Minimum Energy Conformation Research Articles

In Silico Modeling of the Molecular Structure and Binding of Leukotriene A4 into Leukotriene A4 Hydrolase

A combined molecular docking and molecular structure in silico analysis on the substrate and product of leukotriene A4 hydrolase (LTA4H) was performed. The molecular structures of the substrate leukotriene A4 (LTA4) and product leukotirene B4 (LTB4) were studied through density functional theory (DFT) calculations at the B3LYP/6-31 + G(d) level of theory in both gas and condensed phases. The whole LTB4 molecule was divided into three fragments (hydrophobic tail, triene motif, and a polar acidic group) that were subjected to a full conformational study employing the most stable conformations of them to build conformers of the complete molecule and geometry optimize further. LTA4 conformers' structures were modeled from the LTB4 minimum energy conformers. Both protonated and deprotonated species of LTA4 and LTB4 were analyzed according to pKa values found in the literature. Finally, a binding model of LTA4 with LTA4 hydrolase is proposed according to docking results that show intermolecular interactions that position the protonated and deprotonated ligand in the active site, in excellent agreement with the model suggested from LTA4H-inhibitors crystallographic data.

QM study and conformational analysis of an isatin Schiff base as a potential cytotoxic agent

Isatin is an important compound from the biological aspect of view. It is an endogenous substance and moreover; various pharmacological activities have been reported for isatin and its derivatives. In-vitro cytotoxic effects of the prepared isatin Schiff bases toward HeLa, LS180 and Raji human cancer cell lines has been reported in our previous work. 3-(2-(4-nitrophenyl)hydrazono) indolin-2-one was found to be the most potent one among the studied compounds (IC(30) =12.2 and 21.8 μM in HeLa and LS-180 cell lines, respectively). Obtained biological data could be well interpreted using docking binding energies toward vascular endothelial growth factor receptor (VEGFR-2); a key anticancer target being biologically investigated against various isatin derivatives. In the present work, quantum mechanical (QM) method including functional B3LYP in association with split valence basis set using polarization functions (Def2-SVP) was used to estimate individual ligand-residue interaction energies for the docked 3-(2-(4-nitrophenyl)hydrazono) indolin-2-one into VEGFR-2 active site. Results were further interpreted via calculated polarization effects induced by individual amino acids of the receptor active site. A fairly good correlation could be found between polarization effects and estimated binding energies (R(2) =0.7227). Conformational analysis revealed that 3-(2-(4-nitrophenyl) hydrazono) indolin-2-one might not necessarily interact with the VEGFR-2 active site in its minimum energy conformation.

Lanthanide Complexes Based on a Diazapyridinophane Platform Containing Picolinate Pendants

A new macrocyclic ligand, N,N'-bis[(6-carboxy-2-pyridyl)methyl]-2,11-diaza[3.3](2,6)pyridinophane (H(2)BPDPA), was prepared, and its coordination properties toward the Ln(III) ions were investigated. The hydration numbers (q) obtained from luminescence lifetime measurements in aqueous solution of the Eu(III) and Tb(III) complexes indicate that they contain one inner-sphere water molecule. The structure of the complexes in solution has been investigated by (1)H and (13)C NMR spectroscopy, as well as by theoretical calculations performed at the density functional theory (B3LYP) level. The minimum-energy conformation calculated for the Yb(III) complex is in excellent agreement with the experimental structure in solution, as demonstrated by analysis of the Yb(III)-induced paramagnetic (1)H shifts. Nuclear magnetic relaxation dispersion (NMRD) profiles and (17)O NMR measurements recorded on solutions of the Gd(III) complex were used to determine the parameters governing the relaxivity. The results show that this system is endowed with a relatively fast water-exchange rate k(ex)(298) = 63 × 10(6) s(-1). Thermodynamic stability constants were determined by pH-potentiometric titration at 25 °C in 0.1 M KCl. The stability constants, which fall within the range logK(LnL) = 12.5-14.2, point to a relatively low stability of the complexes primarily as a consequence of the low basicity of the ligand.

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum-energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (Dead-End Elimination with Perturbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*-based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower-energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein-ligand interactions.

