Large All-electron Basis Sets Research Articles

Molecular structure and spectra of ytterbium dihalides from first principles

The molecular structure, vibrational frequencies, infrared intensities and electric dipole moments of ytterbium dihalides YbX2 (X = F, Cl, Br, I) in their ground electronic state are studied at the coupled-cluster singles, doubles and perturbative triples CCSD(T) level using a series of large all-electron basis sets together with the complete basis set (CBS) extrapolation procedure, and with both scalar-relativistic and spin–orbit coupling effects taken into account. Excitation energies of low-lying electronic states are calculated at the multireference configuration interaction, equation-of-motion CCSD and single-reference CCSD(T) levels of theory. For all of the molecules under study, the CCSD(T)/CBS equilibrium geometries are found to be non-linear (C2v symmetry). There is a rapid decrease in heights of the barriers to linearity on passing through the YbX2 molecular series from fluoride to iodide: 1587 → 261 → 110 → 7 (all in cm−1) for YbF2 → YbCl2 → YbBr2 → YbI2, respectively. The uncertainties in the molecular structure data published to date are discussed and resolved in the light of the present results.

Challenges with relativistic GW calculations in solids and molecules.

For molecules and solids containing heavy elements, accurate electronic-structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all-electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis sets, particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

A computational study of the non-adiabatic coupling among low-lying doublet states of the CN radical

First principle electronic structure calculations on low-lying doublet states of the CN radical have been performed using the multi-reference configuration interaction method and large all-electron basis sets. Beside the adiabatic interatomic potentials, the non-adiabatic spin-orbit and L-uncoupling electronic matrix elements were evaluated for the mutually perturbed (2)B2Σ+∼(1–4)2Π and (1)A2Π∼(1–3)2Σ+, (1)2Σ−, (1,2)2Δ pairs of states. The radial coupling matrix element was calculated between the X2Σ+ and B2Σ+ states. The reliability of the derived A∼X and A∼B matrix elements was confirmed by comparison with their empirical counterparts. Both local and regular perturbations in the A∼B∼X complex were found to depend mostly on spin-orbit and electronic-rotational interactions between the lowest A2Π, and B2Σ+ states. Excited states, in all their diversity, have little effect on the fine structure of the A∼B complex, except for the qA Λ-doubling function. The ab initio coupling functions can be crucial to providing a global deperturbation treatment for the A, B and X states on a spectroscopic level of accuracy.

A theoretical study on the laser cooling scheme for the three-energy-level system of the CN molecule

The X2Σ+ and B2Σ+ states of the CN molecule are suitable for the closed-loop transition of the optical laser cooling scheme because of the high diagonal Franck-Condon factor. However, the low-lying state of A2Π between X2Σ+ and B2Σ+ states makes the laser cooling scheme for the CN molecule become a three-energy-level system. The treatment of the intervening state is a key issue for laser cooling. To explore the feasibility of the scheme, we calculate the potential energy curves and transition dipole moments of X2Σ+, B2Σ+ and A2Π states of the CN molecule using the multi-reference configuration interaction method and large all-electron basis sets. Based on the obtained potential energy curves, the rotational and vibrational energy levels of the states are obtained by solving the Schrödinger equation of nuclear movement. The calculated spectroscopic parameters for the CN molecule are in good agreement with available theoretical and experimental results. The feasibility of laser cooling for the three-energy-level system of the molecule is examined using the results of the molecular electronic and spectroscopic properties. Based on the examination of the transition dipole moment, Franck-Condon factor, the spectroscopic term and the vibration energy levels, we find that the intervening state A2Π proves to be a significant influence on the closed-loop transition, but a large number of scattering photons are still available. Therefore, the optical schemes for the laser cooling of the three-energy-level system can be designed with a two-energy-level model according to the characteristic of X2Σ+ and B2Σ+ states. Finally, the optical scheme for cooling the CN molecule is constructed with three lasers.

