Computational analysis of thermal-motion effects on the topological properties of the electron density

2015 ◽  
Vol 71 (2) ◽  
pp. 225-234 ◽  
Author(s):  
J. Robert Michael ◽  
Tibor Koritsanszky
Keyword(s):  
Electron Density ◽  
Probability Distribution Function ◽  
Computational Analysis ◽  
Normal Modes ◽  
Bond Critical Point ◽  
Topological Properties ◽  
Hydrogen Atoms ◽  
Bond Stretching ◽  
Negative Skewness ◽  
Thermal Vibrations

The distributions of bond topological properties (BTPs) of the electron density upon thermal vibrations of the nuclei are computationally examined to estimate different statistical figures, especially uncertainties, of these properties. The statistical analysis is based on a large ensemble of BTPs of the electron densities for thermally perturbed nuclear geometries of the formamide molecule. Each bond critical point (BCP) is found to follow a normal distribution whose covariance correlates with the displacement amplitudes of the nuclei involved in the bond. The BTPs are found to be markedly affected not only by normal modes of the significant bond-stretching component but also by modes that involve mainly hydrogen-atom displacements. Their probability distribution function can be decently described by Gumbel-type functions of positive (negative) skewness for the bonds formed by non-hydrogen (hydrogen) atoms.

The Effect of Thermal Vibrations on the Intensities of the Diffracted Beams

1997 ◽  
Author(s):  
Philip Coppens
Keyword(s):  
Electron Density ◽  
Normal Modes ◽  
Unit Cell ◽  
Thermal Motion ◽  
X Ray ◽  
X Ray Scattering ◽  
Point Motion ◽  
Unit Cells ◽  
Thermal Vibrations ◽  
Ray Scattering

The atoms in a crystal are vibrating with amplitudes determined by the force constants of the crystal’s normal modes. This motion can never be frozen out because of the persistence of zero-point motion, and it has important consequences for the scattering intensities. Since X-ray scattering (and, to a lesser extent, neutron scattering) is a very fast process, taking place on a time scale of 10−18 s, the photon-matter interaction time is much shorter than the period of a lattice vibration, which is of the order Thus, the recorded X-ray scattering pattern is the sum over the scattering of a large number of 1/v, or ≈10−13s. instantaneous states of the crystal. To an extremely good approximation, the scattering averaged over the instantaneous distributions is equivalent to the scattering of the time-averaged distribution of the scattering matter (Stewart and Feil 1980). The structure factor expression for coherent elastic Bragg scattering of X-rays may therefore be written in terms 〈ρ(r)〉, of the thermally averaged electron density: . . . F(H)=∫unit cell〈ρ(r)〉 exp (2πi H ·r) dr (2.1) . . . The smearing of the electron density due to thermal vibrations reduces the intensity of the diffracted beams, except in the forward |S| = 0 direction, for which all electrons scatter in phase, independent of their distribution. The reduction of the intensity of the Bragg peaks can be understood in terms of the diffraction pattern of a more diffuse electron distribution being more compact, due to the inverse relation between crystal and scattering space, discussed in chapter 1. The reduction in intensity due to thermal motion is accompanied by an increase in the incoherent elastic scattering, ensuring conservation of energy. In this respect, thermal motion is much like disorder, with the Bragg intensities representing the average distribution, and the deviations from the average appearing as a continuous, though not uniform, background, generally referred to as thermal diffuse scattering or TDS. A crystal with n atoms per unit cell has 3nN degrees of freedom, N being the number of unit cells in the crystal.

scholarly journals ELECTRON DENSITY STUDIES ON THE REGIOSELECTIVITY OF DEPROTONATION REACTIONS

2014 ◽  
Vol 70 (a1) ◽  
pp. C287-C287
Author(s):  
Juan Van der Maelen ◽  
Javier Cabeza
Keyword(s):  
Electron Density ◽  
Theoretical Calculations ◽  
Density Ratio ◽  
Atomic Charge ◽  
Heterocyclic Ring ◽  
Bond Critical Point ◽  
Electron Densities ◽  
Total Energy Density ◽  
Topological Parameters ◽  
Alkyl Groups

