Laplacian Of Electron Density Research Articles

Lone Pairs: An Electrostatic Viewpoint

A clear-cut definition of lone pairs has been offered in terms of characteristics of minima in molecular electrostatic potential (MESP). The largest eigenvalue and corresponding eigenvector of the Hessian at the minima are shown to distinguish lone pair regions from the other types of electron localization (such as π bonds). A comparative study of lone pairs as depicted by various other scalar fields such as the Laplacian of electron density and electron localization function is made. Further, an attempt has been made to generalize the definition of lone pairs to the case of cations.

A comparative computational study on molecular structure, NBO analysis, multiple interactions, chemical reactivity and first hyperpolarisability of imatinib mesylate polymorphs using DFT and QTAIM approach

Imatinib, a phenylaminopyrimidine compound is a therapeutic drug for treatment of chronic myelogeneous leukaemia and gastrointestinal stromal tumours. It is well known that imatinib mesylate (ImM) exists in two polymorphic forms α and β. In this work, a computational study on molecular properties of ImM polymorphs is presented using density functional theory, B3LYP functional and 6-311G(d,p) as basis set. Natural bond orbital analysis is carried out to investigate the various conjugative and hyperconjugative interactions within the molecule and their second-order stabilisation energy (E(2)). The local nucleophilic reactivity descriptors such as Fukui functions (), local softness () and electrophilicity indices () analyses are carried out to determine the reactive sites within the molecule. To determine strength and nature of intra- and intermolecular interactions, topological parameters as electron density (ED) (ρBCP), Laplacian of ED (▽2ρBCP) and total electron energy density (HBCP) at bond critical points have been analysed by ‘quantum theory of atoms in molecules’ in detail. The computed first hyperpolarisability (β0) for both forms of ImM molecule (10.927 and 10.354 × 10− 30 esu) suggests that the investigated molecule is an attractive object in future for non-linear optical properties. Molecular electrostatic potential surface of ImM has been mapped to predict the inhibitory activity and binding affinity with a panel of protein tyrosine kinases.

Pnicogen Bonds: A Theoretical Study Based on the Laplacian of Electron Density

Although, most of the authors classify the pnicogen bonds as σ-hole bonding, there are some evidence that show they do not require any positive electrostatic potential around interacting molecules. In this work, the Laplacian of electron density is used to study pnicogen bonds in different dimer and trimer complexes. It is shown that the noncovalent P···P, P···N, and N···N bonds can be categorized as lump-hole interactions; a region of charge depletion and excess kinetics energy (hole) in the valence shell charge concentration (VSCC) of pnicogen atom combines with a region of charge concentration and excess potential energy (lump) in the VSCC of another molecule and form a pnicogen bond. In fact, since the full quantum potential (according to the local statement of virial theorem) has been used in the definition of the Laplacian, the lump-hole concept is more useful than the σ-hole in which the electrostatic part of potential is only considered. It is shown that the existence of hole in the VSCC of pnicogen atom is responsible for formation and (in the absence of other interactions) geometry of pnicogen bonded complexes. Because there is (at least) one hole in their VSCC, the pnicogen atoms in PH3, PH2F, H2C═PH, H2C═PF, and NH2F can engage in direct pnicogen-pnicogen interactions. However, the VSCC of nitrogen atom in the NH3 is devoid of hole and hence cannot act as an electron acceptor in pnicogen-bonded complexes.

Theoretical investigations on the hydrogen bonding of nitrile isomers with H2O, HF, NH3 and H2S

The hydrogen bonds formed by the interaction of nitriles with water, hydrogen fluoride, ammonia and hydrogen sulphide have been studied using B3LYP and second-order Møller–Plesset perturbation (MP2) methods and 6-311+ + G(d,p) basis set. The energies and structures of 80 hydrogen-bonded complexes between nitriles and small molecules were examined systematically using B3LYP and MP2 procedure. Categorisation of the hydrogen bonds involved in the various complexes led to an ordering of hydrogen bond donor and acceptor abilities for some functional groups. The interaction energies have been corrected for the basis set superposition error using Boy's counterpoise correction method. The Morokuma energy decomposition analysis reveals that the strong interactions are due to the attractive contributions from the electrostatic (ES), polarisation (PL) and charge transfer (CT) components. The topological parameters, electron density and Laplacian of electron density show excellent correlation with the hydrogen bond length. Natural bond orbital (NBO) analysis has also been performed to study the CT from proton acceptor to the antibonding orbital of the H–Y bond in the proton donor part of complexes. The frequency analysis of C–H…Y bond in the complexes indicates the blue-shifting nature largely in case of sp2 hybridised carbon atom.

