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First Steps Towards Quantum Refinement of Protein X-Ray Structures

  • Chapter
Quantum Simulations of Materials and Biological Systems

Abstract

Using standard force-fields and empirical restraints in protein refinement has proven to be a key tool in X-ray protein structure determination. However, detailed analysis of the resulting structural models sometimes reveals chemically unreasonable features, originating in many cases from the representation of multiple configurations using some averaged structure. Quantum chemical methods and computational capabilities have now come to the point at which full quantum refinement of protein structure is feasible, but only complete (meaning real ensembles of) chemical structures may be considered. Density functional theory (DFT) is currently the most popular quantum chemical approach but a large number of approximate functionals are available and most of these do not correctly describe the biologically important London dispersion effects. For small molecules it has been shown that efficient dispersion corrections can overcome this problem, without additional computational effort. We show that this is also the case using linear-scaling dispersion-corrected DFT to refine protein X-ray structures. The study considers the effect on the R factors (i.e. the agreement between modeled and observed diffraction data) when DFT is used to optimize atomic coordinates from the traditionally refined X-ray structure of triclinic hen egg white lysozyme, resolved to 0.65 Å. This particular system was chosen as an ensemble of 8 chemically realistic structures, which are used for the representation of observed structural variability within the crystallographic unit cell and which has been recently published [Falklöf et al. in Theor. Chem. Acc. 131:1076, 2012]. Optimizing only isolated residues within the protein for which all neighboring functional groups are fully identified, we show that in many cases dispersion-corrected DFT (and also Hartree-Fock) optimization competes with conventional refinement techniques. Significant correlations are found between method quality, perceived from small-molecule studies and changes in the R factor, indicating both the high quality of the original refinement but also indicating which methods will be most useful in subsequent full-protein refinements using imbedded DFT constraints.

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References

  1. Sheldrick G, Schneider T (1997) SHELXL high-resolution refinement. Methods Enzymol 277:319–343

    CAS  Google Scholar 

  2. Murshudov GN, Skubak P, Lebedev AA, Pannu NS, Steiner RA, Nicholls RA, Winn MD, Long F, Vagin AA (2011) REFMAC5 for the refinement of macromolecular crystal structures. Acta Crystallogr, D-Biol Crystallogr 67:355–367

    Google Scholar 

  3. Murshudov GN, Vagin AA, Dobson EJ (1997) Refinement of macromolecular structures by the maximum-likelihood method. Acta Crystallogr, D-Biol Crystallogr 53:240–255

    CAS  Google Scholar 

  4. Ryde U (2007) Accurate metal-site structures in proteins obtained by combining experimental data and quantum chemistry. Dalton Trans 2007:607–625

    Google Scholar 

  5. Nilsson K, Lecerof D, Sigfridsson E, Ryde U (2003) An automatic method to generate force-field parameters for hetero-compounds. Acta Crystallogr, D-Biol Crystallogr 59:274–289

    Google Scholar 

  6. Nilsson K, Ryde U (2004) Protonation status of metal-bound ligands can be determined by quantum refinement. J Inorg Biochem 98:1539–1546

    CAS  Google Scholar 

  7. Rulisek L, Ryde U (2006) Structure of reduced and oxidized manganese superoxide dismutase: a combined computational and experimental approach. J Phys Chem B 110:11511–11518

    CAS  Google Scholar 

  8. Ryde U, Nilsson K (2003) Quantum chemistry can locally improve protein crystal structures. J Am Chem Soc 125:14232–14233

    CAS  Google Scholar 

  9. Ryde U, Nilsson K (2003) Quantum refinement—a combination of quantum chemistry and protein crystallography. J Mol Struct, Theochem 632:259–275

    CAS  Google Scholar 

  10. Ryde U, Olsen L, Nilsson K (2002) Quantum chemical geometry optimizations in proteins using crystallographic raw data. J Comput Chem 23:1058–1070

