Hartree-Fock Level Research Articles

Properties of Bose gases with the Raman-induced spin–orbit coupling

In this paper we investigate the properties of Bose gases with Raman-induced spin–orbit (SO) coupling. It is found that the SO coupling can greatly modify the single-particle density of state, and thus leads to the non-monotonic behaviour of the condensate depletion, the Lee–Huang–Yang correction of ground-state energy and the transition temperature of a non-interacting Bose–Einstein condensate (BEC). The presence of the SO coupling also breaks the Galilean invariance, and this gives two different critical velocities, corresponding to the movement of the condensate and the impurity respectively. Finally, we show that with the SO coupling, the interactions modify the BEC transition temperature even at the Hartree–Fock level, in contrast to the ordinary Bose gas without the SO coupling. All results presented here can be directly verified in the current cold atom experiments using the Raman laser-induced gauge field.

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 (2008)] implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include high-level electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: (4)He2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He](+) molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined.

The Study of Bond Selective Photochemistry in CH<sub>2</sub>BrCl

The photodissociation of chlorobromomethane (CH2BrCl) has been studied using unrestricted Hartree-Fock (UHF), configuration-interaction-singles (CIS), and complete active space self-consistent field (CASSCF) levels. The result of oscillator strengths indicate that the photochemistry reactions of CH2BrCl are processes where the n(Br)→σ*(C-Br) transition are excited to repulsive states leading to direct carbon-bromine bond breaking reactions. And the 1A’ →1A’ state is the important transition in photolysis of chlorobromomethane.

Theoretical Study on the Static (Hyper)Polarizabilities of α-t-Bu-ω-CN-Poly(methylphenyl)silane

The static linear and nonlinear optical properties of the σ-conjugated polymer α-t-Bu-ω-CN-poly(methylphenyl)silane (PMS) are studied at the Coupled-Perturbed Hartree-Fock (CPHF) level with 6-31+G(d) basis set. The calculated results reveal that the static first hyperpolarizabilities of this system increase with the main chain length and have a good agreement with experiments. The (hyper)polarizabilities per unit cell have been extrapolated to infinite chain limit and a comparison is made to those of polysilane and polyacetylene (PA). Besides, other structural properties depending on the σ-conjugated Si–Si skeleton length are investigated as well. Electron correlation effect is estimated and it turns out that the MP2 static first hyperpolarizability is about times larger than the corresponding CPHF value for the polymer with .

Non-equilibrium renormalised contacts for transport in nanodevices with interaction: a quasi-particle approach

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions We consider a model single-molecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of the electron density matrix, one interaction is diagonal in the central region and the second off-diagonal between the central region and the left electrode. We use a non-equilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and within a dynamical mean-field-like approach for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasi-resonant regime, and for a wide range of parameters. They show that a non-equilibrium (i.e. bias dependent) dynamical (i.e. energy dependent) renormalisation is obtained for the contact between the left electrode and the central region in the form of a non-equilibrium renormalisation of the lead embedding potential. The conductance is affected by the renormalisation of the contact: the amplitude of the main resonance peak is modified as well as 'the lineshape of the first vibron side-band.

Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers

A direct method (D-ΔMBPT(2)) to calculate second-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The ΔMBPT(2) method is defined as the correlated extension of the ΔHF method. Energy differences are obtained by integrating the energy derivative with respect to occupation numbers over the appropriate parameter range. This is made possible by writing the second-order energy as a function of the occupation numbers. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-ΔMBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the D-ΔMBPT(2) method for IPs and EAs to a second-order approximation of the effective Fock-space coupled-cluster Hamiltonian and a second-order electron propagator method. We also discuss the connection between the D-ΔMBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calculate ionization potentials and excitation energies of some small molecules. For IPs, the ΔMBPT(2) results compare well to the second-order solution of the Dyson equation. For excitation energies, the deviation from equation of motion coupled cluster singles and doubles increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the ΔMBPT(2) values. Most importantly, relaxation beyond the Hartree-Fock level is significant and needs to be included in future research.

ChemInform Abstract: Synthesis of Heteroatomic Zintl Anions in Liquid Ammonia — The New Highly Charged [Sn4Bi4]4‐ and Fully Ordered [Sn2Bi2]2‐.

AbstractCompounds (II) and (IV) are characterized by single crystal XRD, electron spray mass spectrometry, and ab initio calculations on the Hartree Fock level.