Theoretical study of intramolecular hydrogen bonding in the halo derivatives of 1-amino-3-imino-prop-1-ene

Intramolecular hydrogen bonding (IHB) of 1-amino-3-imino-prop-1-ene (AIP), as the simplest resonance-assisted hydrogen bond system in symmetric N–H···N class, and its halo derivatives (F, Cl, and Br) have been studied at the DFT-B3LYP/6-311+ +G ∗ ∗ level of theory. For better understanding of the nature of substituent effects, nitro and methoxy derivatives of AIP were also added to our consideration. Good linear correlations between IHB energies based on Espinosa’s equation and − G(r)/V(r) values, total electronic density, Laplacian of total electronic density in critical points, π-electron delocalization parameter (Q), hyper conjugative interaction energy of lp(N) $\to \upsigma ^{\ast}$ (N–H), ( $F_{i,j}/S_{i,j})^{2}$ parameter, natural charges of bridged hydrogen, frequency shift of the N–H stretching vibration, and chemical shift of bridged hydrogen were obtained.

Study of spectroscopic, reactivity and NLO properties of synthesized dipyrromethane containing cyanovinylhydrazide using experimental and theoretical approaches

In the present work, molecular structure and detailed spectroscopic analysis of a newly synthesized dipyrromethane molecule (3) have been carried out using both experimental and theoretical spectroscopic techniques. Thermodynamic parameters (H, G, S) of all the reactants and products are used to determine the spontaneity of the chemical reaction. Time dependent density functional theory (TD-DFT) is used to calculate wavelength absorption maxima (λmax) of various electronic transitions and their nature within molecule. Natural bond orbitals (NBOs) analysis is carried out to investigate the intramolecular hydrogen-bonding, conjugative and hyperconjugative interactions and their second order stabilization energy (E(2)). The effect of hydrogen-bonding is noticeable in both 1H NMR and FT-IR spectrum as down field chemical shift, vibrational red shift, respectively. The vibrational analysis designates existence of classical hydrogen-bonding (NH⋯N) between pyrrole NH as proton donor and N atom of cyanide as proton acceptor. To investigate the strength and nature of hydrogen-bonding, topological parameters as electron density (ρBCP), Laplacian of electron density (∇ρBCP2), total electron energy density (HBCP) and estimated hydrogen bond energy (EHB) at bond critical points (BCP) are analyzed by ‘Quantum Theory of Atoms in Molecules’ (QTAIM) in detail. The local reactivity descriptors as Fukui functions (fk+,fk-), local softnesses (sk+,sk-) and electrophilicity indices (ωk+,ωk-) analyses are performed to investigate the reactive sites within molecule. The first hyperpolarizability (β0) of (3) has been computed to evaluate the non-linear optical (NLO) response of the investigated molecule.

Hydrogen-bond interactions in hydrated 6-selenoguanine tautomers: a theoretical study