The C-alkyl groups of cationic triruthenium cluster complexes of the type [Ru3(µ-H)(µ-κ2N1,C2-EtnMemPyHk)(CO)10]+ (EtnMemPyHk represents a generic C-alkyl-N-methyl-pyrazium species) have been deprotonated to give kinetic products that contain unprecedented C-alkylidene derivatives and maintain the original edge-bridged decacarbonyl structure. When the starting complexes contain various C-alkyl groups, the selectivity of these deprotonation reactions is related to the atomic charges of the alkyl H atoms, as suggested by DFT/natural-bond orbital (NBO) calculations. Three additional electronic properties of the C-alkyl C-H bonds have also been found to correlate with the experimental regioselectivity since, in all cases, the deprotonated C-H bond has the smallest electron density at the bond critical point (bcp), the greatest Laplacian of the electron density at the bcp, and the greatest total energy density ratio at the bcp (computed by using the quantum theory of atoms in molecules, QTAIM). The kinetic decacarbonyl products evolve, under appropriate reaction conditions that depend upon the position of the C-alkylidene group in the heterocyclic ring, towards face-capped nonacarbonyl derivatives (thermodynamic products). Theoretical calculations support the proposal that the selectivity of these deprotonation reactions is primarily determined by the atomic charge of the alkyl H atoms: the higher the charge the easier the deprotonation when the starting complexes contain various C-alkyl groups. On the other hand, although QTAIM results have been obtained here only from theoretical electron densities for the above clusters, comparisons with local and integral topological parameters derived from both experimental and theoretical electron densities for the related triruthenium complex [Ru3(μ-H)2(μ3-MeImCH)(CO)9] (Me2Im = 1,3-dimethylimidazol-2-ylidene) may easily be made.

Theoretical investigation of the stability, reactivity, and the interaction of methyl-substituted peridinium-based ionic liquids

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Emmanuel A. Bisong ◽  
Hitler Louis ◽  
Tomsmith O. Unimuke ◽  
Victoria M. Bassey ◽  
John A. Agwupuye ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Electron Density ◽  
Density Functional ◽  
Natural Bond Orbital ◽  
Stabilization Energy ◽  
Basis Set ◽  
Bond Critical Point ◽  
Electronic Interaction ◽  
Donor And Acceptor ◽  
The Stability

Abstract This research work focuses on the reactivity, stability, and electronic interaction of pyridinium hydrogen nitrate (PHN)-based ionic liquids and the influence of methyl substituent on this class of ionic liquids: Ortho- (O-MPHN), meta- (M-MPHN), and para- (P-MPHN) substitution. Natural bond orbital (NBO) calculations were performed at the density functional theory (DFT) with Becke’s Lee Yang and Parr functional (B3LYP) methods and DFT/B3LYP/6-311++G(d,p) as basis set using GAUSSIAN 09W and GAUSSVIEW 6.0 software and the most important interaction between donor (Filled Lewis-type NBO’s) and the acceptor (vacant non-Lewis NBOs) were observed. From our natural bond orbital (NBO) result, it could be deduced that the higher the stabilization energy value, the greater the interaction between the donor and acceptor NBOs. The stability of the studied compounds is said to follow the order from O-MPHN > PHN > P-MPHN > M-MPHN based on the hyperconjugative interaction (stabilization energy) of the most significant interaction. The result of the highest occupied molecular orbital (HOMO), shows that PHN has the highest HOMO while the substituted derivatives have similar HOMO values between −7.70 and −7.98 eV thus PHN complex is the best electron donor while the substituted derivatives act as electron acceptors due to the presence of methyl group substituent which is observed to be electron deficient as a result of its withdrawal effect from the aromatic ring. Furthermore, the electron density, real space functions such as energy density and Laplacian of electron density at bond critical point (BCP) of the hydrogen bond interaction of the studied compounds were analyzed using Multifunctional Wavefunction analyzer software version 3.7 and it was observed that the hydrogen at position 6 and oxygen at position 11 (H6–O11) of M-methyl pyridinium nitrate with bond distance of 4.59 (Å) gave binding energy with the strongest electrostatic interaction between the cation and anion of the compounds under investigation. We also observed from our results that, substitution at the ortho position enhances the stability and strengthen the extent of charge transfer. This therefore implies that substitution at ortho position is more favorable for inter- and intramolecular interactions resulting to stabilization of the studied molecules.

