413 research outputs found
Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom
Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of the
one-body potential V(r) in terms of low-order derivatives of the idempotent
Dirac density matrix built from a single Slater determinant of Kohn-Sham
orbitals. Here, this is first combined with the study of Dawson and March (J.
Chem. Phys. 81, 5850 (1984)) to express the single-particle kinetic energy
density of the Be atom ground-state in terms of both the electron density n(r)
and potential V(r). While this is the more compact formulation, we then, by
removing V(r), demonstrate that the ratio t(r)/n(r) depends, though
non-locally, only on the single variable n'(r)/n(r), no high-order gradients
entering for the spherical Be atom.Comment: Submitted to Journal of Mathematical Chemistr
Investigation of the chirality of enantiomers through information theory
In this work [1] we probed the Kullback-Leibler information entropy as a chirality
measure, as an extension of previous studies on molecular quantum similarity evaluated
for different enantiomers (enantiomers possessing two asymmetric centra in [2], with a
single asymmetric carbon atom in [3] and with a chiral axis in [4]). The entropy was
calculated using the shape functions of the R and S enantiomers considering one as
reference for the other, resulting in an information theory based expression useful for
quantifying chirality. It was evaluated for 5 chiral halomethanes possessing one
asymmetric carbon atom with H, F, Cl, Br and I as substituents. To demonstrate the
general applicability, a study of two halogen-substituted ethanes possessing two
asymmetric carbon atoms has been included as well. Avnir’s Continuous Chirality
Measure (CCM) [5] has been computed and confronted with the information deficiency.
By these means we quantified the dissimilarity of enantiomers and illustrated Mezey’s
Holographic Electron Density Theorem in chiral systems [6]. A comparison is made
with the optical rotation and with the Carbó similarity index.
As an alternative chirality index, we recently also calculated the information
deficiency in a way which is consistent with experiments as VCD spectroscopy and
optical rotation measurements. The entropy calculates the difference in information
between the shape function of one enantiomer and a normalized shape function of the
racemate. Comparing the latter index with the optical rotation reveals a similar trend.
[1] S. Janssens, A. Borgoo, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 112, 10560
(2008).
[2] S. Janssens, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 111, 3143 (2007).
[3] G. Boon, C. Van Alsenoy, F. De Proft, P. Bultinck, P. Geerlings, J. Phys. Chem. A,
110, 5114 (2006).
[4] S. Janssens, G. Boon, P. Geerlings, J. Phys. Chem. A, 110, 9267 (2006).
[5] H. Zabrodsky, D. Avnir, J. Am. Chem. Soc., 117, 462 (1995).
[6] P.G. Mezey, Mol. Phys., 96, 169 (1999)
Alternative Kullback-Leibler information entropy for enantiomers
In our series of studies on quantifying chirality, a new chirality measure is proposed in this work based on the Kullback-Leibler information entropy. The index computes the extra information that the shape function of one enantiomer carries over a normalized shape function of the racemate, while in our previous studies the shape functions of the R and S enantiomers were used considering one as reference for the other. Besides being mathematically more elegant (symmetric, positive definite, zero in the case of a nonchiral system), this new index bears a more direct relation with chirality oriented experimental measurements such as circular dichroism (CD) and optical rotation measurements, where the racemate is frequently used as a reference, The five chiral halomethanes holding one asymmetric carbon atom and H, F, Cl, Br, and I as substituents have been analyzed. A comparison with our calculated optical rotation and with Avnir's Continuous Chirality Measure (CCM) is computed. The results show that with this index the emphasis lies on the differences between the noncoinciding substituents
An Overview of Self-Consistent Field Calculations Within Finite Basis Sets
A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree–Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn–Sham–Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn–Sham–Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed
Accurate interaction energies at DFT level by means of an efficient dispersion correction
This paper presents an approach for obtaining accurate interaction energies
at the DFT level for systems where dispersion interactions are important. This
approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)]
method for the evaluation of dispersion energy corrections and a Hirshfeld
method for partitioning of molecular polarizability tensors into atomic
contributions. Due to the availability of atomic polarizability tensors, the
method is extended to incorporate anisotropic contributions, which prove to be
important for complexes of lower symmetry. The method is validated for a set of
eighteen complexes, for which interaction energies were obtained with the
B3LYP, PBE and TPSS functionals combined with the aug-cc-pVTZ basis set and
compared with the values obtained at CCSD(T) level extrapolated to a complete
basis set limit. It is shown that very good quality interaction energies can be
obtained by the proposed method for each of the examined functionals, the
overall performance of the TPSS functional being the best, which with a slope
of 1.00 in the linear regression equation and a constant term of only 0.1
kcal/mol allows to obtain accurate interaction energies without any need of a
damping function for complexes close to their exact equilibrium geometry
Local softness, softness dipole and polarizabilities of functional groups: application to the side chains of the twenty amino acids
The values of molecular polarizabilities and softnesses of the twenty amino
acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to
partition the molecular electronic properties, we demonstrate that the values
of the softness of the side chain of the twenty amino acid are clustered in
groups reflecting their biochemical classification, namely: aliphatic, basic,
acidic, sulfur containing, and aromatic amino acids . The present findings are
in agreement with previous results using different approximations and
partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126,145105
(2007)]. In addition, we show that the polarizability of the side chain of an
amino acid depends mainly on its number of electrons (reflecting its size) and
consequently cannot be used to cluster the amino acids in different biochemical
groups, in contrast to the local softness. Our results also demonstrate that
the global softness is not simply proportional to the global polarizability in
disagreement with the intuition that "a softer moiety is also more
polarizable". Amino acids with the same softness may have a polarizability
differing by a factor as large as 1.7. This discrepancy can be understood from
first principles as we show that the molecular polarizability depends on a
"softness dipole vector" and not simply on the global softness
Optimal Selection of Partial Charge Calculation Method for Rapid Estimation of Enthalpies of Formation from Hartree−Fock Total Energy
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