post-Hartree Fock Methods Research Articles

Molecular hyperpolarizabilities of push–pull chromophores: A comparison between theoretical and experimental results

Electric dipole moments and static first order hyperpolarizabilities of two push–pull molecules with an extended π electron systems have been evaluated at different computational levels and compared with the results of electro-optical absorption measurements, based on the two state model. Calculations show that: (i) the dipole moments of such elongated systems depend significantly on conformation, a thorough conformational search is necessary for a meaningful comparison between theoretical and experimental results; (ii) DFT methods, in particular CAM-B3LYP and M05-2X, yield dipole moments which compare well with those obtained by post Hartree–Fock methods (MP2) and by EOA measurements; (iii) theoretical first order hyperpolarizabilities are largely underestimated, both by MP2 and DFT methods, possibly because of the failure of two state model used in electro-optical measurements.

A tribute to Thomas Frauenheim

This special issue of PSS is in honor of Thomas Frauenheims 60th birthday. His central theme always was the understanding of what he called real materials properties, meaning systems of a size which makes a comparison of their computed properties with experimental observables meaningful. In the 1990's he started to use a DFT based tight-binding (TB) method, and he very quickly became a driving force in developing the applications and capabilities of this methodology. While being originally an approximation to DFT-LDA, Thomas has realized its formal similarity to tight-binding methods used in solid state physics. These TB methods were known to be quite accurate for the materials classes they have been parameterized for, but the parameterization itself could be quite tedious and time-consuming. The approximate DFT method could be viewed as a simple way of getting TB parameters, therefore Thomas introduced the name Density-Functional Tight-Binding (DFTB) for this methodology. Starting out with studies on complex carbon systems, studying their structure and spectroscopic properties, he quickly became interested in a broad range of materials, from molecules, clusters, surface problems, over voids and vacancies in semi-conductor materials to biological molecules. The atomistic description of nano-scale materials was and is in the center of his interest. DFTB has been the workhorse in all these years, although he has never been limited to a single methodology. His science was always rather problem than methodology driven, therefore he augmented the semi-empirical DFTB calculations at both ends with other methods, by empirical force fields on the one hand or plane wave DFT and even post-Hartree Fock methods, on the other, when very accurate calculations have been required. And of course, the nature of those systems often asked for so called ‘multi-scale’ solutions, i.e. a combination of various methods for the different scales in one methodology, like in the QM/MM approaches. Beside that, however, much of his efforts was directed into the extension of DFTB's capabilities in order to cover various materials properties, as there are, for example, vibrational spectra of molecules and solids, optical properties of molecules and clusters within a DFTB adapted time-dependent DFT (TD-DFT) approach, non-adiabatic molecular dynamics simulations to model pump-probe processes, calculations of hyperfine coupling constants for radicals and magnetic properties of clusters with a spin-polarized extension of DFTB, calculations of scanning probe (STM) images of surfaces and the calculation of electronic transport properties within the non-equilibrium Green's function technique, to mention only some of the applications and methodological extensions of the DFTB. All this of course was not possible with the capabilities of a single work group. One of Thomas' most outstanding qualities is his openness and ability to bring co-operations into a family-like setting. Over the years, he has been closely working with various groups in several countries on different continents. These co-operations contributed significantly to the expertise, which is now assembled in the computational machinery, partly manifested in the DFTB+ program suite, partly in many other pieces of code being available now for DFTB. His attitude was never one of competition but rather of cooperation. We hope that he will continue in this spirit to further inspire materials science research in the future. Gotthard Seifert, Marcus Elstner, and Peter Deák (Guest Editors)

Ab-Initio Study of the Adsorption and Separation of NOx and SOx Gases in Functionalized IRMOF Ligands

The interaction of NOx, SOx, and other gases with benzene and the monosubstituted benzene derivatives, aniline, phenol, and toluene, were studied by the MP2 post-Hartree–Fock method. The aromatic molecules were used as models for metal–organic frameworks’ ligands in order to examine the effect of the substituents on the adsorption and separation of these gases. It was found that polar substituents, as exemplified by the case of the amino (−NH2) group, increase the contribution of electrostatic dipole–dipole interactions with polar molecules (particularly NO2 and SO2). This leads to stronger interaction energies and altered minimum-energy structures. Furthermore, we calculated the interaction energy of a variety of gases with the amino-substituted ring in order to examine the possibilities for gas-separation applications. The interaction energies increased in the order H2 < N2 < CH4 < NO < NO2 < CO2 < SO2 < SO3. The forces responsible for the adsorption of these gases were studied with the aid of charge an...

