Picture change error correction of radon atom electron density

The importance of the picture change error (PCE) correction in the quasirelativistic electron density of radon atom is presented. PCE correction is considered for the infinite order two-component (IOTC) and second order Douglas-Kroll-Hess (DKH2) wave functions. Implementation details of PCE correction of electron density are outlined. The result section presents the radial distributions of electron density ρ(r) and the 4πr(2)ρ(r) function of the radon atom in the nuclear region. The PCE corrected and contaminated DKH2, IOTC electron densities are presented and compared with the Dirac-Coulomb Hamiltonian and nonrelativistic electron densities. Besides, some additional effects in electron density and SCF energy are considered, such as spin-orbit coupling, the inclusion of the Gaunt term, and the finite nucleus model effects. The effects of p(2)Vp(2) and p(2)ρ(r)p(2) analytic integral classes within IOTC Hamiltonian and PCE correction of IOTC electron density are considered.     

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model chemistry yields MAD=0.68 kcal/mol, which represents a huge improvement over plain B3LYP/6-31G* (MAD=2.3 kcal/mol). Application of gCP-corrected B97-D3 and HF-D3 on a set of large protein-ligand complexes prove the robustness of the method. Analytical gCP gradients make optimizations of large systems feasible with small basis sets, as demonstrated for the inter-ring distances of 9-helicene and most of the complexes in Hobza's S22 test set. The method is implemented in a freely available FORTRAN program obtainable from the author's website.     

Generalized uniform singlet- and triplet-pair extrapolation of the correlation energy to the one electron basis set limit

The relationship between the triplet- and singlet-pair interaction coefficients in the uniform singlet- and triplet-pair extrapolation method recently suggested for extrapolating ab initio energies to the one-electron basis set limit is analyzed. Based on the premise that such a ratio is invariant over the configuration space of the molecule, generalizations of the method are investigated and their performance tested on extrapolations with MP2, CCD, CCSD, and MRCI(Q) energies. The best variant requires raw energies calculated using augmented correlated consistent basis sets with cardinal numbers up to X = 6 at a single geometry. A scheme is also suggested that performs better than the traditional X(-3) law and possibly the original uniform singlet- and triplet-pair extrapolation method but requires data only up to X = Q.     

The effect of electron correlation on the topological and atomic properties of the electron density distributions of molecules

The topological properties of the electron density and the properties of an atom in a molecule are calculated by means of second-order Møller-Plesset perturbation theory (MP2) and compared with the results of configuration interaction calculations (C12) which include all single and double substitutions from the Hartree-Fock reference configuration. A software package for analyzing the effects of electron correlation on the topological properties of the electron density of molecules is described. H₂CO is used to provide a numerical example and to indicate that the number of bond critical points is unaffected by the inclusion of electron correlation. Correlation leads to only a small shift in the positions of bond critical points and a small change in the electron density at bond critical points. It is further shown that the energy of an atom in a molecule can be calculated to an accuracy of 1 kcal/mol and the electron population of an atom to about 0.001e. A statistical method is used to show that the deviation of the MP2 correlation correction relative to the CI2 correlation correction for a variety of atomic properties is about 25%.     

On the application of the counterpoise correction for the basis set superposition error in geometry optimization calculations of molecular systems: some inconsistent results

It is shown that the conjecture that the total energy for a given molecular or supermolecular system is affected by basis set superposition error (BSSE) leads to inconsistent results. While the calculations of interaction energies, dissociation energies, or energy barriers depend on the fragments (reactants, products) involved in their definitions and, consequently, are affected by BSSE, the total energies of molecular or supermolecular systems do not depend on any virtual fragment partition and are, therefore, BSSE free. Contribution to the Serafin Fraga Memorial Issue.     

Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

On the basis set superposition error in supermolecular calculations of interaction-induced electric properties: many-body components

In the present paper we analyze basis set superposition error (BSSE) removal methods from many-body components of interaction-induced electric properties. The Valiron–Mayer function counterpoise (VMFC), site–site function counterpoise (SSFC) and TB methods have been employed in order to obtain the incremental optical components of linear hydrogen fluoride clusters (HF)n, where n = {3,4}. Following Mierzwicki and Latajka, who have performed similar calculations for the interaction energy, we compare those three methods of eliminating BSSE using several Dunning’s correlation consistent basis sets.     

A comparison of the Raman LAM and electron microscopy in determining crystallite thickness distributions: Polyethylenes with narrow size distributions

A detailed quantitative comparison between thin section electron microscopy, utilizing the chlorosulfonation technique, and the Raman low-frequency acoustical mode (LAM) in determining the crystallite size distribution in polyethylenes having narrow distributions is made. Three different polyethylene systems have been analyzed, one of which was specifically prepared for this work. Very good quantitative agreement is obtained between these two analytical methods when account is taken of the chain tilt and the distribution is restrained to be narrow. Systems having broad crystallite size distributions introduce complexities into this comparison.     

