Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

The sensitivity of conformational free energies of the alanine dipeptide to atomic site charges

Different atomic point charge sets are obtained for the α_R and C_7.eq conformations of the alanine dipeptide by fitting the charges of each conformation to the respective ab initio electrostatic potential surfaces both individually and simultaneously, in both the united atom and the all-atom representations. Using these charge sets, the sensitivity of the relative conformational aqueous free energies to the atomic site charges is investigated. For this particular system, we find that the solute-water contributions to the conformational free energy differences have a rather weak dependence on site charges; the calculated intramolecular contributions, however, show a rather strong dependence on the atomic site charges. It is suggested that the calculated results for the alanine dipeptide using a single, simultaneously fit set of charges for both conformations are in better agreement with experiments than the calculations carried out with charges determined individually for each conformation. © 1997 John Wiley & Sons, Inc.     

A B3LYP and MP2(full) theoretical investigation into explosive sensitivity upon the formation of the molecule-cation interaction between the nitro group of 3,4-dinitropyrazole and H+, Li+, Na+, Be2+ or Mg2+

The explosive sensitivity upon the formation of molecule-cation interaction between the nitro group of 3,4-dinitropyrazole (DNP) and H⁺, Li⁺, Na⁺, Be²⁺ or Mg²⁺ has been investigated using the B3LYP and MP2(full) methods with the 6-311++G** and 6-311++G(2df,2p) basis sets. The bond dissociation energy (BDE) of the C3–N7 trigger bond has also been discussed for the DNP monomer and the corresponding complex. The interaction between the oxygen atom of nitro group and H⁺ in DNP…H⁺ is partly covalent in nature. The molecule-cation interaction and bond dissociation energy of the C3–N7 trigger bond follow the order of DNP…Be²⁺ > DNP…Mg²⁺ > DNP…Li⁺ > DNP…Na⁺. Except for DNP…H⁺, the increment of the trigger bond dissociation energy in comparison with the DNP monomer correlates well with the molecule-cation interaction energy, natural charge of the nitro group, electron density ρ _BCP(C3–N7), delocalization energy E ⁽²⁾ and NBO charge transfer. The analyses of atoms in molecules (AIM), natural bond orbital (NBO) and electron density shifts have shown that the electron density of the nitro group shifts toward the C3–N7 trigger bond upon the formation of the molecule-cation interaction. Thus, the trigger bond is strengthened and the sensitivity of DNP is reduced.     

Beyond CHELP: improved potential derived charges for sugars

The partitioning of the overall molecular charge distribution into atom centered monopole charges, while quantum mechanically ill-defined, is nevertheless a technique which finds applications in several broad classes of chemical problems. Charges derived from fits to electrostatic potentials have an intuitive appeal since, in principle, these could be derived from either theoretical or experimental data. It has been noted, however, that such potential derived charges can be conformationally dependent in ways that do not appear to reflect the changes in the molecular wavefunction. Both the algorithm used for selecting points at which the molecular electrostatic potential will be fit and the density of points used in the fit have been suggested to influence the resultant charges. Recently [Stouch TR, Williams DE (1992) J Comp Chem 13: 622–32; Stouch TR, Williams DE (1993) J Comp Chem 14: 858–66] it has been noted that numerical difficulties may make it impossible to fit all the atomic charges in a molecule. Singular value decomposition (SVD) of the linear least squares matrices used in fitting atom based monopoles to molecular electrostatic potentials provides a tool for evaluating the integrity of the calculated charges. Based on the SVD analysis for a selected group of molecules we have noted particularly that increasing the molecular size reduces the fraction of charges which can be validly assigned. Users of PD derived charges, especially those who are using those charges for tasks other than reproduction of the MEP, should be aware that there is a high probability that a significant portion of those charges are statistically unreliable. Therefore, charges in many biological molecules, such as sugars, prove to be difficult to obtain by potential derived (PD) methods such as CHELP or CHELPG. Results from the SVD can be used to both assess PD charges and to generate an improved, albeit incomplete, set. Improved PD fits are presented for a series of simple saccharides. Abbreviations: HF, Hartree-Fock; LLS, linear least squares; MEP, molecular electrostatic potential; PD, potential derived; SVD, singular value decomposition This revised version was published online in November 2006 with corrections to the Cover Date.     

