of intersection common in high-symmetry molecular geometries. The calculated H₃ energy surfaces are found to be in good agreement with corresponding valence-bond results which include all three-center terms, and are in general accord with accurate values obtained employing conventional high-level computational-chemistry procedures. By avoiding the repeated evaluations of the many-centered one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices in the antisymmetric basis states commonly employed in conventional calculations, and by performing the required atomic and atomic-pair calculations once and for all, the spectral-product approach may provide an alternative potentially efficient ab initio formalism suitable for computational studies of adiabatic potential energy surfaces more generally. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.     

Multinuclear NMR spectra and GIAO/DFT calculations of N-benzylazoles and N-benzylbenzazoles

The ¹H, ¹³C, and ¹⁵N chemical shifts of almost the whole series of N-benzyl azoles and benzazoles, with the exception of the unknown 1-benzyl-1H-pentazole (10) and the very unstable 2-benzyl-2H-isoindole (12), have been measured. In addition, the X-ray crystal structure of 1-benzyl-1H-indazole (14) was solved (monoclinic, space group P2₁/n), its geometry being very close to that used for the calculations. The absolute chemical shieldings were calculated at the gauge-independent atomic orbital (GIAO)/Becke, 3-parameter, Lee-Yang-Parr (B3LYP)/6-311++G(d,p) level and then transformed with very robust empirical equations into chemical shifts of the three nuclei showing an excellent agreement with the 313 experimental values.

     

New computer-assisted methods for the elucidation of molecular structure from 2-D spectra

General principles of the construction of expert systems for the elucidation of the structure of molecules from their spectra were considered. The principal attention was focused on systems based on the use of 2-D NMR spectra. The structural information extracted from 2D NMR spectra was characterized, and the strategy was outlined for structure elucidation under the conditions when the analyzed spectrostructural information is incomplete, fuzzy, and contradictory. The most advanced expert system ACD/Structure Elucidator, which is capable of determining the structure and stereochemistry of large molecules, in particular, those typical in the chemistry of natural compounds, is described as an example.     

Molecular structure and vibrational spectra of o-chlorotoluene, m-chlorotoluene, and p-chlorotoluene by ab initio HF and DFT calculations

In this work, experimental and theoretical study on the molecular structure and the vibrational spectra of o-chlorotoluene (OCT), m-chlorotoluene (MCT) and p-chlorotoluene (PCT) are presented. The vibrational frequencies of these compounds were obtained theoretically by ab initio HF and DFT/B3LYP calculations employing the standard 6-311++G(d,p) basis set for optimized geometries and were compared with Fourier transform infrared (FTIR) in the region of 400-4000 cm(-1) and with Raman spectra in the region of 100-4000 cm(-1). Complete vibrational assignment, analysis and correlation of the fundamental modes for these compounds have been carried out. The vibrational harmonic frequencies were scaled using scale factors, yielding a good agreement between the experimentally recorded and the theoretically calculated values.     

Least-squares numerical Rayleigh-Ritz and minimum-variance methods for molecular calculations

A general method is presented to find in a least-squares sense a set of orthogonal eigenfunctions and their eigenvalues from local energy and numerical integration methods or by any other dissymmetric approach to solve the eigenvalue problem of a Hermitian operator. By this method a generalization of the minimum variance method to more than one eigenfunction is obtained, which is a variant of Scott's method. Also a new method is derived—called the minimum-overlap method—that is a least-squares numerical version of the standard Rayleigh-Ritz method. Test calculations on the atoms Be and Tm and the molecules H₂ and CO have been performed with both numerical Hartree-Fock and Hartree-Fock-Slater methods. The least-squares solutions are an improvement over other methods in the case of accurate basis sets. Numerical Hartree-Fock calculations of moderate accuracy are found to be considerably faster than the analytic method.     

Density functional theory calculations on the molecular structures and vibration spectra of platinum(II) antitumor drugs

A comparison of six density functional theory (DFT) methods and six basis sets for predicting the molecular structures and vibration spectra of cisplatin is reported. The theoretical results are discussed and compared with the experimental data. It is remarkable that LSDA/SDD level is clearly superior to all the remaining density functional methods (including mPW1PW) in predicting the structures of cisplatin. Mean deviation between the calculated harmonic and observed fundamental vibration frequencies for each method is also calculated. The results indicate that PBE1PBE/SDD is the best method to predict all frequencies on average for cisplatin molecule in DFT methods.