Coupling between the convergence behavior of basis set and electron correlation: a quantitative study

The coupling between improvement of the basis set and the valence electron correlation method has been studied quantitatively for the total atomization energies (TAEs) of a number of small molecules, using basis sets of up to [7s6p5d4f3g2h/5s4p3d2f1g] quality. Very significant coupling is found to exist. Using a scaled basis set extrapolation beyond [6s5p4d3f2g/ 4s3p2d1f] at the MP2 or CCSD level, mean absolute errors of 0.18 and 0.15 kcal/mol, respectively, can be obtained for the TAEs of a number of small polyatomic molecules, compared to 0.12 kcal/mol using CCSD(T) throughout. Received: 7 February 1997 / Accepted: 6 May 1997     

Importance of electron correlation effects and basis set superposition error in calculations of interaction energies and interaction-induced electric properties in hydrogen-bonded complexes: a model study

A detailed study of the interaction energies and interaction-induced electric dipole properties in model linear hydrogen cyanide complexes (HCN) _m (m?=?2?C4) is carried out within the finite field HF SCF, MP2, CCSD and CCSD(T) approximations using the recently developed LPol-n (n?=?ds, fs, dl, fl) basis sets. The importance of high-order correlation effects and the basis set superposition error is evaluated. To correct for the latter is crucial for obtaining accurate interaction energy values, but the error can safely be neglected in the estimation of induced electric properties when the LPol-n (n?=?ds, fs, dl, fl) basis sets are used. Correlation effects are important in the evaluation of both the interaction energies and the induced electric properties of the systems.     

On "the complete basis set limit" and plane-wave methods in first-principles simulations of water

Water structure, measured by the height of the first peak in oxygen-oxygen radial distributions, is converged with respect to plane-wave basis energy cutoffs for ab initio molecular dynamics simulations, confirming the reliability of plane-wave methods.     

Measurement of radon and thoron progeny size distributions and dose assessments at the mineral treatment industry in Thailand

A new portable type cascade impactor has been developed to determine the activity size distribution of radon and thoron progeny in a natural environment more efficiently. The modified impactor consists of 4 stages with a back up filter stage for the collection of aerosol samples. The aerosol cut points in the impactor are set for 10, 2.5, 1 and 0.5 μm at a flow rate of 4 L min^?1. Five CR-39 chips were used as alpha detectors for each stage. In order to separate α particles emitted from radon and thoron progeny, CR-39 detectors are covered with aluminum-vaporized Mylar films. The thickness of each film is adjusted to allow α particles emitted from radon and thoron progeny to reach the CR-39 detectors. The technique has been successfully tested in field studies, particularly inside a mineral treatment industry in Thailand to estimate doses in the working environment. The dose calculations by lung dose evaluation program showed that activity median aerodynamic diameters played a significant role in determining the particle size distributions of the attached radon and thoron progeny. The dose conversion factor determined from short term measurements due to exposure from the inhalation of thoron and its progeny was found to be 4 times higher than comparable values for radon and its progeny. The effective dose for workers exposed to radon is about 4–6 times higher than thoron.     

On the use of NDO approximate wavefunctions in the evaluation of momentum density and radial momentum density distributions in polyatomic molecules

The use of single determinantal approximate molecular wavefunctions of the LCAO MO NDO type for the calculation of the momentum densityρ(p) and the radial momentum density distributionJ(p) is discussed. In each case, these expressions should be orientationally invariant and the momentum density should be normalized. Combining these two requirements, it is shown that only two approximations are physically significant:

1. NDO wavefunctions are used andρ(p) andI(p) are approximated respectively up to an INDO and a CNDO level;
2. Overlap integrals are explicitly taken into account when solving the Roothaan SCF equations or deorthogonalized NDO functions are employed, together with the unapproximated expressions.

     

The electron affinity of gallium nitride (GaN) and digallium nitride (GaNGa): the importance of the basis set superposition error in strongly bound systems

The electron affinity of GaN and Ga2N as well as the geometries and the dissociation energies of the ground states of gallium nitrides GaN, GaN(-), Ga2N, and Ga2N(-) were systematically studied by employing the coupled cluster method, RCCSD(T), in conjunction with a series of basis sets, (aug-)cc-pVxZ(-PP), x=D, T, Q, and 5 and cc-pwCVxZ(-PP), x=D, T, and Q. The calculated dissociation energy and the electron affinity of GaN are 2.12 and 1.84 eV, respectively, and those of Ga2N are 6.31 and 2.53 eV. The last value is in excellent agreement with a recent experimental value for the electron affinity of Ga2N of 2.506+/-0.008 eV. For such quality in the results to be achieved, the Ga 3d electrons had to be included in the correlation space. Moreover, when a basis set is used, which has not been developed for the number of the electrons which are correlated in a calculation, the quantities calculated need to be corrected for the basis set superposition error.     