scholarly journals Relationships between Interaction Energy and Electron Density Properties for Homo Halogen Bonds of the [(A)nY–X···X–Z(B)m] Type (X = Cl, Br, I)

Molecules ◽  
2019 ◽  
Vol 24 (15) ◽  
pp. 2733 ◽  
Author(s):  
Maxim L. Kuznetsov
Keyword(s):  
Kinetic Energy ◽  
Interaction Energy ◽  
Electron Density ◽  
Bond Critical Point ◽  
Kinetic Energy Density ◽  
Large Set ◽  
Halogen Bonds ◽  
Absolute Deviation ◽  
The Individual ◽  
Best Estimator

Relationships between interaction energy (Eint) and electron density properties at the X···X bond critical point or the d(X···X) distance were established for the large set of structures [(A)nY–X···X–Z(B)m] bearing the halogen bonds Cl···Cl, Br···Br, and I···I (640 structures in total). The best estimator of Eint is the kinetic energy density (Gb), which reasonably approximates the whole set of the structures as −Eint = 0.128Gb2 − 0.82Gb + 1.66 (R2 = 0.91, mean absolute deviation 0.39 kcal/mol) and demonstrates low dispersion. The potential and kinetic energy densities, electron density, and the d(X···X) distance behave similarly as estimators of Eint for the individual series Cl···Cl, Br···Br, and I···I. A number of the Eint(property) correlations are recommended for the practical application in the express estimates of the strength of the homo-halogen bonds.

Experimental electron density study of ethylene oxide at 100 K

2008 ◽  
Vol 64 (3) ◽  
pp. 397-400 ◽  
Author(s):  
Simon Grabowsky ◽  
Manuela Weber ◽  
Jürgen Buschmann ◽  
Peter Luger
Keyword(s):  
Ethylene Oxide ◽  
Electron Density ◽  
Density Functional ◽  
High Strain ◽  
Membered Ring ◽  
Topological Properties ◽  
X Ray ◽  
Multipole Refinement ◽  
Experimental Electron Density ◽  
Density Study

The experimental electron density of ethylene oxide was derived from a multipole refinement of 100 K X-ray data and complemented by density-functional calculations at experimental and optimized geometry. Atomic and bond-topological properties were derived using the atoms-in-molecules (AIM) formalism. The high strain in the three-membered ring molecule is mainly expressed by the high ellipticities of the three bonds in this ring, while the bond paths are only slightly bent for the C—C bond, but are virtually straight for the C—O bond.

Topological analysis of electron density and the electrostatic properties of isoniazid: an experimental and theoretical study

2014 ◽  
Vol 70 (2) ◽  
pp. 331-341 ◽  
Author(s):  
Gnanasekaran Rajalakshmi ◽  
Venkatesha R. Hathwar ◽  
Poomani Kumaradhas
Keyword(s):  
Hydrogen Bonding ◽  
Charge Density ◽  
Electron Density ◽  
Topological Analysis ◽  
Bond Critical Point ◽  
Potential Region ◽  
Electrostatic Properties ◽  
Structural And Electronic Properties ◽  
Density Analysis ◽  
Mycobacterial Cell Wall

Isoniazid (isonicotinohydrazide) is an important first-line antitubercular drug that targets the InhA enzyme which synthesizes the critical component of the mycobacterial cell wall. An experimental charge-density analysis of isoniazid has been performed to understand its structural and electronic properties in the solid state. A high-resolution single-crystal X-ray intensity data has been collected at 90 K. An aspherical multipole refinement was carried out to explore the topological and electrostatic properties of the isoniazid molecule. The experimental results were compared with the theoretical charge-density calculations performed usingCRYSTAL09with the B3LYP/6-31G** method. A topological analysis of the electron density reveals that the Laplacian of electron density of the N—N bond is significantly less negative, which indicates that the charges at the b.c.p. (bond-critical point) of the bond are least accumulated, and so the bond is considered to be weak. As expected, a strong negative electrostatic potential region is present in the vicinity of the O1, N1 and N3 atoms, which are the reactive locations of the molecule. The C—H...N, C—H...O and N—H...N types of intermolecular hydrogen-bonding interactions stabilize the crystal structure. The topological analysis of the electron density on hydrogen bonding shows the strength of intermolecular interactions.

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