Quasi-harmonic fluctuations of two bound peptides

Binding of two short peptides of sequences ASN-ASP-MET-PHE-ARG-LEU and LEU-LEU-PHE-MET-GLN-HIS and their bound complex structures is studied. Molecular dynamic simulations of the three structures around their respective minimum energy conformations are performed and a quasi-harmonic analysis is performed over the trajectories generated. The fluctuation correlation matrix is constructed for all C(α) -atoms of the peptides for the full trajectory. The spring constant matrix between peptide C(α) -atoms is obtained from the correlation matrix. Statistical thermodynamics of fluctuations, the energies, entropies, and the free energies of binding are discussed in terms of the quasi-harmonic model. Sites contributing to the stability of the system and presenting high affinity for binding are determined. Contribution of hydrophobic forces to binding is discussed. Quasi-harmonic approximation identifies the essential subspace of motions, the important interactions, and binding sites, gives the energetic contribution of each individual interaction, and filters out noise observed in molecular dynamics owing to uncorrelated motions. Comparison of the molecular dynamics results with those of the quasi-harmonic model shows the importance of entropy change, resulting from water molecules being liberated from the surfaces of the two peptides upon binding.

Improved Statistical Sampling and Accuracy with Accelerated Molecular Dynamics on Rotatable Torsions.

In enhanced sampling techniques, the precision of the reweighted ensemble properties is often decreased due to large variation in statistical weights and reduction in the effective sampling size. To abate this reweighting problem, here, we propose a general accelerated molecular dynamics (aMD) approach in which only the rotatable dihedrals are subjected to aMD (RaMD), unlike the typical implementation wherein all dihedrals are boosted (all-aMD). Nonrotatable and improper dihedrals are marginally important to conformational changes or the different rotameric states. Not accelerating them avoids the sharp increases in the potential energies due to small deviations from their minimum energy conformations and leads to improvement in the precision of RaMD. We present benchmark studies on two model dipeptides, Ace-Ala-Nme and Ace-Trp-Nme, simulated with normal MD, all-aMD, and RaMD. We carry out a systematic comparison between the performances of both forms of aMD using a theory that allows quantitative estimation of the effective number of sampled points and the associated uncertainty. Our results indicate that, for the same level of acceleration and simulation length, as used in all-aMD, RaMD results in significantly less loss in the effective sample size and, hence, increased accuracy in the sampling of φ-ψ space. RaMD yields an accuracy comparable to that of all-aMD, from simulation lengths 5 to 1000 times shorter, depending on the peptide and the acceleration level. Such improvement in speed and accuracy over all-aMD is highly remarkable, suggesting RaMD as a promising method for sampling larger biomolecules.

Finding multiple minimum-energy conformations of the hydrophobic-polar protein model via multidomain sampling

We demonstrate the efficiency of the multidomain sampler (MDS) in finding multiple distinct global minima and low-energy local minima in the hydrophobic-polar (HP) lattice protein model. Extending the idea of partitioning energy space in the Wang-Landau algorithm, our approach introduces an additional partitioning scheme to divide the protein conformation space into local basins of attraction. This double-partitioning design is very powerful in guiding the sampler to visit the basins of unexplored local minima. An H-residue subchain distance is used to merge the basins of similar local minima into one domain, which increases the diversity among identified minimum-energy conformations. Moreover, a visit-enhancement factor is introduced for long protein chains to facilitate jumps between basins. Results on three benchmark protein sequences reveal that our approach is capable of finding multiple global minima and hundreds of low-energy local minima of great diversity.

Effect of increasing the energy gap between the two lowest energy states on the mixing time of the Metropolis algorithm

In order to understand what makes natural proteins fold rapidly, Šali, Shakhnovich and Karplus (1994) [6,7] had used the Metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the Metropolis algorithm would find the minimum energy conformation of a chain of beads within an acceptable time scale if and only if there is a large gap between the energies of the minimum energy conformation and that of the second minimum. Clote (1999) [1] attempted to support this conclusion by a proof that the mixing time of the underlying Markov chain would decrease as the gap in energies of the minimum energy conformation and that of the second minimum increased. He was able to show that an upper bound on the mixing time does indeed decrease as the energy gap increases. We show in this paper that the mixing time itself, however, is a non-decreasing function of the value of the energy gap. Therefore, our result contradicts what Clote had attempted to prove.