    CAS  Google Scholar 

  11. Hsiao YW, Sanchez-Garcia E, Doerr M, Thiel W (2010) Quantum refinement of protein structures: implementation and application to the red fluorescent protein DsRed.M1. J Phys Chem B 114:15413–15423

    CAS  Google Scholar 

  12. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:864–871

    Google Scholar 

  13. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev A 140:1133–1138

    Google Scholar 

  14. Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799

    CAS  Google Scholar 

  15. Grimme S (2004) Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem 25:1463–1473

    CAS  Google Scholar 

  16. Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-PU. J Chem Phys 132:154104

    Google Scholar 

  17. Grimme S, Ehrlich S, Goerigk L (2011) Effect of the damping function in dispersion corrected density functional theory. J Comput Chem 32:1456–1465

    CAS  Google Scholar 

  18. Kolar M, Kubar T, Hobza P (2011) On the role of London dispersion forces in biomolecular structure determination. J Phys Chem B 115:8038–8046

    CAS  Google Scholar 

  19. Canfield P, Dahlbom MG, Reimers JR, Hush NS (2006) Density-functional geometry optimization of the 150000-atom photosystem—I trimer. J Chem Phys 124:024301/024301-024315

    Google Scholar 

  20. Ohta K, Yoshioka Y, Morokuma K, Kitaura K (1983) The effective fragment potential method an approximate ab initio MO method for large molecules. Chem Phys Lett 101:12–17

    CAS  Google Scholar 

  21. Stewart JJP (2009) Application of the PM6 method to modeling proteins. J Mol Mod 15:765–805

    CAS  Google Scholar 

  22. Stewart JJP (1997) Calculation of the geometry of a small protein using semiempirical methods. J Mol Struct, Theochem 401:195–205

    CAS  Google Scholar 

  23. Stewart JJP (1996) Application of localized molecular orbitals to the solution of semiempirical self-consistent field equations. Int J Quant Chem 58:133–146

    CAS  Google Scholar 

  24. White CA, Johnson BG, Gill PMW, Head-Gordon M (1996) Linear scaling density functional calculations via the continuous fast multipole method. Chem Phys Lett 253:268–278

    CAS  Google Scholar 

  25. Lee TS, Lewis JP, Yang W (1998) Linear-scaling quantum mechanical calculations of biological molecules: the divide-and-conquer approach. Comput Mater Sci 12:259–277

    CAS  Google Scholar 

  26. Van Alsenoy C, Yu CH, Peeters A, Martin JML, Schäfer L (1998) Ab initio geometry determinations of proteins. 1. Crambin. J Phys Chem A 102:2246–2251

    Google Scholar 

  27. Artacho E, Sánchez-Portal D, Ordejón P, García A, Soler JM (1999) Linear-scaling ab-initio calculations for large and complex systems. Phys Status Solidi B 215:809–817

    CAS  Google Scholar 

  28. Sato F, Yoshihiro T, Era M, Kashiwagi H (2001) Calculation of all-electron wavefunction of hemoprotein cytochrome c by density functional theory. Chem Phys Lett 341:645–651

    CAS  Google Scholar 

  29. Inaba T, Tahara S, Nisikawa N, Kashiwagi H, Sato F (2005) All-electron density functional calculation on insulin with quasi-canonical localized orbitals. J Comput Chem 26:987–993

    CAS  Google Scholar 

  30. Wada M, Sakurai M (2005) A quantum chemical method for rapid optimization of protein structures. J Comput Chem 26:160–168

    CAS  Google Scholar 

  31. Li S, Shen J, Li W, Jiang Y (2006) An efficient implementation of the “Cluster-in-molecule” approach for local electron correlation calculations. J Chem Phys 125:074109

    Google Scholar 

  32. Salek P, Høst S, Thøgersen L, Jørgensen P, Manninen P, Olsen J, Jansik B, Reine S, Pawlowski F, Tellgren E, Helgaker T, Coriani S (2007) Linear-scaling implementation of molecular electronic self-consistent field theory. J Chem Phys 126:114110