A comprehensive theoretical investigation has been performed to study the six most stable complexes of isolated, mono, and hexahydrated 6-selenoguanine tautomers. The ground state geometries are studied at the density-functional theory and Moller–Plesset Perturbation theory implementing the 6-311++G (2d, 2p) basis set. The intermolecular distances between the water molecule and the acceptor atom of 6-selenoguanine is about 0.6 A longer for hydrogen bonds involving selenium atom. The relative Gibbs free energy of the 6-selenoguanine tautomers favors the selenone tautomer. The majority of the stable monohydrated complexes are the one in which the oxygen atom of water accepts the acidic N7-H proton while donating a proton to the carbonyl selenium atom of 6-selenoguanine; the interaction toward N7-H being stronger than that with the selenium site. The amino group planarity has been found to be increased in the hydrated complexes. The examination of molecular orbital reveals a moderate band gap between the donor and acceptor atoms of isolated and hydrated complexes. An excellent linear correlation is found to exist between electron density and laplacian of electron density with hydrogen-bond length through atoms in molecule analysis. The natural bond orbital analysis shows a maximum charge transfer of 0.060e for selenium acceptors and around 0.025e for selenium donors.

Hydrogen-bonded complexes of serotonin with methanol and ethanol: a DFT study

Density functional theoretical studies on hydrogen-bonded complexes of serotonin with methanol/ethanol have been carried out in a systematic way. The conformational analysis led to ten stable conformers that can be either gauche or anti depending on the dihedral angle values taken by ethylamine side chain and the 5-hydroxyl group. Serotonin-molecules strongly bind with ethanol than methanol. Ethylamine side chain is the most reactive site in both methanol/ethanol complexes and it is responsible for the stability order. The topological parameters, electron density, and Laplacian of electron density show excellent correlation with the hydrogen bond length. Natural bond orbital analysis confirms C–H···O hydrogen bond formed between the serotonin–alcohol complexes to be red shift in nature except for Gph(out)anti complex both with methanol and ethanol to be blue shifted. The energy decomposition analysis reveals that strong interactions between serotonin and ethanol/methanol are due to the attractive contributions from the electrostatic component.

Bond Order Analysis Based on the Laplacian of Electron Density in Fuzzy Overlap Space

Bond order is an important concept for understanding the nature of a chemical bond. In this work, we propose a novel definition of bond order, called the Laplacian bond order (LBO), which is defined as a scaled integral of negative parts of the Laplacian of electron density in fuzzy overlap space. Many remarkable features of LBO are exemplified by numerous structurally diverse molecules. It is shown that LBO has a direct correlation with the bond polarity, the bond dissociation energy, and the bond vibrational frequency. The dissociation behavior of LBO of the N-N bond in N2 has been studied. Effects of the basis sets, theoretic methods, and geometrical conformations on LBO have also been investigated. Through comparisons, we discussed in details similarities and discrepancies among LBO, Mayer bond order, natural localized molecular orbital bond order, fuzzy overlap population, and electron density at bond critical points.

Electron density distribution in the ethylene complexes with Pd-containing bimetallic clusters

The complexes of PdM bimetallic clusters (M = Cr, Mn, Fe, Co, Ni, Cu, Zn, Ag, Cd) with ethylene are calculated at the density functional theory level with the quantum theory of atoms in molecule approach for the electron density distribution analysis. Formation of the metal–carbon coordination bonds in the studied complexes is determined by the (3, − 1) critical point appearance between the corresponding atoms. The energy of these interactions is estimated as a measure of the PdM clusters adsorptivity. All the C–C, C–Pd and C–M bonds are classified by the characters of the electron density Laplacian at the bond critical point and by the electron energy density. It is shown that the ethylene molecule is strongly activated by adsorption on the PdM clusters. The estimated binding energy between PdM and C2H4 is in the range of 58.3–97.8 kcal/mol going from the PdCd(C2H4) to the PdNi(C2H4) complexes, respectively.

Topological analysis of tetraphosphorus oxides (P4O6+n (n = 0–4))

Quantum chemical calculations were used to analyze the chemical bonding and the reactivity of phosphorus oxides (P4O6+n (n = 0-4)). The chemical bonding was studied using topological analysis such as atoms in molecules (AIM), electron localization function (ELF), and the reactivity using the Fukui function. A classification of the P-O bonds formed in all structures was done according to the coordination number in each P and O atoms. It was found that there are five P-O bond types and these are distributed among the five phosphorus oxides structures. Results showed that there is good agreement among the evaluated properties (length, bond order, density at the critical point, and disynaptic population) and each P-O bond type. It was found that regardless of the structure in which a P-O bond type is present the topological and geometric properties do not have a significant variation. The topological parameters electron density and Laplacian of electron density show excellent linear correlation with the average length of P-O bond in each bond type for each structure. From the Fukui function analysis it was possible to predict that from P4O6 until P4O8 the most reactive regions are basins over the P.