Contraction of completeness-optimized basis sets: Application to ground-state electron momentum densities

Completeness-optimization is a novel method for the formation of one-electron basis sets. Contrary to conventional methods of basis set generation that optimize the basis set with respect to ground-state energy, completeness-optimization is a completely general, black-box method that can be used to form cost-effective basis sets for any wanted property at any level of theory. In our recent work [J. Lehtola, P. Manninen, M. Hakala, and K. Hämäläinen, J. Chem. Phys. 137, 104105 (2012)] we applied the completeness-optimization approach to forming primitive basis sets tuned for calculations of the electron momentum density at the Hartree-Fock (HF) level of theory. The current work extends the discussion to contracted basis sets and to the post-HF level of theory. Contractions are found to yield significant reductions in the amount of functions without compromising the accuracy. We suggest polarization-consistent and correlation-consistent basis sets for the first three rows of the periodic table, which are completeness-optimized for electron momentum density calculations.

Experimental and quantum chemical studies of a novel synthetic prenylated chalcone

BackgroundChalcones are ubiquitous natural compounds with a wide variety of reported biological activities, including antitumoral, antiviral and antimicrobial effects. Furthermore, chalcones are being studied for its potential use in organic electroluminescent devices; therefore the description of their spectroscopic properties is important to elucidate the structure of these molecules. One of the main techniques available for structure elucidation is the use of Nuclear Magnetic Resonance Spectroscopy (NMR). Accordingly, the prediction of the NMR spectra in this kind of molecules is necessary to gather information about the influence of substituents on their spectra.ResultsA novel substituted chalcone has been synthetized. In order to identify the functional groups present in the new synthesized compound and confirm its chemical structure, experimental and theoretical 1H-NMR and 13C-NMR spectra were analyzed. The theoretical molecular structure and NMR spectra were calculated at both the Hartree-Fock and Density Functional (meta: TPSS; hybrid: B3LYP and PBE1PBE; hybrid meta GGA: M05-2X and M06-2X) levels of theory in combination with a 6-311++G(d,p) basis set. The structural parameters showed that the best method for geometry optimization was DFT:M06-2X/6-311++G(d,p), whereas the calculated bond angles and bond distances match experimental values of similar chalcone derivatives. The NMR calculations were carried out using the Gauge-Independent Atomic Orbital (GIAO) formalism in a DFT:M06-2X/6-311++G(d,p) optimized geometry.ConclusionConsidering all HF and DFT methods with GIAO calculations, TPSS and PBE1PBE were the most accurate methods used for calculation of 1H-NMR and 13C-NMR chemical shifts, which was almost similar to the B3LYP functional, followed in order by HF, M05-2X and M06-2X methods. All calculations were done using the Gaussian 09 software package. Theoretical calculations can be used to predict and confirm the structure of substituted chalcones with good correlation with the experimental data.

Fullerenes patched by flowers

Abstract Stability measures, such as the total energy and the HOMO-LUMO gap, calculated at the Hartree-Fock and DFT levels of theory, and the aromatic character of five circulenes/flowers with a hexagonal core and petals consisting of 5-, 6- and 7-membered rings are investigated. Geometric (HOMA) and magnetic (NICS) criteria are used to estimate the local aromatic character of every ring of the investigated circulenes. The local aromaticity of the coronene and sumanene patches in two tetrahedrally spanned fullerenes were calculated and compared with the HOMA and NICS values of the corresponding isolated circulenes.

Ab initio study of the circular intensity difference in electric-field-induced second harmonic generation of chiral natural amino acids

We present a systematic computational study of circular intensity difference (CID) in electric-field-induced second harmonic generation (EFISHG) of some representative chiral natural amino acids (Alanine, Arginine, Aspartic Acid, Cysteine and Tryptophan), taking into account the electric-dipole, electric-quadrupole and magnetic-dipole interactions. The calculations are performed by applying cubic response theory at both Hartree-Fock and Density Functional theory levels, the latter with the popular Becke-three parameters, Lee, Yang and Parr (B3LYP) functional. Special focus is given to the basis set, electron correlation and origin dependence of the properties. The full set of molecular parameters defined by Lam and Thirunamachandran in their reference theoretical paper published in 1982 [J. Chem. Phys., 1982, 77, 3810] is obtained and discussed. This permits the prediction of the CID observable for different possible experimental setups.