Spectroscopic parameters of the low-lying electronic states and laser cooling feasibility of NH+ cation and NH− anion

The potential energy curves and transition dipole moments of 12Σ+, 22Σ+, 12Π and 22Π states of NH+ cation and NH− anion are calculated by using multi-reference configuration interaction method and large all-electron basis sets. Based on the obtained potential energy curves, the rotational and vibrational energy levels of the states are obtained by solving the Schrödinger equation of nuclear movement. The calculated spectroscopic parameters for NH+ cation and NH− anion are in good agreement with available theoretical and experimental results. The spin orbit coupling effect of the 2Π states for both NH+ cation and NH− anion are calculated. The feasibility of laser cooling of the two molecules is examined by using the results of the molecular structure and spectroscopy. The highly diagonal Franck-Condon factors for the 12Π (v″=0)↔12Σ+ (v′=0) transition of NH+ and NH− are 0.821 and 0.999, while the radiative lifetimes of the 12Σ+ (v′=0) state for the two molecules are 384ns and 52.4ns, respectively. The results indicate that NH+ cation and NH− anion are good candidate molecules for laser cooling. The cooling scheme via Sisyphus process for the NH+ cation and NH− anion are proposed in the paper. The laser wavelengths for the close cycles of the absorption and radiation are also determined. Unfortunately, the potential energy curve of the ground state of the neutral NH molecule shows that the auto-detachment of NH− anion is possible, implying the optical scheme of laser cooling for NH− anion is not easy to achieve in the experiment although it has larger Franck-Condon factor.

Water at hydroxyapatite surfaces: the effect of coverage and surface termination as investigated by all-electron B3LYP-D* simulations

Hydroxyapatite [HA, Ca10(PO4)6(OH)2], the main constituent of bones and teeth enamels, is a widely studied and employed biomaterial. Its applications span from dental to orthopedic implants, including bone tissue engineering scaffolds, coating, filler and many others. Previous theoretical and experimental studies have already characterized the physical–chemical foundations of water adsorption on a number of HA surfaces, an essential step in the mechanism of biomaterial integration. Here, we extend such knowledge by simulating, at a hybrid DFT level of theory, different HA surface terminations, both stoichiometric and non-stoichiometric, as free and in interaction with water. Such a goal is achieved at an unprecedented accuracy, with a large all-electron basis set and including dispersion forces contributions. The calculated results are then compared with experimental micro-calorimetric data, showing a good agreement in the loading trend of the (010) surfaces. More generally, this theoretical approach is confirmed to be an efficient tool to analyze these biomaterials, giving the possibility to investigate the HA behavior toward more complex molecules, from amino acids to collagen, at the here-presented level of theory, to shed some light on the complex biomineralization process of human bones and teeth.

Ab initio study on the ground and low-lying states of BAlk (Alk = Li, Na, K) molecules.

The potential energy curves (PECs) and dipole moment functions of (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states of BAlk (Alk = Li, Na, K) are calculated using multireference configuration interaction method and large all-electron basis sets. The effects of inner-shell correlation electron for BAlk are considered. The ro-vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the ab initio PECs. The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The dipole moment functions for the states of BAlk are presented. The transition dipole moments for (1)Σ(+) → (1)Π and (3)Σ(+) → (3)Π states of BAlk are obtained. The interactions between the outermost electron of Alk and B 2p electrons for (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states are also analyzed, respectively.

Surface structures and thermodynamics of low-index of rutile, brookite and anatase – A comparative DFT study

Titania surfaces have been studied theoretically and experimentally for many decades due to their photocatalytic properties. In this paper we present a theoretical study where we compare the low-index surfaces of rutile, anatase and brookite in terms of their stability and relaxation. The convergence behavior with the number of layers is analyzed with large all-electron basis sets and a hybrid DFT method (PW1PW). With this method a good agreement with recent experimental results for the surface relaxation is achieved. Frequency calculations for all considered surfaces were performed to obtain surface enthalpies and analyze the stability of the 1×1 surface-patterns.