Synthesis, molecular structure, and spectral analyses of ethyl-4-[(2,4-dinitrophenyl)-hydrazonomethyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate

Ethyl-4-[(2,4-dinitrophenyl)-hydrazonomethyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate (3) has been newly synthesized by the condensation of ethyl-4-formyl-3,5-dimethyl-1H-pyrrole-2-carboxylate and 2,4-dinitrophenylhydrazine, characterized by FT-IR, 1H NMR, UV–Vis, DART Mass and elemental analysis. The formation of compound (3) and its properties have been evaluated by quantum chemical calculations. The calculated thermodynamic parameters show that the formation reaction of (3) is exothermic and spontaneous at room temperature. The vibrational analysis indicates that (3) forms dimer in the solid state by heteronuclear double hydrogen bonding (N–H···O). Topological parameters electron density (ρ BCP), Laplacian of electron density (∇2 ρ BCP), and total electron energy density (H BCP) at bond critical points (BCP) have been analyzed using “atoms in molecules” (AIM) theory. The interaction energies of dimer formation using DFT and AIM calculations are found to be −14.6509 and −15.5308 kcal/mol, respectively. AIM ellipticity analysis confirms the presence of resonance-assisted hydrogen bonding in dimer. The global electrophilicity index (ω = 5.91 eV) shows that title molecule is a strong electrophile. The local reactivity descriptors Fukui functions (f k + , f k − ), softness (s k + , s k − ), and electrophilicity indices (ω k + , ω k − ) analyses are performed to determine the reactive sites within molecule.

Exploring the effect of metal electrodes and the transport properties of 4,4′-Di-prop-1-ynyl-biphenyl molecular nanowire using quantum chemical calculation and charge density study

A theoretical charge density analysis has been carried out on the organic molecular nanowire 4,4′-Di-prop-1-ynyl-biphenyl (DPBP) using density functional theory (DFT) with the LANL2DZ basis set coupled with the Bader’s theory of atoms in molecules to understand the effect of Au and Pt metal atoms and the external electric field in the molecule. Introduction of Au and Pt atoms in the molecule significantly altered the geometry and the charge density distribution of the molecule. The bond topological analysis of the molecule reveals that, the AuS and PtS bonds exhibit positive Laplacian of electron density [∇2ρbcp(r)] indicates the existence of closed-shell interaction between the metal and the thiol atoms i.e. the non-covalent interaction. The applied electric field changes the conformation as well as the electronic energy levels of molecule rigorously; presumably, this effect may enhance the conductivity of the molecule. Further, the field reduces the HOMO–LUMO gap of Au and thiol substituted DPBP molecule appreciably from −1.8 to −0.7eV; this variation well indicates that, as the field increases, the HOMO and LUMO levels are approach each other. Whereas, in the Pt attached molecule, there is no such kind of features were found for the applied field. The current–voltage characteristics of DPBP molecule has been calculated theoretically using Landaure formalism. The conductivity of Pt substituted DPBP molecule is notably higher than Au substituted molecule.

The explicit interactions of five-membered saturated heterocyclics containing one and two heteroatoms with single water molecule

In this article, the hydrogen bonding interaction between saturated five-membered heterocyclic molecules and water has been investigated. Molecular orbital and density functional theory methods have been used to evaluate the stabilization energies associated with the adduct formation between heterocyclic molecules and water. The hydrogen bond acceptor ability of O, S, Se, and N as members of five-membered ring has been analyzed. The effect of the presence of second heteroatom N in the ring on the hydrogen bond interaction has also been evaluated. Atoms in molecules theory calculations were carried out to characterize the hydrogen bond through the changes in electron density and Laplacian of electron density. A natural energy decomposition analysis and natural bond orbital analysis is also performed to understand the nature of hydrogen bonding interaction in monohydrated five-membered heterocyclic adducts.