    Google Scholar 

  33. Cankurtaran BO, Gale JD, Ford MJ (2008) First principles calculations using density matrix divide-and-conquer within the siesta methodology. J Phys Condens Matter 20:294208

    Google Scholar 

  34. Gordon MS, Mullin JM, Pruitt SR, Roskop LB, Slipchenko LV, Boatz JA (2009) Accurate methods for large molecular systems. J Phys Chem B 113:9646–9663

    CAS  Google Scholar 

  35. Fedorov DG, Ishida T, Uebayasi M, Kitaura K (2007) The fragment molecular orbital method for geometry optimizations of polypeptides and proteins. J Phys Chem A 111:2722–2732

    CAS  Google Scholar 

  36. Nagata T, Brorsen K, Fedorov DG, Kitaura K, Gordon MS (2011) Fully analytic energy gradient in the fragment molecular orbital method. J Chem Phys 134:124115

    Google Scholar 

  37. Nagata T, Fedorov DG, Sawada T, Kitaura K, Gordon MS (2011) A combined effective fragment potential-fragment molecular orbital method II analytic gradient and application to the geometry optimization of solvated tetraglycine and chignolin. J Chem Phys 134:034110

    Google Scholar 

  38. Kobayashi M, Kunisada T, Akama T, Sakura D, Nakai H (2011) Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: exact formula and its approximate treatment. J Chem Phys 134:034105

    Google Scholar 

  39. Mayhall NJ, Raghavachari K (2010) Molecules-in-molecules: an extrapolated fragment-based approach for accurate calculations on large molecules and materials. J Chem Theory Comput 7:1336–1343

    Google Scholar 

  40. Reine S, Krapp A, Iozzi MF, Bakken V, Helgaker T, Pawowski F, Saek P (2010) An efficient density-functional-theory force evaluation for large molecular systems. J Chem Phys 133:044102

    Google Scholar 

  41. Dapprich S, Komaromi I, Byun KS, Morokuma K, Frisch MJ (1999) A new ONIOM implementation in Gaussian98. Part I. The calculation of energies gradients vibrational frequencies and electric field derivatives. J Mol Struct, Theochem 461:1–21

    Google Scholar 

  42. Wang J, Dauter M, Alkire R, Joachimiak A, Dauter Z (2007) Triclinic lysozyme at 0.65 Å resolution. Acta Crystallogr, D-Biol Crystallogr 63:1254–1268

    Google Scholar 

  43. Falklöf O, Collyer CA, Reimers JR (2012) Toward ab initio refinement if protein X-ray crystal structures: interpreting and correlating structural fluctuations. Theor Chem Acc 131:1076–1091

    Google Scholar 

  44. Berman HM, Henrick K, Nakamura H (2003) Announcing the world wide protein data bank. Nat Struct Biol 10:980

    CAS  Google Scholar 

  45. Blundell TL, Johnson LN (1976) Protein crystallography. Academic Press, London

    Google Scholar 

  46. Sheldrick GM (2010) Experimental phasing with SHELXC/D/E: combining chain tracing with density modification. Acta Crystallogr, D-Biol Crystallogr 66:479–485

    Google Scholar 

  47. Chapman HN, Fromme P, Barty A, White TA, Kirian RA, Aquila A, Hunter MS, Schulz J, DePonte DP, Weierstall U, Doak RB, Maia FRNC, Martin AV, Schlichting I, Lomb L, Coppola N, Shoeman RL, Epp SW, Hartmann R, Rolles D, Rudenko A, Foucar L, Kimmel N, Weidenspointner G, Holl P, Liang M, Barthelmess M, Caleman C, Boutet S, Bogan MJ, Krzywinski J, Bostedt C, Bajt S, Gumprecht L, Rudek B, Erk B, Schmidt C, Homke A, Reich C, Pietschner D, Struder L, Hauser G, Gorke H, Ullrich J, Herrmann S, Schaller G, Schopper F, Soltau H, Kuhnel K-U, Messerschmidt M, Bozek JD, Hau-Riege SP, Frank M, Hampton CY, Sierra RG, Starodub D, Williams GJ, Hajdu J, Timneanu N, Seibert MM, Andreasson J, Rocker A, Jonsson O, Svenda M, Stern S, Nass K, Andritschke R, Schroter C-D, Krasniqi F, Bott M, Schmidt KE, Wang X, Grotjohann I, Holton JM, Barends TRM, Neutze R, Marchesini S, Fromme R, Schorb S, Rupp D, Adolph M, Gorkhover T, Andersson I, Hirsemann H, Potdevin G, Graafsma H, Nilsson B, Spence JCH (2011) Femtosecond X-ray protein nanocrystallography. Nature 470:73–77