Hybridization-displaced charges for amino-acids: a new model using two point charges per atom along with bond-center charges

A new charge distribution is proposed for the amino acids where each atom is associated with two point charges while each bond center is associated with one point charge. Centroids of charges arising due to atomic orbital hybridization called hybridization-displaced charges (HDC) and those located at the atomic sites and bond centers obtained by a modified form of the Mulliken scheme were combined. The density matrix calculations required for this analysis were performed at the B3LYP/6-31G** level of density functional theory. The combination of HDC centroids with the modified Mulliken charges was found to yield dipole moments and surface molecular electrostatic potentials (MEP) of the amino acids in good agreement with those obtained by rigorous DFT calculations or those obtained using the MEP-fitted CHelpG charges. This study shows that the combination of HDC centroids with the modified Mulliken charges is significantly superior to the conventional Mulliken charges.     

Electronic aspects of serine protease catalysis

A new electrostatic approach is applied to serine protease catalysis. It is is based upon the demonstration that the polarities, or partial charges, of the atomic components of the molecules involved in the reaction alternate in sign. When the atomic components of opposite polarities of the enzyme and substrate approach close to each other during the catalysis, the electrostatic interactions between them increase in intensity. These increasing interactions are related to the decrease in the energy barrier. When the serine protease--catalyzed reaction is followed from this perspective, it is shown to result in a marked simplification of the catalytic mechanism. A number of concerted proton transfers and electron density displacements around the active site are indicated. This approach is not inconsistent with other electrostatic methods, and is supported by independent partial charge calculations.     

σ-hole bonding between like atoms; a fallacy of atomic charges

Covalently bonded atoms, at least in Groups V–VII, may have regions of both positive and negative electrostatic potentials on their surfaces. The positive regions tend to be along the extensions of the bonds to these atoms; the origin of this can be explained in terms of the σ-hole concept. It is thus possible for such an atom in one molecule to interact electrostatically with its counterpart in a second, identical molecule, forming a highly directional noncovalent bond. Several examples are presented and discussed. Such “like-like” interactions could not be understood in terms of atomic charges assigned by any of the usual procedures, which view a bonded atom as being entirely positive or negative. Figure Calculated electrostatic potential on the surface of SCl₂. The sulfur is in the foreground, the chlorines are at the back. Color ranges (kcal mol⁻¹): purple negative, blue between 0 and 8, green between 8 and 15, yellow between 15 and 20, red more positive than 20. Note that the sulfur has regions of both positive (red) and negative (purple) electrostatic potential     

Theoretical investigations of the H···π and X (X = F,Cl, Br,I)···π complexes between hypohalous acids and benzene

The H···π and X (X = F, Cl, Br, I)···π interactions between hypohalous acids and benzene are investigated at the MP2/6-311++G(2d,2p) level. Four hydrogen-bonded and three halogen-bonded complexes were obtained. Ab initio calculations indicate that the X···π interaction between HOX and C₆H₆ is mainly electrostatically driven, and there is nearly an equal contribution from both electrostatic and dispersive energies in the case of XOH–C₆H₆ complexes. Natural bond orbital (NBO) analysis reveals that there exists charge transfer from benzene to hypohalous acids. Atom in molecules (AIM) analysis locates bond critical points (BCP) linking the hydrogen or halogen atom and carbon atom in benzene.     

Hydroxyl group as a substituent with varying electronic properties: Effect of strength of H-bonding on charge density changes in Ph–OH…F<Superscript>−</Superscript> complexes

Due to gradual and controlled changes of interatomic distances between heavy atoms in OH…F⁻ of C₆H₅OH…F⁻ systems it was possible to study the electronic structure evolution. Computation at B3LYP/6-311+G(d,p) level of theory was performed for this purpose. Changes in charges at atoms and characteristics at bond critical points (BCPs) of the H-bond region and also in distant parts of the systems were investigated by means of natural bond orbitals (NBO) and atoms in molecules (AIM) analyses. It is shown that at the border line between partially covalent and non-covalent H-bonding (Espinosa et al. in J Chem Phys 117:5529, 2002; Grabowski et al. in J Phys Chem B 110:6444, 2006) with the H…F interatomic distance ∼1.8 Ǻ the hydrogen atom has the most positive charge. In addition, the change in the atomic charge values in the interacting region affects the phenyl ring properties. The decrease of the sum of atomic charges as well as of the aromaticity was noticed when the OH….F distance is shortened.     