Conformational aspects of glutathione tripeptide: electron density topological & natural bond orbital analyses

Glutathione tripeptide (γ-glutamyl-cysteinyl-glycine) is a flexible molecule and its conformational energy landscape is strongly influenced by forming intramolecular hydrogen bond, its charge and the environment. This study employs DFT-B3LYP method with the 6-31+G (d,p) basis set to carry out conformational analysis of neutral, zwitterionic, cationic, and anionic forms of glutathione. In analyzing the structural characteristics of these structures, intramolecular hydrogen bonds were identified and characterized in details by topological parameters such as electron density ρ(r) and Laplacian of electron density \( \nabla^{2} \)ρ(r) from Bader’s atom in molecules theory. Charge transfer energies based on natural bond orbital analysis are also considered to interpret these intramolecular hydrogen bonds. Our results show that these hydrogen bonds are partially electrostatic and partially covalent in nature, in which the covalent contribution increases as the stabilization energy of hydrogen bond increases. Furthermore, the back bone and side chain (Ramachandran map) orientations of various ionic forms of glutathione have been studied and conformation of each constitution of glutathione tripeptide (i.e., Glu, Cys, and Gly moieties) was determined. In most species side chain conformation were found to be hindered gauche–gauche orientation by intramolecular hydrogen bonds.

A computational study of novel MF3H2 and MF3H2⋯Y clusters (M = Li; Y = OH2, OH(CH3), O(CH3)2, NCH and NH3) or (M = Na, K; Y = NCH)

Energetically stable clusters MF3H2 (M=Li, Na, K) were predicted at the MP2/6-311++G(d,p) level of theory, with the stability increasing with the size of the metal atom M. These species are dominated by strong electrostatic interactions resulting from a combination of H-bonding and M–F bonding. These clusters are further stabilized by complexation to bases like OH2, OH(CH3), O(CH3)2, NCH and NH3. The atomic charge distributions, electron density and negative Laplacian of the electron density were found to be useful parameters in rationalizing the structural, spectroscopic and bonding characteristics of these novel species.

Molecular structure, spectral studies, intra and intermolecular interactions analyses in a novel ethyl 4-[3-(2-chloro-phenyl)-acryloyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate and its dimer: A combined DFT and AIM approach

A newly synthesized chalcone, Ethyl 4-[3-(2-chloro-phenyl)-acryloyl]-3,5-dimethyl-1H-pyrrole-2-carboxylate (ECPADMPC) has been characterized by 1H NMR, 13C NMR, UV–Vis, FT-IR, Mass spectroscopy and elemental analysis. Quantum chemical calculations have been performed by DFT level of theory using B3LYP functional and 6-31G(d,p) as basis set. The time dependent density functional theory (TD-DFT) is used to find the various electronic transitions within molecule. A combined theoretical and experimental wavenumber analysis confirms the existence of dimer. Topological parameters-electron density (ρBCP), Laplacian of electron density (▿2ρBCP), energetic parameters-kinetic electron energy density (GBCP), potential electron density (VBCP) and the total electron energy density (HBCP) at the bond critical points (BCP) have been analyzed by ‘Atoms in molecules’ AIM theory in detail. The intermolecular hydrogen bond energy of dimer is calculated as −12.3kcal/mol using AIM calculations. AIM ellipticity analysis is carried out to confirm the presence of resonance assisted intermolecular hydrogen bonds in stabilization of dimer. The analysis clearly depicts the presence of different kind of interactions in dimer. This dimer may work as model system to understand the H-bonding interaction in biomolecules. The local reactivity descriptor analysis is performed to find the reactive sites within molecule.