    CAS  Google Scholar 

  48. Rupp B (2010) Biomolecular crystallography—principles practice and application to structural biology. Garland Sciene, New York

    Google Scholar 

  49. Cromer DT, Mann JB (1968) X-ray scattering factors computed from numerical Hartree-Fock wave functions. Acta Crystallogr, A-Cryst Phys Diffr Theor Gen Crystallogr 24:321

    CAS  Google Scholar 

  50. Brunger AT (1992) Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. Nature 355:472–475

    CAS  Google Scholar 

  51. Engh RA, Huber R (1991) Accurate bond and angle parameters for X-ray protein structure refinement. Acta Crystallogr, A-Cryst Phys Diffr Theor Gen Crystallogr 47:392–400

    Google Scholar 

  52. Pellegrini M, Grønbech-Jensen N, Kelly JA, Pfluegl GMU, Yeates TO (1997) Highly constrained multiple-copy refinement of protein crystal structures. Proteins, Struct Funct Bioinform 29:426–432

    CAS  Google Scholar 

  53. Levin EJ, Kondrashov DA, Wesenberg GE, Phillips GN Jr (2007) Ensemble refinement of protein crystal structures: validation and application. Structure 15:1040–1052

    CAS  Google Scholar 

  54. Terwilliger TC, Grosse-Kunstleve RW, Afonine PV, Adams PD, Moriarty NW, Zwart P, Read RJ, Turk D, Hung LW (2007) Interpretation of ensembles created by multiple iterative rebuilding of macromolecular models. Acta Crystallogr, D-Biol Crystallogr 63:597–610

    Google Scholar 

  55. Stewart JJP (2006) Application of the PM6 method to modeling the solid state. J Mol Mod 14:499–535

    Google Scholar 

  56. Stewart KA, Robinson DA, Lapthorn AJ (2008) Type II dehydroquinase: molecular replacement with many copies. Acta Crystallogr, D-Biol Crystallogr 64:108–118

    Google Scholar 

  57. Genheden S, Diehl C, Akke M, Ryde U (2010) Starting-condition dependence of order parameters derived from molecular dynamics simulations. J Chem Theory Comput 6:2176–2190

    CAS  Google Scholar 

  58. Genheden S, Ryde U (2011) A comparison of different initialization protocols to obtain statistically independent molecular dynamics simulations. J Comput Chem 32:187–195

    CAS  Google Scholar 

  59. Fleming A (1922) On a remarkable bacteriolytic element found in tissues and secretions. Proc Roy Soc Ser B 93:306–317

    CAS  Google Scholar 

  60. Blake CCF, Fenn RH, North ACT, Phillips DC, Poljak RJ (1962) Structure of lysozyme. Nature 196:1173–1176

    CAS  Google Scholar 

  61. Vocadlo DJ, Davies GJ, Laine R, Withers SG (2001) Catalysis by hen egg-white lysozyme proceeds via a covalent intermediate. Nature 412:835–838

    CAS  Google Scholar 

  62. Bottoni A, Miscione GP, De Vivo M (2005) A theoretical DFT investigation of the lysozyme mechanism: computational evidence for a covalent intermediate pathway. Proteins, Struct Funct Genet 59:118–130