Intrinsic conformational preferences of substituted cyclohexanes and tetrahydropyrans evaluated at the CCSD(T) complete basis set limit: implications for the anomeric effect

A series of MP2 and CCSD(T) computations have been carried out with correlation consistent basis sets as large as aug-cc-pV5Z to determine the intrinsic equatorial-axial conformational preference of CH(3)-, F-, OCH(3)-, and OH-substituted cyclohexane and tetrahydropyran rings. The high-accuracy relative electronic energies reported here shed new light on the intrinsic energetics of these cyclic prototypes for the anomeric effect. At the CCSD(T) complete basis set (CBS) limit, the energy of the equatorial conformation relative to the axial position (DeltaE (CBS)(CCSD(T))) is -1.75, -0.20, -0.21, and -0.56 kcal mol(-1) in methyl-, fluoro-, methoxy-, and hydroxycyclohexane, respectively, while DeltaE(CBS)(CCSD(T) is -2.83, +2.45, +1.27, and +0.86 kcal mol(-1) for 2-methyl-, 2-fluoro-, 2-methoxy-, and 2-hydroxytetrahydropyran, respectively. Note that the equatorial and axial conformers are nearly electronically isoenergetic in both fluoro- and methoxycyclohexane. For all eight cyclic species, a zero-point vibrational energy correction decreases Delta by a few tenths of a kilocalorie per mole. Relative energies obtained with popular methods and basis sets are unreliable, including Hartree-Fock theory, the B3LYP density functional, and the 6-31G and 6-311G families of split-valence basis sets. Even with the massive pentuple-zeta basis sets, the HF and B3LYP methods substantially overestimate the stability of the equatorial conformers (by as much as 0.99 and 0.73 kcal mol(-1), respectively, for 2-methoxytetrahydropyran). Only because of a consistent cancellation of errors do these popular approaches sometimes provide reasonable estimates of the anomeric effect.     

Benchmark Dyson orbital study of the ionization spectrum and electron momentum distributions of ethanol in conformational equilibrium

An extensive study, throughout the valence region, of the electronic structure, ionization spectrum, and electron momentum distributions of ethanol is presented, on the ground of a model that focuses on a mixture of the gauche and anti conformers in their energy minimum form, using weight coefficients obtained from thermostatistical calculations that account for the influence of hindered rotations. The analysis is based on accurate calculations of valence one-electron and shakeup ionization energies and of the related Dyson orbitals, using one-particle Green's Function (1p-GF) theory in conjunction with the so-called third-order Algebraic Diagrammatic Construction scheme [ADC(3)]. The confrontation against available UPS (HeI) measurements indicates the presence in the spectral bands of significant conformational fingerprints at outer-valence ionization energies ranging from approximately 14 to approximately 18 eV. The shakeup onset is located at approximately 24 eV, and a shoulder at approximately 14.5 eV in the He I spectrum can be specifically ascribed to the minor anti (C(s)) conformer fraction. Thermally and spherically averaged Dyson orbital momentum distributions are computed for seven resolvable bands in model (e, 2e) ionization spectra at an electron impact energy of 1.2 keV. A comparison is made with results obtained from standard (B3LYP) Kohn-Sham orbitals and EMS measurements employing a high-resolution spectrometer of the third generation. The analysis is qualitatively in line with experiment and reveals a tremendously strong influence of the molecular conformation on the outermost electron momentum distributions. Quantitatively significant discrepancies with experiment can nonetheless be tentatively ascribed to strong dynamical disorder in the gas phase molecular structure.     

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences for the development of standard DFT to a method that can correctly describe multi-reference electron systems by treating dynamic and non-dynamic electron correlation on an equal footing, is discussed. In this connection, the seminal work of Colle and Salvetti on wave function-based correlation functionals that do no longer suffer from a SIE is essential. It is described how the Colle–Salvetti correlation functional is an anchor point for the derivation of a functional multi-reference DFT method.     

Calculation of the vibration frequencies of alpha-quartz: the effect of Hamiltonian and basis set

The central-zone vibrational spectrum of alpha-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree-Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm(-1), respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm(-1).