Molecular structure, heteronuclear resonance assisted hydrogen bond analysis, chemical reactivity and first hyperpolarizability of a novel ethyl-4-{[(2,4-dinitrophenyl)-hydrazono]-ethyl}-3,5-dimethyl-1H-pyrrole-2-carboxylate: A combined DFT and AIM approach

A new ethyl-4-{[(2,4-dinitrophenyl)-hydrazono]-ethyl}-3,5-dimethyl-1H-pyrrole-2-carboxylate (EDPHEDPC) has been synthesized and characterized by FT-IR, 1H NMR, UV–vis, DART-Mass spectroscopy and elemental analysis. Quantum chemical calculations have been performed by DFT level of theory using B3LYP functional and 6-31G(d,p) as basis set. The 1H NMR chemical shifts are calculated using gauge including atomic orbitals (GIAO) approach in DMSO as solvent. The time dependent density functional theory (TD-DFT) is used to find the various electronic transitions and their nature within molecule. A combined theoretical and experimental wavenumber analysis confirms the existence of dimer. Topological parameters such as electron density (ρBCP), Laplacian of electron density (▿2ρBCP), kinetic electron energy density (GBCP), potential electron density (VBCP) and the total electron energy density (HBCP) at bond critical points (BCP) have been analyzed by Bader's ‘Atoms in molecules’ AIM theory in detail. The intermolecular hydrogen bond energy of dimer is calculated as −12.51kcal/mol using AIM calculations. AIM ellipticity analysis is carried out to confirm the presence of resonance assisted intra and intermolecular hydrogen bonds in dimer. The calculated thermodynamic parameters show that reaction is exothermic and non-spontaneous at room temperature. The local reactivity descriptors such as Fukui functions (fk+, fk−), local softnesses (sk−, sk+) and electrophilicity indices (ωk+, ωk−) analyses are performed to determine the reactive sites within molecule. Nonlinear optical (NLO) behavior of title compound is investigated by the computed value of first hyperpolarizability (β0).

Synthesis, molecular structure and spectral analysis of ethyl 4-formyl-3,5-dimethyl-1H-pyrrole-2-carboxylate thiosemicarbazone: A combined DFT and AIM approach

A new ethyl 4-formyl-3,5-dimethyl-1H-pyrrole-2-carboxylate thiosemicarbazone (EFDMPCT) has been synthesized and characterized by elemental analysis and FT-IR, 1H NMR, UV–Visible, DART-mass spectroscopy. Quantum chemical calculations have been performed by DFT level of theory using B3LYP functional and 6-31G (d,p) as basis set. The calculated 1H NMR chemical shifts using gauge including atomic orbitals (GIAO) approach are in good agreement with the observed chemical shifts. The electronic transitions within molecule have been interpreted using the time dependent density functional theory (TD-DFT). The calculated and experimental wavenumbers analyses confirm the existence of dimer. Topological parameters electron density, Laplacian of electron density, kinetic electron energy density, potential electron density and the total electron energy density at the bond critical points (BCP) analyzed using ‘Atoms in Molecules’ AIM theory reveals intra and inter molecular hydrogen bonding other weaker interactions in detail. The calculated intermolecular hydrogen bond energy of dimer is −12.2176 kcal/mol using AIM calculation. The results of AIM ellipticity confirm the existence of resonance assisted hydrogen bonds in dimer. The calculated thermodynamic parameters show that reaction is exothermic and non-spontaneous at room temperature. The local reactivity descriptors find the reactive sites within molecules have been calculated.

Characteristics of beryllium bonds; a QTAIM study

The nature of beryllium bonds formed between BeX2 (X is H, F and Cl) and some Lewis bases have been investigated. The distribution of the Laplacian of electron density shows that there is a region of charge depletion around the Be atom, which, according to Laplacian complementary principal, can interact with a region of charge concentration of an atom in the base and form a beryllium bond. The molecular graphs of the investigated complexes indicate that beryllium in BeH2 and BeF2 can form “beryllium bonds” with O, N and P atoms but not with halogens. In addition, eight criteria based on QTAIM properties, including the values of electron density and its Laplacian at the BCP, penetration of beryllium and acceptor atom, charge, energy, volume and first atomic moment of beryllium atom, have been considered and compared with the corresponding ones in conventional hydrogen bonds. These bonds share many common features with very strong hydrogen bonds, however,some differences have also been observed.