Theoretical investigation of the molecular structures and excitation spectra of triphenylamine and its derivatives

The molecular geometries, electronic structures, and excitation energies of NPh 3, NPh 2Me, NPhMe 2, and NMe 3, were investigated using DFT and post-Hartree Fock methods. When the structural stabilities of these compounds were compared to results obtained by using MP4(SDQ) method, it was confirmed that the optimized geometries by using MP2 method were sufficiently reliable. The excited states with large oscillator strengths consisted of transition components from the HOMO. It should be noted that the orbitals of the nitrogen atom mix with the π-orbital of the phenyl group in an anti-bonding way in the HOMO, and the orbital energy increases with this mixing. The unoccupied orbitals are generated from bonding and anti-bonding type interactions between the π-orbitals of the phenyl groups; therefore, the number of phenyl groups strongly affects the energy diagram of the compounds studied. The differences in the energy diagram cause a spectral change in these compounds in the ultraviolet region.

Large Amplitude Motions in Cyclopentene and 1-Butene: Quantum Chemical Insights into the Ground- and Excited State Potential Energy Surfaces

Abstract The ring-puckering motion in cyclopentene as well as the hindered internal rotation around the central C–C bond in 1-butene have been studied by high-level quantum chemical calculations. Relevant potential energy surfaces of these molecules along these large-amplitude motions are provided as well as rotational constants are given allowing for thorough comparison with recent results from time-resolved femtosecond degenerate four-wave mixing (fs DFWM) spectroscopy. Emphasis is put on the performance of various post-Hartree Fock methods, the required level of electron correlation as well as the basis set quality.

Tensor decomposition in post-Hartree–Fock methods. I. Two-electron integrals and MP2

A new approximation for post-Hartree-Fock (HF) methods is presented applying tensor decomposition techniques in the canonical product tensor format. In this ansatz, multidimensional tensors like integrals or wavefunction parameters are processed as an expansion in one-dimensional representing vectors. This approach has the potential to decrease the computational effort and the storage requirements of conventional algorithms drastically while allowing for rigorous truncation and error estimation. For post-HF ab initio methods, for example, storage is reduced to O(d·R·n) with d being the number of dimensions of the full tensor, R being the expansion length (rank) of the tensor decomposition, and n being the number of entries in each dimension (i.e., the orbital index). If all tensors are expressed in the canonical format, the computational effort for any subsequent tensor contraction can be reduced to O(R(2)·n). We discuss details of the implementation, especially the decomposition of the two-electron integrals, the AO-MO transformation, the Møller-Plesset perturbation theory (MP2) energy expression and the perspective for coupled cluster methods. An algorithm for rank reduction is presented that parallelizes trivially. For a set of representative examples, the scaling of the decomposition rank with system and basis set size is found to be O(N(1.8)) for the AO integrals, O(N(1.4)) for the MO integrals, and O(N(1.2)) for the MP2 t(2)-amplitudes (N denotes a measure of system size) if the upper bound of the error in the l(2)-norm is chosen as ε = 10(-2). This leads to an error in the MP2 energy in the order of mHartree.