Ab initio molecular dynamics simulations of the adsorption of the methylguanidine or methylguanidinium on Ag(111)

A density-functional and Car–Parrinello molecular dynamics methods were employed to study the adsorption of the methylguanidine or methylguanidinium on Ag(111) surface with Vanderbilt pseudopotentials and PBE functional. The geometry, interacting energy, vibrational frequency, Mayer bond order and electrostatic fit charges were calculated. The results show that the methylguanidine interacts with the Ag(111) surface mainly through the interaction between the sp² hybridisation imine nitrogen and its nearest silver atom on top site, assisted with the Ag???H interaction, with the most stabilising interacting energy ?78.83 kJ/mol. The Car–Parrinello molecular dynamics results at 293.15 or 300.00 K indicate that the Ag???N interaction exists stably for more than 6 ps and the Mayer bond order analysis shows that it is the main interaction in adsorption. For the methylguanidinium on Ag(111) surface, the weak interaction between N?H and its neighbour silver atoms, with the energy of ?40.73–?42.68 kJ/mol and the interacting time of 0.2–0.3 ps at 300 K, could not keep it steady on Ag(111). The CP dynamics results show that only the methylguanidine could adsorb on Ag(111) at the room temperature.     

Halogen bonding: the σ-hole

Halogen bonding refers to the non-covalent interactions of halogen atoms X in some molecules, RX, with negative sites on others. It can be explained by the presence of a region of positive electrostatic potential, the σ-hole, on the outermost portion of the halogen’s surface, centered on the R–X axis. We have carried out a natural bond order B3LYP analysis of the molecules CF₃X, with X = F, Cl, Br and I. It shows that the Cl, Br and I atoms in these molecules closely approximate the configuration, where the z-axis is along the R–X bond. The three unshared pairs of electrons produce a belt of negative electrostatic potential around the central part of X, leaving the outermost region positive, the σ-hole. This is not found in the case of fluorine, for which the combination of its high electronegativity plus significant sp-hybridization causes an influx of electronic charge that neutralizes the σ-hole. These factors become progressively less important in proceeding to Cl, Br and I, and their effects are also counteracted by the presence of electron-withdrawing substituents in the remainder of the molecule. Thus a σ-hole is observed for the Cl in CF₃Cl, but not in CH₃Cl. Figure Schematic representation of the atomic charge generation. The molecular electrostatic potential (MEP) is calculated using the AM1* Hamiltonian. The semiempirical MEP is then scaled to DFT or ab initio level and atomic charges are generated from it by the restrained electrostatic potential (RESP) fit method.     

Parametrization of halogen bonds in the CHARMM general force field: Improved treatment of ligand–protein interactions

A halogen bond is a highly directional, non-covalent interaction between a halogen atom and another electronegative atom. It arises due to the formation of a small region of positive electrostatic potential opposite the covalent bond to the halogen, called the ‘sigma hole.’ Empirical force fields in which the electrostatic interactions are represented by atom-centered point charges cannot capture this effect because halogen atoms usually carry a negative charge and therefore interact unfavorably with other electronegative atoms. A strategy to overcome this problem is to attach a positively charged virtual particle to the halogen. In this work, we extend the additive CHARMM General Force Field (CGenFF) to include such interactions in model systems of phenyl-X, with X being Cl, Br or I including di- and trihalogenated species. The charges, Lennard-Jones parameters, and halogen-virtual particle distances were optimized to reproduce the orientation dependence of quantum mechanical interaction energies with water, acetone, and N-methylacetamide as well as experimental pure liquid properties and relative hydration free energies with respect to benzene. The resulting parameters were validated in molecular dynamics simulations on small-molecule crystals and on solvated protein–ligand complexes containing halogenated compounds. The inclusion of positive virtual sites leads to better agreement across experimental observables, including preservation of ligand binding poses as a direct result of the improved representation of halogen bonding.     

