Standard Ab Initio Methods Research Articles

Accurate equilibrium structures of some challenging molecules: FNO, ClNO, HONO, FNO2, and N2O

It is sometimes difficult to determine the structure of some molecules because the optimization using standard ab initio methods (coupled-cluster with single, double, and perturbative triples [CCSD(T)] level) does not give the correct result and the experimental and semiexperimental methods are not accurate because the system of normal equations of the least-squares method is ill-conditioned. In such a case, it may be still possible to derive an accurate equilibrium structure in the following way: the experimental rotational constants are compared to those obtained at the CCSD(T) level, the latter being corrected to take into account the rovibrational correction (and, if necessary, the electronic correction). Extrapolating (or interpolating) the rotational constants calculated with different basis sets (e.g. cc-pwCVTZ and cc-pwCVQZ) towards the experimental values as a function of the bond lengths and angles permits to obtain an accurate equilibrium structure. This method is first tested on two molecules for which the multireference effects are important: O3 and HOON. It is then, applied to molecules with a weak N–X bond (HONO, FNO, ClNO, FNO2, and N2O) for which the single reference CCSD(T) method gives bonds that are too short. The results are compared to the experimental and semiexperimental equilibrium structures. As a further check, the structure of ClNO is calculated at the CCSDTQ level and the structures of FNO and ClNO are calculated at the MRCI-F12 level. From a comparison of the different results, it appears that the accuracy of the proposed method is better than 0.002 Å for the bond lengths and 0.3° for the angles.

Hard antiphase domain boundaries in strontium titanate unravelled using machine-learned force fields

We investigate the properties of hard antiphase boundaries in ${\mathrm{SrTiO}}_{3}$ using machine-learned force fields. In contrast to earlier findings based on standard ab initio methods, for all pressures up to $120\phantom{\rule{0.16em}{0ex}}\mathrm{kbar}$ the observed domain wall pattern maintains an almost perfect N\'eel character in quantitative agreement with Landau-Ginzburg-Devonshire theory, and the in-plane polarization ${P}_{3}$ shows no tendency to decay to zero. Together with the switching properties of ${P}_{3}$ under reversal of the N\'eel order parameter component, this provides hard evidence for the presence of rotopolar couplings. The present approach overcomes the severe limitations of ab initio simulations of wide domain walls and opens avenues toward concise atomistic predictions of domain-wall properties even at finite temperatures.

Metal-insulator transition in V2O3 with intrinsic defects

Vanadium sesquioxide (${\mathrm{V}}_{2}{\mathrm{O}}_{3}$) is a Mott insulator exhibiting a temperature-dependent metal-insulator transition (MIT) at 165 K accompanied by both a magnetic and structural transition. Although it is expected to be a metal under conventional band theory, electron interactions at low temperature cause it to behave like an insulator, making it difficult to accurately model its electronic properties with standard ab initio methods. As such, accurate theoretical assessments of the MIT with point defects requires special attention to the type of functionals used. In this study, we conclude that the $\mathrm{PBE}+U$ functional provides the best compromise between accuracy and efficiency in calculating the properties related to the MIT between low-temperature and high-temperature ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$. We use this functional to explore the various influences that intrinsic point defects will have on the MIT in ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$.

Efficient magnetic superstructure optimization with [formula omitted

Simulating the incommensurate spin density waves (ISDW) states is not a simple task within the standard ab initio methods. Moreover, in the context of new material discovery, there is a need for fast and reliable tool capable to scan and optimize the total energy as a function of the pitch vector, thus allowing to automatize the search for new materials. In this paper we show how the ISDW can be efficiently obtained within the recently released ΘΦ program. We illustrate this on an example of the single orbital Hubbard model and of γ-Fe, where the ISDW emerge within the mean-field approximation and by using the twisted boundary conditions. We show the excellent agreement of the ΘΦ with the previously published ones and discuss possible extensions. Finally, we generalize the previously given framework for spin quantization axis rotation to the most general case of spin-dependent hopping matrix elements.

Accurate thermoelastic tensor and acoustic velocities of NaCl

Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.

H4: A challenging system for natural orbital functional approximations.

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D(2h) to D(4h) symmetry in H4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H4 D(4h)/D(2h) potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D(2h)-D(4h) transition of H4 has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.

Thermodynamic Parameters and Electrochemical Behavior of Tetrafluoro-p-Quinone in Aqueous Solution

The electrochemical behavior of tetrafluoro-p-quinone, TFQ, at bare and activated glassy carbon electrodes (BGCE and AGCE) was studied in aqueous solution by cyclic voltammetry. The effects of scan rate, pH and concentration on the electrochemical behavior of TFQ indicate that the reduced form of TFQ (tetrafluoro-p-hydroquinone, TFHQ) is adsorbed weakly at the AGCE surface whereas the oxidized form does not show any adsorption at this surface. The temperature dependency of the TFQ redox potential has been used for determination of the changes of entropy, enthalpy and Gibbs free energy of the electrochemical reaction of TFQ. Theoretical calculations have been also carried out by means of standard ab initio modern composite methods (G3B3 and G4 theories). Theoretical and experimental values for the standard redox potential of TFQ are in good agreement with each other.