    CAS  Google Scholar 

  63. Weiner SJ, Kollman PA, Case DA, Singh UC, Ghio C, Alagona GS, Profeta J, Weiner P (1984) A new force field for molecular mechanical simulation of nucleic acids and proteins. J Am Chem Soc 106:765–784

    CAS  Google Scholar 

  64. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) A second generation force field for the simulation of proteins nucleic acids and organic molecules. J Am Chem Soc 117:5179–5197

    CAS  Google Scholar 

  65. Kristyán S, Pulay P (1994) Can (semi)local density-functional theory account for the London dispersion forces. Chem Phys Lett 229:175–180

    Google Scholar 

  66. Hobza P, Šponer J, Reschel T (1995) Density-functional theory and molecular clusters. J Comput Chem 16:1315–1325

    CAS  Google Scholar 

  67. Šponer J, Leszczynski J, Hobza P (1996) Base stacking in cytosine dimer a comparison of correlated ab initio calculations with three empirical potential models and density functional theory calculations. J Comput Chem 17:841–850

    Google Scholar 

  68. Pérez-Jordá JM, Becke AD (1995) A density-functional study of van der Waals forces—rare-gas diatomics. Chem Phys Lett 233:134–137

    Google Scholar 

  69. Pérez-Jordá JM, San-Fabián E, Pérez-Jiménez AJ (1999) Density-functional study of van der Waals forces on rare-gas diatomics: Hartree-Fock exchange. J Chem Phys 110:1916–1920

    Google Scholar 

  70. Couronne O, Ellinger Y (1999) An ab initio and DFT study of (n−2)(2) dimers. Chem Phys Lett 306:71–77

    CAS  Google Scholar 

  71. Grimme S (2011) Density functional theory with London dispersion corrections. Wiley Interdiscip Rev-Comput Mol Sci 1:211–228

    CAS  Google Scholar 

  72. Zhao Y, Truhlar DG (2008) Density functionals with broad applicability in chemistry. Acc Chem Res 41:157–167

    CAS  Google Scholar 

  73. Johnson ER, Mackie ID, DiLabio GA (2009) Dispersion interactions in density-functional theory. J Phys Org Chem 22:1127–1135

    CAS  Google Scholar 

  74. von Lilienfeld OA, Tavernelli I, Rothlisberger U, Sebastiani D (2004) Optimization of effective atom centered potentials for London dispersion forces in density functional theory. Phys Rev Lett 93:153004

    Google Scholar 

  75. Sun YY, Kim YH, Lee K, Zhang SB (2008) Accurate and efficient calculation of van der Waals interactions within density functional theory by local atomic potential approach. J Chem Phys 129:154102

    CAS  Google Scholar 

  76. Dion M, Rydberg H, Schroder E, Langreth DC, Lundqvist BI (2004) Van der Waals density functional for general geometries. Phys Rev Lett 92:246401

    CAS  Google Scholar 

  77. Lee K, Murray ED, Kong LZ, Lundqvist BI, Langreth DC (2010) Higher-accuracy van der Waals density functional. Phys Rev B 82:081101

    Google Scholar 

  78. Vydrov OA, Van Voorhis T (2010) Nonlocal van der Waals density functional: the simpler the better. J Chem Phys 133:244103

    Google Scholar 

  79. Goerigk L, Grimme S (2011) A thorough benchmark of density functional methods for general main group thermochemistry kinetics and noncovalent interactions. Phys Chem Chem Phys 13:6670–6688

    CAS  Google Scholar 

  80. Goerigk L, Kruse H, Grimme S (2011) Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions. Chem Phys Chem 12:3421–3433

    CAS  Google Scholar 

  81. Hujo W, Grimme S (2011) Comparison of the performance of dispersion-corrected density functional theory for weak hydrogen bonds. Phys Chem Chem Phys 13:13942–13950

    CAS  Google Scholar 

  82. Hujo W, Grimme S (2011) Performance of the van der Waals density functional VV10 and (hybrid)GGA variants for thermochemistry and noncovalent interactions. J Chem Theory Comput 7:3866–3871