An ab initio study of the ground and low-lying excited states of KBe with the effect of inner-shell electrons

The potential energy curves (PECs) of 1(2)Σ(+), 2(2)Σ(+), 1(2)Π, and 2(2)Π states of KBe are calculated using multireference configuration interaction method and large all-electron basis sets. Four sets of frozen core orbitals (FCOs) are considered to examine the effect of inner-shell correlation electrons on the molecular properties. The ro-vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the ab initio PECs. The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The dipole moment functions of the states for KBe calculated with different FCOs are presented. The transition dipole moments for KBe between 1(2)Σ(+) and 2(2)Σ(+) states, 1(2)Π and 1(2)Σ(+) states, and 2(2)Π and 1(2)Σ(+) states are also obtained.

The effect of inner-shell electrons on the ground and low-lying excited states of KLi: Ab initio study with all-electron basis sets

The potential energy curves (PECs) have been calculated for the X1Σ+, A1Σ+, 13Σ+, 23Σ+ states of KLi using multireference configuration interaction method and large all-electron basis sets. The calculations take into account the effect of inner-shell electrons with different active spaces. The rotational and vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the PECs. The spectroscopic parameters are determined from the rotational and vibrational levels and compared with the theoretical and experimental reports in the literature. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The effect of inner-shell electrons on the PECs, rotational and vibrational energy levels and spectroscopic parameters is analyzed.

Ab initio and DFT analysis of the low-lying electronic states of metal dihalides: quantum chemical calculations on the neutral BrMCl (M = Cu, Ag, Au)

The electronic configuration of the electronic ground and low-lying doublet excited states of neutral metal dihalides BrMCl (M = Cu, Ag, Au) has been investigated on the basis of CASSCF/CASPT2 methods taking into account scalar relativistic effects. A preliminary study of the electronic problem in BrAgCl, based on DFT and CASSCF/CASPT2 approaches and using various basis sets, namely relativistic all-electron basis sets, effective core potentials and ab initio model potentials (AIMP), as well as non-relativistic AIMP is discussed. It is shown that single-determinant methods are not flexible enough to describe the bonding of the neutral species in the electronic ground state regardless of the basis set. The failure to allocate the single electron of BrAgCl correlates with a wrong charge distribution within the complex, which is more accentuated when using pseudopotential basis sets. The inclusion of static and dynamic correlation effects by means of CASSCF/CASPT2 methods using large relativistic all-electron basis sets provides a correct qualitative picture of the electronic structure of the BrMCl series (M = Cu, Ag, Au). The spin unrestricted KS-DFT approach leads to a reasonable description of the degenerate electronic ground state ((2)Σ/(2)Π) bonding in these complexes with negligible spin contamination providing comparative spin densities in the series of molecules under investigation.

The IR vibrational properties of six members of the garnet family: A quantum mechanical ab initio study

The IR vibrational properties and the corresponding reflectance spectra of the six most common members of the garnet family (pyrope Mg3Al2Si3O12, almandine Fe3Al2Si3O12, spessartine Mn3Al2Si3O12, grossular Ca3Al2Si3O12, uvarovite Ca3Cr2Si3O12, and andradite Ca3Fe2Si3O12) were simulated at the ab initio level with the CRYSTAL09 code by using a large all-electron Gaussian-type basis set and the B3LYP hybrid functional. The 17 IR active F1u transverse optical (TO) and longitudinal optical (LO) frequencies, the oscillator strengths, the high frequency and static dielectric constants, and the reflectance spectrum were computed. The agreement with experiments for the TO and LO peaks is always excellent, the mean absolute difference for the whole set of data (overall 178 peaks) being 5 cm-1. Oscillator strengths, calculated from the mass-weighted effective Born charges, are found in semi-quantitative agreement with the experimental data. The reflectance spectra, simulated through the classical dispersion relation, reproduce the experimental curves extremely well. The availability of the full set of simulated frequencies and intensities, obtained by using uniform computational tools (computer code, variational basis sets, density functional), permits the establishment of correlations between IR wavenumbers and structural features suggested, but only partially documented, in the past