Experimental and Computational Thermochemistry of 3- and 4-Nitrophthalic Anhydride.

In order to understand the influence that the position of the nitro group on the aromatic ring has on the relative stability of two isomers, the standard enthalpies of formation of 3- and 4-nitrophthalic anhydride in the gaseous phase, at T = 298.15 K, were obtained by experimental thermochemistry and theoretical studies. The standard enthalpies of formation in the crystalline phase, at T = 298.15 K, were obtained by combustion calorimetry and the enthalpies of sublimation by the Knudsen method. For the theoretical calculations, a standard ab initio molecular orbital method at the G3 level was used. The enthalpies of formation in the gaseous phase were obtained from atomization and isodesmic reactions. A theoretical study of the molecular and electronic structures of these compounds was also performed. Differences of -9.7 kJ·mol-1, for 3-nitrophthalic anhydride, and -2.6 kJ·mol-1 for 4-nitrophthalic anhydride, were found from a comparison between our theoretical and experimental results.

The H4 model revisited within the framework of the G-particle-hole Hypervirial equation

In this paper we report the results obtained when calculating the electronic structure of the H4 molecular system within the framework of the G-particle-hole Hypervirial equation (GHV). This method determines directly the G-particle-hole matrix of the state considered without a previous knowledge of the wave-function. Our primary aim is to compare the GHV performance with that of other standard ab initio methods having as ultimate reference the FCI results, when the system considered is strongly correlated.

Hookean atom with four electrons: On the formation of a tetrahedral Wigner molecule in the weak trapping limit

Numerical results are presented on states ${}^{5}{S}_{u}$ and ${}^{3}{P}_{g}$ of the Hookean atom with four electrons. Using standard ab initio quantum chemistry methods, the quintet configuration is shown to be the ground state for the weak harmonic trapping constant $k$. For large $k$ values, there is a crossover to the triplet ${}^{3}{P}_{g}$ ground state. Finally, it is concluded that the Coulombic potential energy approaches the localized electron limit of a tetrahedral Wigner molecule as the harmonic force constant $k$ tends to zero.

The Smallest “Aurophilic Species”

The existence of the C2v symmetric closed-shell di[gold(I)]hydronium cation [Au2H]+ (1), is predicted. It is shown that 1 is the smallest possible molecular species containing aurophilic contacts. Equilibrium structural parameters, vibrational frequencies and formation energies of 1 from Au+ and AuH, have been calculated, employing a series of highly correlated but available standard relativistic ab initio methods up to CCSD(T) level of theory and all-electron basis sets of quadruple-ζ quality with double polarizations. Relativistic effects have been taken into account by employing pseudorelativistic electron core potentials (ECP) or a scalar relativistic treatment using a Douglas-Kroll-Heß Hamiltonian of 2nd, 3rd and 4th order (DKH2, DKH3, DKH4).

Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions

Calculations on small molecular systems indicate that the variational approach employing the two-particle reduced density matrix (2-RDM) as the basic unknown and applying the P, Q, G, T1, and T2 representability conditions provides an accuracy that is competitive with the best standard ab initio methods of quantum chemistry. However, in this paper we consider a simple class of Hamiltonians for which an exact ground state wave function can be written as a single Slater determinant and yet the same 2-RDM approach gives a drastically nonrepresentable result. This shows the need for stronger representability conditions than the mentioned ones.

First-principles study of lattice instabilities in ferromagnetic L12 Fe3Ni: direct force constants method versus linear response

The phonon-dispersion relations for ferromagnetic Fe3Ni in the L12 structure are computed along the high symmetry directions using two powerful first-principles techniques: direct force constants method, which is used in conjunction with a standard ab-initio method, and the linear response approach that is based entirely on the density-functional-perturbation theory. The two methods have been applied with success to reveal the experimental observations that characterize the Invar problem in Fe3Ni most especially in the [110] direction. They also help to shed more light on the additional softening of the TA mode being speculated in [111] direction.

Hybrid correlation models based on active-space partitioning: Seeking accurate O(N5) ab initio methods for bond breaking

Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.

Theory of the short-range correlation hole model

While standard ab initio methods have provided a route towards highly accurate calculations of a vast array of chemical properties, the applicability of these methods is limited essentially because the computational effort of a correlated calculation grows very rapidly with the number of atomic basis functions while the accuracy does not. Thus, extensive one-particle basis sets are required for reasonable accuracy and, therefore, only small systems can be treated routinely. A great deal of effort has gone into finding ways to circumvent this difficulty, which has been attributed to the improper description of short-range electron correlation. In a recent paper, we introduced a technique intended to partially correct this improper description by using a local density approximation for the short-range correlation hole. Here, we wish to elaborate on the basic concept in several ways. We introduce a more reliable cut-off procedure, discuss the effects of gradient corrections and show how a Hamiltonian can be constructed. This points the way towards the calculation of properties, gradients, excitation energies and so forth; hiding basis set effects in the Hamiltonian is essential to developing a generally applicable method for molecules.