Correcting for dispersion interaction and beyond in density functional theory through force matching

The force matching method is used to improve density functional theory (DFT) by designing a supplemental potential to capture the difference in atomic forces between a DFT functional and a high-quality post Hartree-Fock method. The supplemental potential has two-body terms designed to correct for dispersion and hydrogen bond interactions. The potential also has one-body terms to improve the description of the intramolecular potential energy surface. Our procedure is tested by providing corrections to the Becke-Lee-Yang-Parr exchange-correlation functional for water and is found to perform significantly better than the standard DFT-D approach, giving QCISD quality predictions for relative cluster energies, atomic forces, and molecular structures. It is found that a simple Lennard-Jones term does a good job at correcting for van der Waals interactions and possibly also providing corrections to exchange repulsion. The one-body corrections, while contributing only slightly to improving relative cluster energies, significantly reduce the errors in binding energies and atomic forces for the systems studied.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree–Fock methods

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree–Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree–Fock or numerical OEP data. Results from the localized Hartree–Fock and Krieger–Li–Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Canonical Tensor Products as a Generalization of Gaussian-type Orbitals

Abstract We propose a possible generalization of Gaussian-type orbital (GTO) bases by means of canonical tensor products. The present work focus on the application of tensor products as an alternative to conventional GTO based density fitting schemes. Tensor product approximation leads to highly nonlinear optimization problems which require sophisticated algorithms. We give a brief description of the optimization problem and algorithm. The present work extends our previous paper [S. R. Chinnamsetty, M. Espig, B. N. Khoromskij, W. Hackbusch and H.-J. Flad, J. Chem. Phys. 127 (2007), 084110], where we discussed tensor product approximations of the electron density and the Hartree potential, to orbital products which are required for the exchange part of Hartree-Fock and in post Hartree-Fock methods. We provide a detailed error analysis for the Coulomb and exchange terms in Hartree-Fock calculations. Furthermore, a comparison is given between all-electron and pseudopotential calculations.

Performance of multi-reference CI method in calculations of weakly bonded Sr2 and Ba2 molecules

It is shown that excited configurations in configuration expansions of the ground state wave functions of Sr2 and Ba2 molecules have relatively large coefficients and are very important for correct descriptions of their potential curves. Therefore, post Hartree-Fock methods of multi-reference type are more suitable for ab initio calculations of such molecules. The present MRCI calculations of Ba2 molecule give a new estimation of dissociation energy equal to 1090 ± 30 cm−1.

Essential oil Composition of Dendropanax Gonatopodus from Monteverde, Costa Rica. An ab Initio Examination of Aromadendrane Sesquiterpenoids

The leaf essential oil of Dendropanax gonatopodus from Monteverde, Costa Rica, has been obtained by hydrodistillation and the chemical composition determined by GC-MS. The major components in the leaf oil were ( E)-2-hexenal (16.9%), terpinolene (14.8%), δ-cadinene (13.5%), ( E)-caryophyllene (9.9%), and α-copaene (7.3%). Minor amounts of the aromadendrane sesquiterpenoids aromadendrene (0.3%), alloaromadendrene (0.3%), spathulenol (0.6%) and globulol (0.6%) were also detected. An ab initio investigation of the aromadendrane sesquiterpenoids has been carried out using both density functional (B3LYP/6-31G*) and post Hartree-Fock (MP2/6-31G**) methods. The calculated relative energies of the aromadendranes belie their relative concentrations generally observed in essential oil compositions.

A comparative post-Hartree–Fock and density functional theory study of monochalcogenide diatomic molecules

In this paper, we present a comparative post-Hartree–Fock and density functional theory study of monochalcogenide diatomic molecules of the XSe and XTe types (where X atom belongs to group 15), including neutral and cationic species. The corresponding bond lengths, vibrational frequencies and ionization potentials are calculated and compared with experimental data or advanced post-Hartree–Fock methods. The choice of the basis sets is also discussed. Finally, dissociation energies of the cationic and neutral species are computed and discussed.