The 3D-QSAR study of 110 diverse, dual binding, acetylcholinesterase inhibitors based on alignment independent descriptors (GRIND-2). The effects of conformation on predictive power and interpretability of the models

The 3D-QSAR analysis based on alignment independent descriptors (GRIND-2) was performed on the set of 110 structurally diverse, dual binding AChE reversible inhibitors. Three separate models were built, based on different conformations, generated following next criteria: (i) minimum energy conformations, (ii) conformation most similar to the co-crystalized ligand conformation, and (iii) docked conformation. We found that regardless on conformation used, all the three models had good statistic and predictivity. The models revealed the importance of protonated pyridine nitrogen of tacrine moiety for anti AChE activity, and recognized HBA and HBD interactions as highly important for the potency. This was revealed by the variables associated with protonated pyridinium nitrogen, and the two amino groups of the linker. MIFs calculated with the N1 (pyridinium nitrogen) and the DRY GRID probes in the AChE active site enabled us to establish the relationship between amino acid residues within AChE active site and the variables having high impact on models. External predictive power of the models was tested on the set of 40 AChE reversible inhibitors, most of them structurally different from the training set. Some of those compounds were tested on the different enzyme source. We found that external predictivity was highly sensitive on conformations used. Model based on docked conformations had superior predictive ability, emphasizing the need for the employment of conformations built by taking into account geometrical restrictions of AChE active site gorge.

Electronic spectral studies of some fluorescent probes: A comparison of two approaches

Schiff base derivatives were synthesized and characterized by NMR spectra, mass and CHN analysis. The fluorescence properties of these dyes are strongly solvent dependent and the wavelength of maximum fluorescence emission shifts to red. The Kamlet–Taft and Catalan’s solvent scales were found to be the most suitable for describing the solvatochromic shifts of the absorption and fluorescence emission. From the NMR chemical shifts and DFT studies, it was found that the azomethine hydrogen is anti to the amine aryl ring i.e., these dyes exist in anti conformation. DFT calculation was also carried out to determine the orientation of hydroxyl group in more stabilized minimum energy conformation.

EFFECTS OF STIFFNESS ON SHORT, SEMIFLEXIBLE HOMOPOLYMER CHAINS

Conformational and transition behavior of finite, semiflexible homopolymers is studied using an extension of the Wang–Landau algorithm. Generation of a flat distribution in the sampling parameters energy and stiffness allows for efficient investigation of transitions between various conformational phases. Of particular importance is the ability to predict behavior for a given stiffness value, where three classes of minimum energy conformations are expected: Solid-globular, rod-like and toroidal. We present first results highlighting the behavior of a single N = 20 length chain.

Quantitative Structure Property Relationship Modeling for Prediction of Retention Index for a Set of Some Organic Compounds

One of the most ubiquitous challenges of the scientists is the theoretical evaluation of experimental parameters to validate and improve their ability. Plant essential oils and their extracts have been greatly employed in folk medicine, food flavoring, fragrance and pharmaceutical industries. This work is a part of our comprehensive investigation to correlate the experimental and calculated retention indices (RI) of the some organic compounds from K. Javidnia et al. The structures of all organic compounds were drawn into the HYPERCHEM program and optimized using semi-empirical AM1 method, applying a gradient limit of 0.01 kcal/A as a stopping criterion for optimized structures prior to geometry optimization step. Then molecular descriptors were calculated for each compound by the DRAGON software on the minimal energy conformations. The Stepwise SPSS was used for the selection of the variables that resulted in the best fitted models. By molecular modeling and calculation of descriptors, four significant descriptors (XMOD, PCD, MATS2e, GATS2e) related to the retention indices values of the essential oils, were identified. After the variables selection, the MLR method used for building the regression models. The statistical figures obtained by the proposed model are R 2 =0.989, RMSEP=53.08, REP =3.83 and SEP =54.94. In the final step, models generated were used to predict the retention index for a set of test compounds.