Calculation of 13C Nuclear Magnetic Shielding Constants Using Optimally Selected Basis Functions in 4-(phenyl) Acetyl Morpholine

The wave functions for calculation of 13C nuclear magnetic shielding tensors of this molecule have been optimally selected using factorial design as a multivariate method. The calculating of 13C shielding constants engaged the Gaussian 03 implementation of the GIAO by using 16 different basis sets at both the Hartree-Fock (HF) and density functional levels of theories (DFT).The outcomes of GIAO technique using the planned wave functions are in a good linear correlation between the calculated chemical shielding tensors and experimental values. Consequently, the B3LYP method owns better data.

Kinetic and Equilibrium Lithium Acidities of Substituted Toluenes: Semitheoretical Brönsted Correlations

Semitheoretical Brönsted correlations are compared between previously measured experimental rates of hydrogen isotope exchange of substituted toluenes labeled in the α-position and relative equilibrium acidities computed at several theory levels. The Brönsted correlations show less scatter at the Hartree-Fock level than at higher theory levels. This effect is rationalized on the basis of enhanced steric effects in the more constrained structures of the higher theory levels.

Understanding the Binding Mechanism of Various Chiral SWCNTs and ssDNA: A Computational Study

Molecular dynamics (MD) simulations have been carried out to understand the binding mechanism of various chiral single-walled carbon nanotubes (SWCNTs) and single-stranded DNA (ssDNA) of four different nucleobase sequences (i.e., ssdA(14), ssdT(14), ssdG(14), and ssdC(14), where, A, T, G, and C are adenine, thymine, guanine, and cytosine, respectively) in aqueous media at room temperature (300 K) and atmospheric pressure (1 atm). The simulations studies reveal that ssDNA undergoes rapid structural changes and wrap around the SWCNTs via π-stacking interactions between SWCNT's wall and the nucleobases of ssDNA. Our computations demonstrate that the length of the ssDNA plays an important role during the wrapping process. Moreover, it suggests that the length of the sequence should be proportional to the diameter of the SWCNT, in order to overcome the intralocked π-stacking interactions between the nucleobases of ssDNA sequence. Also, in our classical MD simulation, we do not observe the correlation between the diameter of SWCNTs and the sequences of ssDNA, which indicates the importance of electronic factors of these systems. In order to understand the electronic contributions of these systems, the quantum calculations have been performed at Hartree-Fock level for the 17 ns MD simulated structures. The quantum chemical calculations provide evidence that the highly stable ssDNA@SWCNT hybrid possesses a larger HOMO-LUMO gap.

Nonequilibrium transport with self-consistent renormalized contacts for a single-molecule nanodevice with electron-vibron interaction

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions [Phys. Rev. B 84, 235428 (2011)]. We consider a model single-molecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of electron density matrix, one interaction is diagonal in the central region and the second is off-diagonal between the central region and the left electrode. We use a nonequilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and at the Hartree level for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasiresonant regime and for a wide range of parameters. They show that a nonequilibrium (i.e., bias dependent) static (i.e., energy independent) renormalization is obtained for the nominal hopping matrix element between the left electrode and the central region. Such a renormalization is highly nonlinear and nonmonotonic with the applied bias; however, it always leads to a reduction of the current and also affects the resonances in the conductance. Furthermore, we show that the relationship between the nonequilibrium charge susceptibility and dynamical conductance still holds even in the presence of crossing interaction.

Geometry optimization for large systems by the elongation method

Geometry optimization using the elongation method is developed at the Hartree–Fock level of theory. The formalism of elongation energy gradient and its accuracy have been validated by model systems calculations. The linear poly-hydrogen fluoride, polyethylene, planar polyacetylene and extended polyalanine are optimized using different basis sets and compared with conventional results. The results show that the elongation Hartree–Fock geometry optimization (ELG-HF-OPT) can reproduce conventional calculation results with high accuracy for various basis sets. For the poly-hydrogen fluoride calculation at 6-31G(d,p) basis set, moreover, ELG-HF-OPT gives a structure with lower ground state energy than conventional results with the same optimization convergence threshold. This means the potential possibility of ELG-HF-OPT can locate a more stable structure than conventional calculations with the same optimization convergence criteria. Therefore, the ELG-HF-OPT would provide one more choice for performing optimization on complicated large systems.