Frontier Orbital Consistent Quantum Capping Potential (FOC-QCP) for Bulky Ligand of Transition Metal Complexes

Chemically reasonable models of PR3 (R = Me, Et, iPr, and tBu) were constructed to apply the post Hartree-Fock method to large transition metal complexes. In this model, R is replaced by the H atom including the frontier orbital consistent quantum capping potential (FOC-QCP) which reproduces the frontier orbital energy of PR3. The steric effect is incorporated by the new procedure named steric repulsion correction (SRC). To examine the performance of this FOC-QCP method with the SRC, the activation barriers and reaction energies of the reductive elimination reactions of C2H6 and H2 from M(R1)2(PR2(3))2 (M = Ni, Pd, or Pt; R1 = Me for R2 = Me, Et, or iPr, or R1 = H for R2 = tBu) were evaluated with the DFT[B3PW91], MP4(SDQ), and CCSD(T) methods. The FOC-QCP method reproduced well the DFT[B3PW91]- and MP4(SDQ)-calculated energy changes of the real complexes with PMe3. For more bulky phosphine, the SRC is important to present correct energy change, in which the MP2 method presents reliable steric repulsion correction like the CCSD(T) method because the systems calculated in the SRC do not include a transition metal element. The monomerization energy of [RhCl(PiPr3)2]2 and the coordination energies of CO, H2, N2, and C2H4 with [RhCl(PiPr3)2]2 were theoretically calculated by the CCSD(T) method combined with the FOC-QCP and the SRC. The CCSD(T)-calculated energies agree well with the experimental ones, indicating the excellent performance of the combination of the FOC-QCP with the SRC. On the other hand, the DFT[B3PW91]-calculated energies of the real complexes considerably deviate from the experimental ones.

Influence of Pt complex binding on the guanine–cytosine pair: A theoretical study

Energetic and structural changes in the hydrogen bonds of guanine (G) and cytosine (C) base pair due to Pt complex binding are investigated by post-Hartree–Fock methods. When the ligands are NH 3 or H 2O, the structure undergoes intermolecular proton transfer from G to C (denoted as G ∗C pair) resulting in an increase in the bonding energy of 3–10 kcal/mol. This renders the structure to be metastable due to: (a) successive processes of charge transfer from G to cisplatin thereby stabilizing the GC and G ∗C pairs and (b) an additional hydrogen bond between G and the ligand of Pt atom.

Lewis base interaction with gallium hydrides: a computational study

The recent synthesis and structural characterization of the complex of 3,5-dimethyl-4-hydropyridyl-gallane 1 with the Lewis base 3,5-dimethylpyridine revealed an unusually large angle α = H–Ga–H, 127(2)°, at variance with expected steric effects of the bulky substituents at the tetrahedrally coordinated Ga center. This finding prompted us to study computationally gallium hydrides using density functional and post-Hartree–Fock methods. For 1, we estimated α at 131° from a calculation on 4-hydropyridyl-gallane, GaH 2(Hpy). This value is reduced by 3° due to the interaction with Lewis base pyridine, to yield α = 128°, in excellent agreement with experiment. With an analysis of orbital interactions and a natural bond orbital analysis, we rationalized structural variations of donor–acceptor adducts LGaH 2X where X is a substituent and L is a Lewis base. Angle α is mainly determined by the polarity of the Ga–X bond: the more electronegative substituent X, the larger α and the stronger the interaction of GaH 2X with L. Interaction with a weak base L slightly distorts the initially planar geometry of the dihydride to a trigonal pyramidal form; for a strong base, the structure can become pseudo-tetrahedral.

Ab initio and DFT gas phase investigations of the C 7H 11+ potential energy surfaces of bicyclobutonium species and related carbocations