Theoretical and experimental studies of vibrational spectra and thermal analysis of 2-nitroaniline and its cation

The FTIR spectrum of 2-nitroaniline was recorded in the regions 4000–400 cm⁻¹. The optimized molecular geometry, bond orders, atomic charges, harmonic vibrational wave numbers and intensities of vibrational bands of 2-nitroaniline and its cation were calculated at DFT levels invoking two different basis sets 6-31G** and 6-31+G** using Gaussian 03W program. The X-ray geometry and FTIR vibrational frequencies were compared with the results of DFT calculations. The thermal stability of 2NA is studied by the thermo gravimetric analysis (TGA). Experimental degradation process of 2-nitroaniline was interpreted with the bond order analysis. The Mulliken atomic charge analysis was also made in the present study. Based on the molecular geometry and Mulliken charge analysis, intra molecular hydrogen bonding was identified.     

Bonding and electronic structures in W@Au12AE complexes (AE= NO+, CO, BF, CN–, or BO–): analogies among ligands isoelectronic to carbon monoxide

A theoretical study on the geometries and electronic structures of W@Au₁₂AE (AE=NO⁺, BF, CN^–, or BO^–) was carried out to gain insight into interactions between W@Au₁₂ and ligands isoelectronic with CO. The best configuration for the adsorption site is on-top type for all five complexes. After complexing with boron ligands (BF or BO^–), the axial Au–W bond distance in W@Au₁₂ is lengthened notably, but NO⁺ has the opposite effect on the axial Au–W bond. A charge transfer and energy decomposition analysis shows that the metal–ligand bonds have enhanced σ-donation strength from NO⁺ to BO^–. Furthermore, the A–E bond strength in the complexes becomes weaker with stronger π-back-donation interactions. Finally, W@Au₁₂CO has the largest HOMO–LUMO gap, making it the most stable in terms of kinetic stability.     

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order.     

The influence of Li+, Na+, Mg2+, Ca2+, and Zn2+ ions on the hydrogen bonds of the Watson-Crick base pairs

The interaction of mono- and divalent metal ions with the nucleic acid base pairs A:T and G:C has been studied using ab initio self-consistent field Hartree-Fock computations with minimal basis sets. Energy-optimized structures of the two base pairs with a final base-base distance of L = 10.35 A have been determined and were further used in calculations on ternary complexes Mn+ - A:B together with previously computed coordination geometries of the cations at adenine (Ade), thymine (Thy), and guanine (Gua). Besides the binding energy of the various metal ions to the base pairs, changes in the stability of the H bonds between Ade and Thy or Gua and Cyt have been determined. Polarization effects of the metal ion on the ligand turned out to increase the binding between complementary bases. Regardless of the metal species, cation binding to Gua N(3) and Thy O(2) leads to a special increase in H-bond stability, whereas binding to Ade N(3) changes the H-bond stability least. Situated in between are the stabilizing effects caused by Gua and Ade N(7) coordination. A remarkable relation between the stability of the H bond and the distance from metal binding site to H bonds was found. This relationship has been rationalized in terms of partial charges of the atoms participating in H bonding, which can reveal the trend in the electrostatic part of total H bond energy. It can be shown that a short distance between coordination site and acceptor hydrogen increases the H-bond strength substantially, while a long distance shows minor effects as supposed. On the other hand, the opposite effect is observed for the influence of the distance between binding site and donor atom. A comparison of our findings with a new model of transition metal ion facilitated rewinding of denatured DNA proposed by S. Miller, D. VanDerveer, and L. Marzilli is given [(1985) J. Am. Chem. Soc. 107, 1048-1055].     