    CAS  Google Scholar 

  83. Antony J, Grimme S (2006) Density functional theory including dispersion corrections for intermolecular interactions in a large benchmark set of biologically relevant molecules. Phys Chem Chem Phys 8:5287–5293

    CAS  Google Scholar 

  84. Valdes H, Pluhackova K, Pitonak M, Rezac J, Hobza P (2008) Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field. Phys Chem Chem Phys 10:2747–2757

    CAS  Google Scholar 

  85. Valdes H, Spiwok V, Rezac J, Reha D, Abo-Riziq AG, de Vries MS, Hobza P (2008) Potential-energy and free-energy surfaces of glycyl-phenylalanyl-alanine (GFA) tripeptide: experiment and theory. Eur J Chem 14:4886–4898

    CAS  Google Scholar 

  86. Antony J, Grimme S, Liakos DG, Neese F (2011) Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods. J Phys Chem A 115:11210–11220

    CAS  Google Scholar 

  87. Johnson ER, Becke AD (2006) A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections. J Chem Phys 124:174104

    Google Scholar 

  88. DFTD3 V21. Rev 6 (2011) SG University Muenster

    Google Scholar 

  89. Perdew JP, Ruzsinszky A, Tao J, Staroverov VN, Scuseria GE, Csonka GI (2005) Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. J Chem Phys 123:062201

    Google Scholar 

  90. Goerigk L, Grimme S (2010) A general database for main group thermochemistry kinetics and noncovalent interactions—assessment of common and reparameterized (meta-)GGA density functionals. J Chem Theory Comput 6:107–126

    CAS  Google Scholar 

  91. Goerigk L, Grimme S (2011) Efficient and accurate double-hybrid-meta-GGA density functionals-evaluation with the extended GMTKN30 database for general main group thermochemistry kinetics and noncovalent interactions. J Chem Theory Comput 7:291–309

    CAS  Google Scholar 

  92. Grimme S (2006) Semiempirical hybrid density functional with perturbative second-order correlation. J Chem Phys 124:034108

    Google Scholar 

  93. Neese F, Schwabe T, Grimme S (2007) Analytic derivatives for perturbatively corrected “Double hybrid” density functionals: theory implementation and applications. J Chem Phys 126:124115

    Google Scholar 

  94. Reha D, Valdes H, Vondrasek J, Hobza P, Abu-Riziq A, Crews B, de Vries MS (2005) Structure and IR spectrum of phenylalanyl-glycyl-glycine tripetide in the gas-phase: IR/UV experiments ab initio quantum chemical calculations and molecular dynamic simulations. Eur J Chem 11:6803–6817

    CAS  Google Scholar 

  95. Tao JM, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys Rev Lett 91:146401

    Google Scholar 

  96. Zhao Y, Truhlar DG (2005) Design of density functionals that are broadly accurate for thermochemistry thermochemical kinetics and nonbonded interactions. J Phys Chem A 109:5656–5667

    CAS  Google Scholar 

  97. Becke AD (1993) Density-functional thermochemistry III. The role of exact exchange. J Chem Phys 98:5648–5652

    CAS  Google Scholar 

  98. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98:11623–11627

    CAS  Google Scholar 

  99. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Atoms molecules solids and surfaces—applications of the generalized gradient approximation for exchange and correlation. Phys Rev B 46:6671–6687

    CAS  Google Scholar 

  100. Lambropoulos NA, Reimers JR, Hush NS (2002) Binding to gold(0): accurate computational methods with application to AuNH3. J Chem Phys 116:10277–10286

    CAS  Google Scholar 

  101. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic-behavior. Phys Rev A 38:3098–3100

    CAS  Google Scholar 

  102. Perdew JP, Wang Y (1986) Accurate and simple density functional for the electronic exchange energy—generalized gradient approximation. Phys Rev B 33:8800–8802