The potential energy surface relating to the C 7H 11 + bicyclobutonium cation and its isomers was investigated in the gas phase using the ab initio and density functional calculations. The unsymmetrical bicyclobutonium ion 5 was identified with the MP2/6-31G * method as a global minimum, which is slightly more stable by 0.8 kcal/mol than the boat conformer of the bicyclo[3.1.0]heptyl-1-carbinyl cation 6. Similar results were obtained when larger basis sets, such as 6-311+G **, were used to optimize the geometries. However, the energy gap between the bicyclobutonium ion 5 and the chair conformer of cyclopropylcarbinyl cation 6 became even smaller when the MP4(SDQ)/6-31G * method was used. The small differences in terms of relative energies between these minima located at the MP2/6-31G * and MP4(SDQ)/6-31G * levels reflect the flat profile of the corresponding part of C 7H 11 + potential energy surfaces. The geometries of other types of C 7H 11 + isomeric carbocations were also optimized such as the allyl cation 7, the chair conformer of bicyclo[3.1.0]heptyl-1-carbinyl ion 8, and π-complex 9, with the latter species being clearly less stable by 15.2 kcal/mol than 5. Becke's hybrid density functional, B3LYP, combined with the 6-31G * and 6-311+G ** basis sets, was also utilized to investigate the C 7H 11 + potential energy surface. The majority of B3LYP results were comparable to those obtained with the post Hartree–Fock methods; however, the unsymmetrical bicyclobutonium ion 5 could not be found with this density functional method. Low energy barriers separate the two cyclopropylcarbinyl cations 6 and 8, preventing them from rearranging into the bicyclobutonium type of ion 5. A much higher barrier is found for the rearrangement of the two cyclopropylcarbinyl cations 6 and 8 into allyl and π-complex species. The carbocation with the positive charge localized at the bridgehead position does not represent a minimum at any level of theory used throughout this investigation.

Hydrogen-bonding between the hydrogen peroxide molecule and the hydroperoxy radical (H 2O 2–HO 2): the global minimum

Spectroscopic properties of H 2O 2–HO 2 have been re-investigated by post Hartree–Fock methods including anharmonic vibrational effects through a second order perturbative approach. The results have been compared to recent experimental data. The very low barrier height computed for the conversion of the five-membered complex into its more stable six-membered counterpart (27 cm −1) explains why only the six-membered hydrogen-bonded complex is observed in argon matrices. The calculated anharmonic frequencies of the latter complex are in excellent agreement with experimental data.

Hydrogen-bonding between the hydrogen peroxide molecule and the hydroperoxy radical (H2O2?HO2): the global minimum

Spectroscopic properties of H 2 O 2 –HO 2 have been re-investigated by post Hartree–Fock methods including anharmonic vibrational effects through a second order perturbative approach. The results have been compared to recent experimental data. The very low barrier height computed for the conversion of the five-membered complex into its more stable six-membered counterpart (27 cm −1 ) explains why only the six-membered hydrogen-bonded complex is observed in argon matrices. The calculated anharmonic frequencies of the latter complex are in excellent agreement with experimental data.

Time-dependent density functional theoretical study of low lying excited states of F 2

The utility of time-dependent density functional theory (TDDFT) in predicting excitation energies is tested for the low lying excited states of F 2, a system that has posed severe challenges to ab initio quantum theory. It is shown that TDDFT using B3LYP functional predicts the excitation energies in good agreement with experiment. In some cases, the agreement is better than that for the post-Hartree–Fock methods like CASSCF and MRCI.

Quantum Chemical Studies of Carbohydrate Reactivity: Acid Catalyzed Ring Opening Reactions

The appropriate quantum mech. method for the investigation of enzymic reactions, which involve oxocarbenium ions as reactive intermediates, is examd. 2-Methoxy-tetrahydro-2H-pyran was chosen as a model acetal for pyranose sugars, and its reactivity upon protonation of the glycosidic and the ring oxygen atom has been investigated using various d. functional and post Hartree-Fock methods. Proton affinities calcd. at the DFT levels of theory predict glycosidic protonation to be favorable by 2.5 kcal/mol. For ring-protonated 2-methoxy-tetrahydro-2H-pyran, among the d. functionals, a strong dependence of the mol. structure on the d. functional employed is found. Structures obtained with the BLYP and B3LYP functionals are at variance with those from the ab initio methods, MP2 and CCSD, as shown by differences in bond lengths of more than 0.4 .ANG. for equiv. structures. By means of a valence bond anal. of the electron densities obtained at the DFT levels of theory, it is shown that this method dependence in this closed-shell species is caused by spurious self-interaction. This failure appears to be due to the subtle interplay between electron donating and accepting groups present. The BHLYP functional is found to perform best among the functionals under investigation, for describing the hypersurfaces for protonated pyranose sugars. [on SciFinder (R)]