Quantitative Structure Property Relationship Modeling for Prediction of Retention Index for a Set of Some Organic Compounds

One of the most ubiquitous challenges of the scientists is the theoretical evaluation of experimental parameters to validate and improve their ability. Plant essential oils and their extracts have been greatly employed in folk medicine, food flavoring, fragrance and pharmaceutical industries. This work is a part of our comprehensive investigation to correlate the experimental and calculated retention indices (RI) of the some organic compounds from K. Javidnia et al. The structures of all organic compounds were drawn into the HYPERCHEM program and optimized using semi-empirical AM1 method, applying a gradient limit of 0.01 kcal/A as a stopping criterion for optimized structures prior to geometry optimization step. Then molecular descriptors were calculated for each compound by the DRAGON software on the minimal energy conformations. The Stepwise SPSS was used for the selection of the variables that resulted in the best fitted models. By molecular modeling and calculation of descriptors, four significant descriptors (XMOD, PCD, MATS2e, GATS2e) related to the retention indices values of the essential oils, were identified. After the variables selection, the MLR method used for building the regression models. The statistical figures obtained by the proposed model are R 2 =0.989, RMSEP=53.08, REP =3.83 and SEP =54.94. In the final step, models generated were used to predict the retention index for a set of test compounds.

Reversible crystal-to-crystal phase transition of a 4,4′-bipyridine-linked dinuclear copper(II) complex

The crystal-to-crystal phase transition of the previously reported dinuclear C i-symmetric complex [{Cu(NO3)2(phen)}2(4,4′-bipy)] (1) (phen = 1,10-phenanthroline; 4,4′-bipy = 4,4′-bipyridine) [Seidel et al. (2011) Z Anorg 637:1545–1554, 10] was studied in detail by differential scanning calorimetry (DSC), powder X-ray diffraction and variable temperature determinations of the unit cell parameters on a single-crystal. A density functional theory (DFT) study was undertaken to elucidate effects of crystal packing on the molecular structure in the solid-state. The DFT study confirmed that the molecular structures of 1 found in the solid-state do not represent the minimum energy conformation of the free molecule, especially with respect to the twist of the 4,4′-bipy bridging ligand. The DSC analysis revealed that the phase transition is a fully reversible process, and suggests that the relationship between the dimorphic forms of 1 is enantiotropic.

Molecular structure–surface property relationships for heterocyclic and dipropylamino derivatives of hexadecylphosphocholine and cetyltrimethylammonium bromide in NaBr and salt-free aqueous solutions

Interfacial area per surfactant molecule values at the air/liquid interface for heterocyclic and dipropylamino derivatives of zwitterionic hexadecylphosphocholine and cationic cetyltrimethylammonium bromide derivatives were calculated from surface tension measurements in NaBr and salt-free aqueous solutions. The interfacial area values were found to be in the range of 0.45–0.86nm2 for both zwitterionic and cationic derivatives. The interfacial area data were correlated with the structure and arrangement of surfactants molecules at the interface. In NaBr solutions, cationic cetyltrimethylammonium bromide derivatives acquire denser packing in the interfacial layer due to the repulsion reduction between cationic headgroups by bromide ions which resulted in smaller interfacial area values. In salt-free aqueous solutions, interfacial area of cetyltrimethylammonium bromide derivatives increased above the level of that of hexadecylphosphocholine derivatives due to the repulsion between positively charged headgroups of adjacent cationic surfactant molecules. The arrangement of hexadecylphosphocholine derivative molecules in the interfacial layer is tighter due to the absence of repulsive electrostatic interactions between neighboring ammonium and phosphate groups. The introduction of electrolyte ions in the hexadecylphosphocholine derivative surfactant aqueous solution results in electrostatic disruption of tight arrangement of its molecules and hence, in the interfacial area increase. The comparison of the experimentally obtained interfacial area values with the surfaces of minimum energy conformers representing the surfactants headgroup parts obtained from molecular models indicates that the arrangement of molecules of hexadecylphosphocholine derivatives in the interfacial layer can be affected more by inter- and intramolecular interactions than the arrangement of cetyltrimethylammonium bromide derivatives.