Calibration and applications of the ΔMP2 method for calculating core electron binding energies

We calibrated a method for the evaluation of core electron binding energies, based on the energy differences between the cation and neutral molecule evaluated at the level of Møller-Plesset perturbation theory. The central feature of the method is the use of a mixed basis set: a large all-electron basis set is used for the atom whose core electron is removed, while the model core potential basis set is employed for all remaining atoms. Calibration was carried out for 55 molecules and 114 binding energies of 1s core electrons for the atoms C, N, O, and F. The average absolute deviation for all the core electron binding energies is 0.163 eV. The method was applied to the calculation of the core electron binding energies of five nucleic acid bases (uracil, adenine, cytosine, guanine, and thymine) and several of their low-energy tautomers.

Performance of Relativistic Effective Core Potentials in DFT Calculations on Actinide Compounds

Density functional theory (DFT) calculations using relativistic effective core potentials (RECPs) have emerged as a robust and fast method of calculating the structural parameters and energy changes of the thermochemical reactions of actinide complexes. A comparative investigation of the performance of the Stuttgart small-core and large-core RECPs in DFT calculations has been carried out. The vibrational frequencies and reaction enthalpy changes of several uranium(VI) compounds computed using these RECPs were compared to those obtained using DFT and a four-component one-electron scalar relativistic approximation of the full Dirac equation with large all-electron basis sets (AE). The relativistic AE method is a full solution of the Dirac equation with all spin components separated out. This method gives the "correct" answer (with respect to scalar relativity) which should be closest to experimental values when an adequate density functional is used and in the absence of significant spin-orbit effects. The small-core RECP always show better agreement with the four-component scalar- relativistic AE method than the large-core RECP. We conclude that the 5s, 5p, and 5d orbitals are of great importance in determining the chemistry of actinide complexes. Instances in which large-core RECPs give better agreement with experimental data are attributed to either experimental uncertainties or error cancellations.

How Strong Is an Agostic Bond? Direct Assessment of Agostic Interactions Using the Generalized Compliance Matrix

The strength of an α-agostic bond in CH2TiHF has been evaluated using the generalized compliance matrix from HF (Hartree−Fock), MP2 (second-order Møller−Plesset perturbation), CCSD(T) (coupled cluster theory with single and double substitutions with noniterative triple excitations), and several formulations of DFT (density functional theory) in combination with large all-electron basis sets. While HF underestimates the agostic interaction, both MP2 and the local spin density approximation (LSDA) dramatically overestimate the agostic Ti···H interaction strength. Hybrid DFT (B3LYP) and pure DFT (BLYP) are in line with the CCSD(T) level of theory. The DFT compliance constants and their coupling values are further used to characterize the agostic C−H···W interaction in [W(⋮CCMe3)(CHCMe3)(CH2CMe3)(dmpe)] (1; dmpe = (dimethylphosphino)ethane). The strength of this agostic bond is analyzed as a function of the metal atom and the molecular environment.

Why is the F2 bond so weak? A bond energy decomposition analysis

The bond energies of F2, Cl2, Br2 and I2 have been studied computationally using gradient-corrected, relativistic density functional theory with large all-electron basis sets. The bond energies of all four compounds have been broken down into electrostatic, Pauli (exchange) and orbital terms at the equilibrium internuclear separation and as a function of r(X–X) using the Ziegler–Rauk energy decomposition scheme. The comparative weakness of the F2 bond is traced to the electrostatic energy, which is considerably smaller than would be expected on extrapolation of the trend in the I2 → Cl2 data. The small electrostatic term is itself a result of the F–F bond being c. 0.1 A longer than might be expected, due to the large gradient in the Pauli repulsion around the equilibrium internuclear separation. The weakness of the F2 bond is therefore a combination of quantum mechanical (Pauli) and classical (electrostatic) factors. The present conclusions are placed throughout in the context of previous research.