    Google Scholar 

  103. Slater JC (1951) A simplification of the Hartree-Fock method. Phys Rev 81:385–390

    CAS  Google Scholar 

  104. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin-density calculations—a critical analysis. Can J Phys 58:1200–1211

    CAS  Google Scholar 

  105. Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys Chem Chem Phys 7:3297–3305

    CAS  Google Scholar 

  106. Jensen F (2007) Introduction to computational chemistry, 2nd edn. Wiley, New York

    Google Scholar 

  107. Ahlrichs R et al (2009) Turbomole University of Karlsruhe

    Google Scholar 

  108. Ahlrichs R, Bär M, Häser M, Horn H, Kölmel C (1989) Electronic-structure calculations on workstation computers—the program system turbomole. Chem Phys Lett 162:165–169

    CAS  Google Scholar 

  109. Eichkorn K, Treutler O, Ohm H, Haser M, Ahlrichs R (1995) Auxiliary basis-sets to approximate Coulomb potentials. Chem Phys Lett 240:283–289

    CAS  Google Scholar 

  110. Kendall RA, Dunning TH, Harrison RJ (1992) Electron-affinities of the 1st-row atoms revisited—systematic basis-sets and wave-functions. J Chem Phys 96:6796–6806

    CAS  Google Scholar 

  111. Hehre WJ, Ditchfield R, Pople JA (1972) J Chem Phys 56:2257

    CAS  Google Scholar 

  112. Frisch et al. (2009) GAUSSIAN09. Gaussian Inc., Wallingford

    Google Scholar 

  113. Yin S, Dahlbom MG, Canfield PJ, Hush NS, Kobayashi R, Reimers JR (2007) Assignment of the Qy absorption spectrum of photosystem—I from thermosynechococcus elongatus based on CAM-B3LYP calculations at the PW91-optimized protein structure. J Phys Chem C 111:9923–9930

    CAS  Google Scholar 

  114. Koide A (1976) New expansion for dispersion forces and its application. J Phys B, At Mol Opt Phys 9:3173–3183

    CAS  Google Scholar 

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Acknowledgements

L.G. is supported by a postdoctoral scholarship by the German Academy of Science Leopoldina Fellowship Programme under the grant number LPDS 2011-11. This project was also supported by the Australian Research Council under the grant number DP110102932. We thank Garib Murshudov for providing us a modified REFMAC version that allows a mere isotropic B factor refinement. We thank Stefan Grimme for freely providing the DFTD3 program and Holger Kruse for technical help in combining the DFTD3 program with GAUSSIAN09, to be able to carry out the ONIOM geometry optimizations. We would finally like to acknowledge the grants of computer time and technical support, particularly from Dr. Rika Kobayashi, from the National Computational Infrastructure (NCI) National Facility in Canberra, Australia.

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Authors and Affiliations

  1. School of Chemistry, The University of Sydney, Sydney, New South Wales, 2006, Australia

    Lars Goerigk & Jeffrey R. Reimers

  2. Department of Physics, Chemistry and Biology, Linköping University, 581 83, Linköping, Sweden

    Olle Falklöf

  3. School of Molecular Bioscience, The University of Sydney, Sydney, New South Wales, 2006, Australia

    Charles A. Collyer

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  1. Lars Goerigk
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  4. Jeffrey R. Reimers
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Correspondence to Jeffrey R. Reimers .

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  1. Office G26, Monash University, Royal Parade 399, Parkville, 3052, Victoria, Australia

    Jun Zeng

  2. Department of Physics & Material Science, City University of Hong Kong, Hong Kong SAR, China, People's Republic

    Rui-Qin Zhang

  3. Office G26, Monash University, Royal Parade 399, Parkville, 3052, Victoria, Australia

    Herbert R. Treutlein

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Goerigk, L., Falklöf, O., Collyer, C.A., Reimers, J.R. (2012). First Steps Towards Quantum Refinement of Protein X-Ray Structures. In: Zeng, J., Zhang, RQ., Treutlein, H. (eds) Quantum Simulations of Materials and Biological Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4948-1_6

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