Efficient Calculation of ROA Tensors with Analytical Gradients and Fragmentation

We present the results of calculations of Raman optical activity spectra of sizable systems from optical tensors of the fragments, the tensors calculated by an analytic approach at the time-dependent Hartree-Fock level of theory. The analytic approach permits large basis sets which, together with the limited geometrical extent of the fragments, obviates the need for the use of London-type orbitals. The implementation of the analytical gradient approach is formulated in the atomic orbital basis by using the elements of the density matrix as variational parameters. This makes the approach directly applicable to linear scaling methods. We do not solve the response equations for the geometrical distortions of the nuclei but determine instead the second-order perturbed densities with respect to the electromagnetic field perturbations. The number of perturbed density matrices that needs to be determined is thus independent of the number of nuclei, making the approach applicable to fragments with many nuclei and with good quality basis sets. Compared to numerical differentiation schemes, the analytical approach is about 10 times faster even for moderately sized molecules.

The localized pair model of electronic structure analysis

We introduce the localized pair model of electronic structure analysis and propose the two-electron reduced density matrix as an important interpretive tool in chemistry. Interelectronic probability distributions in position and momentum space are calculated for individual localized molecular orbitals corresponding to intuitive chemical features such as lone pairs and chemical bonds. It is demonstrated that these may be interpreted as the distribution of electrons within a chemical bond or lone pair and we refer to this model as the localized pair model of electronic structure analysis. Specifically, the Hartree–Fock level of theory is employed in conjunction with a completely uncontracted 6-311G (d,p) basis set to construct our localized orbitals. Spherically averaged position and momentum intracules are calculated for each orbital and we present results for orbitals of p-block hydrides, saturated main group compounds, fluorinated species, N→B dative structures, and small cyclic molecules. We find that our analysis generally agrees quite well with intuitive predictions based on bond lengths and electronegativities of the bonded atoms. However the trends in the data cannot be predicted using the bond length or electronegativity alone, which demonstrates the unique features of this model.

Theoretical Studies on the Mechanistic Insertions of Singlet Methylene and Halomethylene into Polar S‒H Bonds of Methanethiol, Ethanethiol, 1-Propanethiol and 2-Propanethiol

The insertion of 1CH2, 1CHF, 1CF2,1CHCl, and 1CCl2 into primary and secondary polar S‒H bonds of methanethiol, ethanethiol, 1-propanethiol, and 2-propanethiol have been investigated at HF (Hartree–Fock), MP2 (Møller–Plesset Perturbation Theory), and DFT (density functional theory) levels using 6-31G (d, p) basis set. The insertions follow a two-step mechanism. The potential energy surface exploration identifies ylide-like structures undergoing the 1,2-sigmatropic hydrogen shift concertedly giving the thioether product. But 1CF2 forms weak complexes involving 1,2-hydrogen shift. The barrier height in the concerted mechanism varies with the type of carbene moiety and S‒H bond. The initial interaction seems to be a function of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energies of thiols and carbenes, respectively. The natural bond orbital charge analysis showing a net charge flow from the substrate thiol to the reagent carbene at the transition states corroborates this fact.

Electronic structures and molecular structures of polyynes

AbstractRecently, many interesting materials made from carbon atoms have been discovered such as carbon nanotubes, fullerenes, and graphenes. In this article, we studied electronic structures and molecular structures of polyynes with sp2 carbons on both ends. Polyynes calculated were H2CCnCH2 with various number of n. These molecules have two π systems which are perpendicular to each other and these π systems have their tendency to make double bond nature by Peierls instability but for different alternating bonds. In other words, these two π systems are competing to form the double bond formations. The calculations were performed at Hartree–Fock level geometry optimization with 6‐31G, 6‐311G, and 6‐31G** basis sets. For CH2(C)2mCH2, we have found that there are two metastable structures, one of which is the bond‐alternating structure and another is nearly equi‐bond structure. The former has small highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap while the latter has relatively large gap although it is smaller in comparison with the value of polyyne with sp carbon atoms on both ends: H(C)2mH. The small highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap in bond‐alternating structure is due to the fact that HOMO and MO's near to HOMO have relatively localized electronic distribution in both end regions, and thus, the weak interaction between the both regions leads to the small HOMO–LUMO gap. The stability is larger for the former especially in long polyynes. For CH2(C)2m+1CH2, we have found only one stable structure, that is, equi‐bond structure. This type of polyyne oligomers has two terminal CH2 groups which are perpendicular with each other. It is found that the longer the length of oligomer is, the smaller the HOMO–LUMO gap is as is usually expected. By summarizing these results, we proposed a design for a single‐chain electronically conductive polymers. © 2012 Wiley Periodicals, Inc.