Evaluation of reaction thermochemistry using DFT calculated molecular properties: application to trans-HONO (X¹A') à HO(X²P) + NO(X²P)

B3LYP calculations using basis sets up to 6-311G(3d2f,3p2d) have been employed to predict accurate thermochemical properties related to the bond dissociation reaction trans-HONO(X¹A') -> HO(X²P) + NO(X² P). A systematic study of the influence of the basis set was performed and results were compared with experimental data and with other calculated results, obtained using standard Gaussian methods (G2 and G2MP2), complete basis set extrapolation methods (CBS) and ab initio calculations (CCSD(T) and QCISD). The results suggest that, for this kind of unimolecular process: B3LYP calculations produce bond dissociation enthalpies that are more accurate than standard ab initio methods and) the best agreement with the experimental enthalpy has been found with B3LYP/6-311G(3d2f,3p2d) calculations: 49.2 kcal mol-1 and 49.0 kcal mol-1, respectively. Also, entropy and Gibbs free energy have been calculated and equilibrium constants have been determined as Keq(T) = 1.16 × 10(28) × exp(-48.34/RT), for the temperature range 200 - 500 K.

Comparison of the polarizabilities of HRgF (Rg = He, Ar, Kr) molecules

Molecular dipole polarizabilities of HHeF, HArF and HKrF were computed with the standard ab initio theoretical methods, SCF, MP2 and QCISD, using a 6-311++G(2d,2p) basis set. These results were compared with polarizabilities obtained from density functional theory (DFT) using the B3LYP, HCTH and VSXC functionals. It was found that, in contrast with a molecule like HF, the HRgF molecules (Rg = rare gas) have large average polarizabilities and polarizability anisotropies. Good agreement was found between the MP2 and QCISD methods, but (for HRgF) the corresponding SCF and DFT values are smaller in magnitude.

Response theory in the multipole reaction field model for equilibrium and nonequilibrium solvation: Exact theory and the second order polarization propagator approximation

Exact response functions are derived for a multipole solvent reaction field model of equilibrium and nonequilibrium solvation using the generalized Ehrenfest theorem and assuming a spherical cavity surrounding the solute. The starting point is the Schrödinger equation and we shortly review how the reaction field is introduced into the Schrödinger equation in order to clearly identify the limitations of describing solute–solvent interactions with a reaction field model. The solvent is described as an isotropic homogeneous linear dielectric medium characterized by a static and an optical dielectric constant. From the exact response functions we derive linear response functions within the higher random phase and the second order polarization propagator approximation. Excitation energies, oscillator strengths, and polarizabilities are then calculated for solvated H2S and furan using the augmented correlation consistent triple-ζ (aug-cc-pVTZ) and double-ζ (aug-cc-pVDZ) basis sets for H2S and furan, respectively. We have also calculated excitation energies and oscillator strengths for H2S with standard (vacuum) ab initio methods using a variety of basis set, as there has been no previously reported values of these quantities calculated with the second order polarization propagator approximation. The second order polarization propagator approximation gives excitation energies and oscillator strengths close to values obtained by coupled cluster methods for a solvated H2S molecule, whereas the higher random phase approximation tends to overestimate the value of these quantities. The solvent effect of the excitation energies follow the same trends for all of the reaction field ab initio methods used in the present study, but some oscillator strengths show different solvent effects whether they are calculated with correlated or with noncorrelated ab initio methods. The calculated polarizabilities show the same solvent effect independent of any inclusion of dynamical electron correlation. It is also shown that the equilibrium solvation model is not appropriate for high-frequency perturbations.

FTIR-Spectroscopy of isolated and argon coated (HBr)n≤4 clusters in supersonic slit-jet expansions

Presented are the ragout-jet FTIR spectra of isolated (HBr)n clusters (n≤4) in pulsed slit-jet expansions. These are the first gas phase infrared spectra of (HBr)3 and (HBr)4 reported so far. The assignment is based on a direct comparison with hydrogen chloride and MP2/6-311++G(d,p) ab initio calculations. Despite the well known difficulties of standard ab initio methods and standard basis sets to predict frequency shifts in hydrogen halide clusters, the method and basis set chosen in this work gives at least a correct qualitative description. In addition argon coated HBr clusters up to the tetramer could be observed in co-expansions of HBr with argon, confirming the general capability of the ragout-jet spectroscopy to investigate argon coated molecular clusters of a wide variety of molecules.

Calculation of the intermolecular energy of large molecules by a fragmentation scheme: Application to the 4-n-pentyl-4′- cyanobiphenyl (5CB) dimer

We present a method for computing intermolecular energies of large molecules based on a suitable fragmentation scheme, which allows one to express the complete interaction energy as a sum of interaction energies between pairs of fragments. The main advantage consists in the possibility of using standard ab initio quantum methods to evaluate the fragment energies. For the 4-n-pentyl-4′-cyanobiphenyl (5CB) dimer, the present results indicate that the most favorite arrangement corresponds to an antiparallel side-by-side geometry with a stabilization energy of about 16 kcal/mol. It is shown that, by the present method, the interaction energy of the 5CB dimer can be evaluated for all geometrical conformations and, in principle, it can be used for bulk simulations.