Molecular mechanical perspective on halogen bonding

The nature and strength of halogen bonding in halo molecule-Lewis base complexes were studied in terms of molecular mechanics using our recently developed positive extra-point (PEP) approach, in which the σ-hole on the halogen atom is represented by an extra point of positive charge. The contributions of the σ-hole (i.e., positively charged extra point) and the halogen atom to the strength of this noncovalent interaction were clarified using the atomic parameter contribution to the molecular interaction (APCtMI) approach. The molecular mechanical results revealed that the halogen bond is electrostatic and van der Waals in nature, and its strength depends on three types of interaction: (1) the attractive electrostatic interaction between the σ-hole and the Lewis base, (2) the repulsive electrostatic interaction between the negative halogen atom and the Lewis base, and (3) the repulsive/attractive van der Waals interactions between the halogen atom and the Lewis base. The strength of the halogen bond increases with increasing σ-hole size (i.e., magnitude of the extra-point charge) and increasing halogen atom size. The van der Waals interaction's contribution to the halogen bond strength is most favorable in chloro complexes, whereas the electrostatic interaction is dominant in iodo complexes. The idea that the chloromethane molecule can form a halogen bond with a Lewis base was revisited in terms of quantum mechanics and molecular mechanics. Although chloromethane does produce a positive region along the C-Cl axis, basis set superposition error corrected second-order M?ller-Plesset calculations showed that chloromethane-Lewis base complexes are unstable, producing halogen-Lewis base contacts longer than the sum of the van der Waals radii of the halogen and O/N atoms. Molecular mechanics using the APCtMI approach showed that electrostatic interactions between chloromethane and a Lewis base are unfavorable owing to the high negative charge on the chlorine atom, which overcomes the corresponding favorable van der Waals interactions.     

An overview of halogen bonding

Halogen bonding (XB) is a type of noncovalent interaction between a halogen atom X in one molecule and a negative site in another. X can be chlorine, bromine or iodine. The strength of the interaction increases in the order Cl<Br<I. After a brief review of experimental evidence relating to halogen bonding, we present an explanation for its occurrence in terms of a region of positive electrostatic potential that is present on the outermost portions of some covalently-bonded halogen atoms. The existence and magnitude of this positive region, which we call the σ-hole, depends upon the relative electron-attracting powers of X and the remainder of its molecule, as well as the degree of sp hybridization of the s unshared electrons of X. The high electronegativity of fluorine and its tendency to undergo significant sp hybridization account for its failure to halogen bond. Some computed XB interaction energies are presented and discussed. Mention is also made of the importance of halogen bonding in biological systems and processes, and in crystal engineering. Figure The computed B3PW91/6-31G(d,p) electrostatic potential, in kcal mol⁻¹, on the 0.001 electrons/bohr³ surface of NC–C≡C–Cl. The chlorine atom is at the right. The color ranges are: red, more positive than 15; yellow between 7 and 15; green, between 0 and 7; blue, between −10 and 0; purple, more positive than −10. Proceedings of “Modeling Interactions in Biomolecules II”, Prague, September 5th–9th, 2005.     

TCNE-aniline charge transfer complex: ab initio and TDDFT investigations in gas phase

The geometric and electronic structure of tetracyanoethylene (TCNE)-aniline (donor-acceptor type) complex has been investigated in gas phase using ab initio and time dependent density functional theory calculations. Both the above calculations predict a composed structure for the complex, in which the interacting site is a C≡N and C=C bond center in the TCNE and, –NH₂ and π-electrons of aniline. The N atom of aniline is oriented toward the TCNE molecule. The charge transfer transition energy, estimated by calculating the ground-to-excited state transition electric dipole moments of the complex, agree well with the reported experimental value in chloroform medium. TCNE-aniline at ground state. TCNE-aniline at excited state     

A DFT study of the effect of NNN Al atom on strength of Brönsted acid sites of HY zeolite

A density functional theory study has been employed to investigate the effect of next-nearest-neighbours aluminium (NNN Al) atom on the acid strength of Brönsted acid site in Y zeolite. Additionally, the distribution of NNN Al atom was also studied. The obtained results show that thermodynamically, the favourable sites for location of NNN Al atom are the diagonal sites of the four-membered ring and meta-position of hexagon I. Furthermore, the increase of NNN Al atoms causes the nonlinear reduction of the strength of Brönsted acid sites. When the number of NNN Al atoms is greater than two, the increasing extent of acid strength is not obvious with the reduction in the number of NNN Al atoms. But the acid strength will increase linearly with the further reduce of the number of NNN Al atoms. Compared with deprotonation energy (E_D), ammonia adsorption energy (E_ads) could give a more reasonable measuring result for the acid strength.