Novel miscible blends of poly(p-dioxanone) with poly(vinyl phenol)

Poly(p-dioxanone) (PPDO) has been blended with poly(vinyl phenol) (PVPh) and the PPDO/PVPh blends have been investigated using DSC, FTIR and POM. According to the single Tg criterion, miscibility has been found in the whole composition range for the blends obtained by solvent casting from dioxane solutions. The dependence of the Tg on composition shows negative deviation from the Fox equation. The interaction parameter, obtained from melting point depression analysis, χ12=−1.0, confirms a thermodynamically miscible blend. Specific interactions have been analyzed by FTIR. The OH stretching region of PVPh indicates that upon addition of PPDO the hydroxyl–hydroxyl autoassociation interactions are mainly replaced by hydroxyl–carbonyl interassociation contacts, in detrimental of the possible hydroxyl–ether interactions. The carbonyl stretching region of pure PPDO is sensitive to intramolecular ether-ester interactions occurring in the oxyethanoate structures (–O–CH2–CO–O–) present along the PPDO chain. The –O–CH2–CO–O– structure presents only two minimum energy conformations, trans and cis, resulting in two different absorptions in the CO stretching region located respectively at about 1757 and 1732cm−1. Blending with PVPh promotes two new contributions red shifted by about 23cm−1 relative to the “free” CO components. Finally, POM analysis shows that the addition of PVPh to PPDO significantly decreases the crystallization rate of PPDO.

Novel piperidine-fused benzoxazino- and quinazolinonaphthoxazines—synthesis and conformational study

The reactions of 1-(amino(2-hydroxyphenyl)methyl)-2-naphthol (3) and 1-(amino(2-aminophenyl)methyl)-2-naphthol (6) with glutardialdehyde resulted in the formation of piperidine-fused benzoxazinonaphthoxazine 4 and quinazolinonaphthoxazine 7, respectively, both in diastereopure form.The full conformational search protocols of 4 and 7 were successfully carried out by NMR spectroscopy and accompanying molecular modelling; the global minimum-energy conformers of all diastereomers were computed, and the assignments of the most stable stereoisomers, Gtct1 for 4 and Gtct1 for 7, were corroborated by spatial NOE information relating to the H7a-H10a-H15b and H,H coupling patterns of the protons in the flexible part of the piperidine moiety. Additionally, mass spectrometric fragmentation was investigated in collision-induced dissociation experiments. The elemental compositions of the ions were determined by accurate mass measurements.

Direct Formation of the C5′-Radical in the Sugar–Phosphate Backbone of DNA by High-Energy Radiation

Neutral sugar radicals formed in DNA sugar-phosphate backbone are well-established as precursors of biologically important damage such as DNA strand scission and cross-linking. In this work, we present electron spin resonance (ESR) evidence showing that the sugar radical at C5' (C5'(•)) is one of the most abundant (ca. 30%) sugar radicals formed by γ- and Ar ion-beam irradiated hydrated DNA samples. Taking dimethyl phosphate as a model of sugar-phosphate backbone, ESR and theoretical (DFT) studies of γ-irradiated dimethyl phosphate were carried out. CH(3)OP(O(2)(-))OCH(2)(•) is formed via deprotonation from the methyl group of directly ionized dimethyl phosphate at 77 K. The formation of CH(3)OP(O(2)(-))OCH(2)(•) is independent of dimethyl phosphate concentration (neat or in aqueous solution) or pH. ESR spectra of C5'(•) found in DNA and of CH(3)OP(O(2)(-))OCH(2)(•) do not show an observable β-phosphorus hyperfine coupling (HFC). Furthermore, C5'(•) found in DNA does not show a significant C4'-H β-proton HFC. Applying the DFT/B3LYP/6-31G(d) method, a study of conformational dependence of the phosphorus HFC in CH(3)OP(O(2)(-))OCH(2)(•) shows that in its minimum energy conformation, CH(3)OP(O(2)(-))OCH(2)(•), has a negligible β-phosphorus HFC. On the basis of these results, the formation of radiation-induced C5'(•) is proposed to occur via a very rapid deprotonation from the directly ionized sugar-phosphate backbone, and the rate of this deprotonation must be faster than that of energetically downhill transfer of the unpaired spin (hole) from ionized sugar-phosphate backbone to the DNA bases. Moreover, C5'(•) in irradiated DNA is found to be in a conformation that does not exhibit β-proton or β-phosphorus HFCs.

