Comparison of semiempirical MO methods applied to large molecules

The heats of formation for 19 molecules have been calculated with PM3 and AM1 semiempirical methods. The values obtained have been compared with experimental heats of formation. With PM3 and AM1 the average differences between calculated and experimental heats of formation are 8.45 and 12.34 kcal mol^?1 respectively. There are significant differences when large molecules are considered: this suggests that the parameterization should be done including larger molecules.     

An unconventional scf method for calculations on large molecules

An unconventional SCF method for calculations on large molecules with more than 100 basis functions is described. Storage problems which arise in conventional SCF schemes when storing more than 10⁷ integrals are avoided by repeated calculation of integrals. The resulting increase in computational times is kept at a reasonable level by (a) improving the initial guess, (b) accelerating convergence, (c) employing a recursive construction of the Fock matrix, and (d) eliminating insignificant integrals from the calculation by a density-weighted cutoff criterion. Sample calculations show that, compared with conventional SCF calculations, computational times increase by 25%–75% depending on the basis set and the shape of the molecule.     

An improved Hellmann-type pseudopotential for atoms and molecules

The concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium. The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree-Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li₂, Na₂, and K₂ show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.     

Note on the generation of Gaussian bases for pseudopotential calculations

We present a technique to generate Cartesian Gaussian bases for electronic configuration and cross-section calculations on molecules. The technique is specially useful for pseudopotential work, when the bases cannot be tabulated because they depend on the specific choice of the pseudopotential. © 1996 John Wiley & Sons, Inc.     

Capability of pseudopotential methods to simulate all-electron calculations with floating spherical gaussian orbitals

A pseudopotential method has been applied to the calculation of local molecular orbitals for the water molecule in its ground state. Calculated values of the bond length and of the bond angle are in good agreement with those obtained from analogous calculations involving all the electrons. Comparison with experimental data is of the same quality in the two types of calculations.     

On the accuracy of one-component pseudopotential spin-orbit calculations

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calculation, include valence spin-orbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spin-orbit configuration interaction (CI) with singles from the reference ground-state configuration gives rise to double counting of these spin-orbit effects. Two new methods that avoid such double counting have been investigated. The first, so-called "explicit" method, calculates explicitly, by means of a four-component spin-orbit CI, the double-counted spin-orbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spin-orbit effects as well as the so-called "pseudovariational collapse," this method is shown to be cumbersome. In the second "implicit" method the spin-orbit pseudopotential is extracted at the spin-orbit polarized and relaxed level by means of a single-excitation spin-orbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the double-counting problem.     

A fragment energy assembler method for Hartree-Fock calculations of large molecules

We present a fragment energy assembler approach for approximate Hartree-Fock (HF) calculations of macromolecules. In this method, a macromolecule is divided into small fragments with appropriate size, and then each fragment is capped by its neighboring fragments to form a subsystem. The total energy of the target system is evaluated as the sum of the fragment energies of all fragments, which are available from conventional HF calculations on all subsystems. By applying the method to a broad range of molecules, we demonstrate that the present approach could yield satisfactory HF energies for all studied systems.     

A localized molecular-orbital assembler approach for Hartree-Fock calculations of large molecules

We describe an alternative fragment-based method, the localized molecular-orbital assembler method, for Hartree-Fock (HF) calculations of macromolecules. In this approach, a large molecule is divided into many small-size fragments, each of which is capped by its local surroundings. Then the conventional HF calculations are preformed on these capped fragments (or subsystems) and the canonical molecular orbitals of these systems are transferred into localized molecular orbitals (LMOs). By assembling the LMOs of these subsystems into a set of LMOs of the target molecule, the total density matrix of the target molecule is constructed and correspondingly the HF energy or other molecular properties can be approximately computed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations with double-zeta and polarized double-zeta basis sets demonstrate that the present approach is able to reproduce the conventional HF energies within a few millihartrees for a broad range of molecules.     

Small gaussian basis sets for AB initio calculations on large molecules

Gaussian basis sets of (5s, 2p) for carbon, nitrogen, and oxygen, and (7s, 4p) for phosphorous and sulfur have been developed for ab initio calculations of biological molecules. Double zeta contracted bases are given for all five atoms. Minimum bases are given for carbon, nitrogen and oxygen, and a method is developed for replicating primitives in order to minimize the energy loss when contracting small bases. The contracted bases are applied to formamide and the results are compared with those obtained from other small basis sets.     

Ab initio calculations on large molecules: The multiplicative integral approximation

In the multiplicative integral approximation (MIA), two-electron integrals are evaluated using an expansion of a product of two Gaussians in terms of auxiliary functions. An estimator of the error introduced by the approximation is incorporated in the self-consistent field (SCF) calculations and the integrals for which the error estimate is larger than a preset value are systematically corrected. In this way the results of a MIA-assisted calculation have the same accuracy as a conventional calculation. The full exploitation of the expansion technique while constructing the Fock-matrix allows important time savings. Results are presented for a number of test cases.     

On a scheme for the calculations of large molecules in the molecular orbital approximation

The possibility of decreasing the number of molecular integrals to be calculated by using the same basis of high symmetry for all molecules is discussed.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Quantum chemical calculations of fluoroethylene molecules by the CNDO and INDO methods

Conclusions A quantum chemical calculation of seven fluoroethylene molecules and two fluorochloroethylene molecules and two fluorochloroethylene molecules by the CNDO and INDO methods has made it possible to explain the experimentally observed change in reactivity and direction of addition reactions at the double bond. The data of a calculation of the relative stability of various isomers also agree with the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2199–2202, October, 1973.     

g-Hartree ab-initio calculations of the total energies of the four-electron isoelectronic series

The atomic total energies of the four-electron isoelectronic series are calculated by theg-Hartree 2nd order perturbation theory and the Dirac-Hartree-Fock-Rayleigh-Schrödinger 2nd order perturbation theory. The Coulomb correlation energy is calculated by these theories. The Breit interaction, vacuum polarization, self-energy and Q.E.D. corrections are calculated by the lowest order approximation. The results show that theg-Hartree approach overestimates the Coulomb correlation energy. However, with an increase of the nuclear charge, it overestimates much less. In the case of the Hartree-Fock 2nd order calculation, it underestimates the Coulomb correlation energy. With an increase of the nuclear charge, it underestimates much more.     

Comparisons between crystallographic results and theoretical calculations on phenol molecules

The internal angles in the benzene ring and the external C-C-O angles have been determined by the MNDO method for phenol, the three cresols and 4-nitrophenol. Despite the fact they are supposed to be related to the isolated molecules, the results are in very good agreement with crystal structure determinations.     

A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds

Summary Improved energy-adjusted quasirelativistic pseudopotentials for lanthanoid atoms with fixed valency are presented and tested in molecular calculations for CeO, CeF, EuO, GdO, YbO, and YbF. The pseudopotential calculations treat the lanthanoid 4f shell as part of the core and yield accurate estimates for average bond lengths, vibrational frequencies and dissociation energies of all states belonging to a superconfiguration. Information for each individual state of the considered superconfiguration may be obtained from subsequent ligand field model calculations. The results of this combined pseudo-potential and ligand field approach (PPLFT) are compared to more accurate calculations with ab initio pseudopotentials that include the lanthanoid 4f orbitals explicitly in the valence shell and to available experimental data.