Intermolecular Self-Interactions of the Titanium Tetrahalides TiX4 (X = F, Cl, Br)

Ab initio calculations have been performed on the closed-shell molecules TiX4 and Ti2X8 (X = F, Cl, Br) in order to determine the magnitude and the nature of the intermolecular self-interactions of the titanium tetrahalides. Geometry optimizations have been carried out using an effective core potential basis set with polarization, including the effects of dynamic electron correlation through second-order perturbation theory (MP2). The importance of higher order correlation effects is examined through coupled cluster single-point energy calculations. Basis set effects are investigated using MP2 single-point energy calculations with large all-electron basis sets. Ti2F8 is predicted to be a bound C2h dimer with bridging bonds, lower in energy than the separated monomers by 10.5 kcal/mol. Ti2Cl8 and Ti2Br8 are predicted to be weakly bound dimers whose structures are that of associated monomers with overall D3d point group symmetry. Ti2Cl8 is lower in energy than separated monomers by 4.9 kcal/mol. Transition ...

The CuC bond dissociation energy of CuCH 3. A dramatic failure of the QCISD(T) method

The coppercarbon bond dissociation energy of CuCH 3 is calculated using coupled cluster (CC) theory and the quadratic CI approach (QCI) in conjunction with an effective core potential (ECP) for Cu. The results at the CCSD ( D e=45.4 kcal/mol) and CCSD(T) level ( D e=48.0 kcal/mol) are in good agreement with previous high-level calculations using the MCPF approch ( D e=48.4 kcal/mol). The theoretically predicted dissociation energy at the QCISD(T) level shows a dramatic failure of the estimate for the triple excitations in CuCH 3. The QCISD value is D e=55.4 kcal/mol, the QCISD(T) values is D e=6.0 kcal/mol. The QCISD(T) method predicts clearly different dissociation energies when the core electrons are explicitly included in the calculations, while the CCSD(T) method gives similar results to the ECP calculations. The predicted dissociation energy using a large all-electron basis set is D e=52.7 kcal/mol at QCISD and D e=29.4 kcal/mol at QCISD(T). The CCSD method gives with the same basis set D e=46.0 kcal/mol; the value at CCSD(T) is D e=49.7 kcal/mol.

Comparison of ab initioMODPOT interaction energy components against large basis set MBPT (4) calculations for nitromethane dimer

Ab-Initio MODPOT SCE calculations using our own optimized well-balanced minimal basis sets have little basis set superposition error (BSSE) and have proven over the years to give reliable intermolecular geometries and interaction energies. Another approach, using ab initio potential functions from energy partitioned ab initio calculations, has also yielded reliable interaction energies and intermolecular geometries, including crystal structures. We used both of these techniques in comparing the results of a published large all-electron basis set calculation on the nitromethane dimer with the above methods. Our SCF intermolecular minimum energy was at the same internuclear distance as the large all-electron basis set. Our SCF interaction energy, corrected for BSSE, was only 0.4 kcal above the SCF energy of the large basis set SCF calculation corrected for BSSE. We also calculated the energy partitioned components with our ab initio MODPOT basis set and with the larger all-electron basis set and showed that the small difference in interaction energy was due to a small difference in the first-order electrostatic multipolar term. (We also calculated this term from correlated wave functions [SDQ-MBPT (4)] using both ab initio MODPOT and the larger all-electron basis sets). From values of the first-order electrostatic multipolar term from SCF and correlated monomer wave functions, the contribution to intermolecular interaction energy due to the use of correlated monomer wave functions has been estimated. Our results indicate either the dominant role of electrostatic term or near cancellation of the remaining components of intermolecular interaction energy. For cyclic nitromethane dimer at equilibrium distance these effects approach 0.9 kcal/mol (nearly 1/4 of total interaction energy). In addition, we showed that the semitheoretical expression and parameters we use for estimating the dispersion energy gave results very close to the published variation perturbation results from the larger basis set calculation.