Importance of Kier-Hall Topological Indices in the QSAR of Anticancer Drug Design

An important area of theoretical drug design research is quantitative structure activity relationship (QSAR) using structural invariants. The impetus for this research trend comes from various directions. Researchers in chemical documentation have searched for a set of invariants which will be more convenient than the adjacency matrix (or connection table) for the storage and comparison of chemical structures. Molecular structure can be looked upon as the representation of the relationship among its various constituents. The term molecular structure represents a set of nonequivalent and probably disjoint concepts. There is no reason to believe that when we discuss diverse topics (e.g. chemical synthesis, reaction rates, spectroscopic transitions, reaction mechanisms, and ab initio calculations) using the notion of molecular structure, the different meanings we attach to the single term molecular structure originate from the same fundamental concept. On the contrary, there is a theoretical and philosophical basis for the non-homogeneity of concepts covered by the term molecular structure. In the context of molecular science, the various concepts of molecular structure (e.g. classical valence bond representations, various chemical graph-theoretic representations, ball and spoke model of a molecule, representation of a molecule by minimum energy conformation, semi symbolic contour map of a molecule, or symbolic representation of chemical species by Hamiltonian operators) are model objects derived through different abstractions of the same chemical reality. In each instance, the equivalence class (concept or model of molecular structure) is generated by selecting certain aspects while ignoring some unique properties of those actual events. This explains the plurality of the concept of molecular structure and their autonomous nature, the word autonomous being used in the same sense that one concept is not logically derived from the other. At the most fundamental level, the structural model of an assembled entity (e.g. a molecule consisting of atoms) may be defined as the pattern of relationship among its parts as distinct from the values associated with them. Constitutional formulae of molecules are graphs where vertices represent the set of atoms and edges represent chemical bonds. The pattern of connectedness of atoms in a molecule is preserved by constitutional graphs. A graph (more correctly a non-directed graph) G = [V, E] consists of a finite non-empty set V of points together with a prescribed set E of unordered pairs of distinct points of V. Thus the mathematical characterization of structures represents structural invariants having successful applications in chemical documentation, characterization of molecular branching, enumeration of molecular constitutional associated with a particular empirical formula, calculation of quantum chemical parameters for the generation of quantitative structure-property-activity correlations. Kier developed a number of structural invariants which are now-a-days called as topological indices with wide range of practical applications for QSAR and drug design. The present paper is restricted to the review of Kier-Hall topological indices for QSAR and anticancer drug design for 2,5-bis(1-aziridinyl) 1,4-benzoquinone (BABQ), pyridopyrimidine, 4-anilinoquinazoline and 2-Phenylindoles compounds utilizing various statistical multivariate regression analyses.

Density functional theory study of the multimode Jahn‐Teller problem in the fullerene anion

AbstractThe fullerene anion, C60−, within the Ih point group, is a spherical molecule subject to the T ⊗ h Jahn–Teller (JT) distortion. The descent in symmetry goes to the three epikernel subgroups, namely D5d, D3d, and D2h. The last one completely removes the electronic degeneracy, whereas D5d and D3d structures are subject to further JT distortion, leading to C2h minimum energy structure. The multideterminantal density functional theory approach was applied to calculate the JT parameters for all seven different structures of lower symmetry. The multimode problem in this system was addressed using the intrinsic distortion path method, in which the JT distortion is expressed as a linear combination of all totally symmetric normal modes in the particular low symmetry minimum energy conformation. Results obtained by both methods are consistent and give direct insight into the coupling of electronic distribution and nuclear movements in C. © 2012 Wiley Periodicals, Inc.