Divide and Conquer Hartree-Fock Calculations on proteins

Divide and Conquer Hartree-Fock Calculations on proteins

(Parte 2 de 3)

the two-electronintegrals.10 When we apply eq 2 to construct the subsystem Fock matrix, the long-rangeCoulomb interactions between the local subsystem and distant atoms cannot be circumvented; thus, it should be emphasized that the DC algorithm itself does not reduce the scale of Coulomb and exchange matrix evaluations, and other approaches are necessary to achieve this result (e.g., CFMM).14,16,17,49

MFCC Initial Guess for DC-HF Calculations.Next, we compare the number of SCF cycles necessary to reach convergence when the SAD (superposition of atomic densities) and MFCC initial guesses are used in the divide and conquer scheme using the 6-31G* basis set (see Table 1). The convergence criterion in all examples was set to 10-6 au on the root-mean-squared change of the density matrix elementsand 10-4 au for the maximumchange of the density matrix elements. Nakai and co-workers35 and Shaw and St- Amant32 noted that DIIS causes SCF calculationsto oscillate at the final stage of the SCF convergence process due to the slight errors introduced by the DC approximation for assembling the density matrix (see eq 3). In our HF DC calculations, the DIIS technique was turned off when the root-mean-squared change of the density matrix elements reaches 10-4 au. We also found that although DIIS works in the early stages of the SCF procedure, we get the best performance when only two previous Fock matrices were stored in the DIIS calculations. One can see from Table 1 that the HF DC calculationsusually require more SCF cycles than the non-DC runs; however, for the polyglycine and polyalanine systems, the MFCC initial guess helps to reduce the number of SCF cycles in both DC and non-DC cases.

Residue-Centric Core Region versus Atom-Centric

Core Region. Previously, all calculations used a residue- based definition for the core region. We also examined an atom-based subsetting strategy for the core region in polyglycines and polyalanines. One can see from Table 2 that the converged total energies using the atom-centric core region were almost identical to those using a residue-based cutoff. Indeed, the overall mean unsigned deviation is as low as 0.054 kcal mol-1. This is an attractive aspect of the divide and conquer approach since it allows for parallelization at the atom level rather than at the much larger reside-based cutoff scheme.

Validation on Three-Dimensional Protein Systems. No previous studies have utilized the divide and conquer HF approach on three-dimensional globular proteins. In order to address this point, we validated the accuracy of divide and conquerHF/6-31G*calculationson 1 real proteins.The systemsrangedfrom 304 to 608 atoms and are listedin Table 3. The proteins consisted of R-helical structures (see Figure 8a) or are mixed R- structures (see Figure 8b). As shown

Figure 8. Two representative three-dimensional protein structures studied in this work.

Table 3. Total Energies (au) of Three-Dimensional Globular Proteins Obtained Using Standard Full System HF/6-31G* Calculations and Divide and Conquer HF/6-31G* Calculations Using the MFCC Initial Guessa system number of atoms number of basis functions standard full system calculation

DC using MFCC initial guess deviation (kcal mol-1) a MUD: mean unsigned deviation. b Did not converge using the SAD initial guess.

Divide and Conquer Hartree-Fock Calculations J. Chem. Theory Comput., Vol. x, No. x, X E in Table 3, the largest deviation is 2.25 kcal mol-1 and the overall mean unsigned deviation is only 0.97 kcal mol-1 compared to standard full system calculations. Importantly, the observed error is larger than what was observed for the one-dimensional examples but is still within acceptable limits. This study sets the stage for the wide application of divide and conquer calculations on real protein systems. Furthermore, we found that for five proteins the divide and conquer HF calculations are not able to reach convergence using the simple SAD initial guess while all cases converged using the MFCC initial guess. Therefore, we conclude that the quality of the initial guess plays an important role in ensuring the convergenceof divide and conquer calculations. Fragment-based electron density provides a much better quality initial guess with linear-scaling computational cost and, ultimately, much less computational time when compared to full system calculations.

Conclusions

In this study, divide and conquer HF theory was revisited in order to examine its potential to study three-dimensional constructs and a new and effective initial guess scheme was introduced. We first validated the accuracy of the divide and conquer HF/6-31G* calculations on 1 three-dimensional globular proteins. The overall mean unsigned error was within 1 kcal mol-1 when compared to standard full system calculations. Furthermore, we found that the fragment-based initial guess using the MFCC approach reduces the number of SCF cycles for polyglycine and polyalanine systems. Moreover, the MFCC initial guess facilitated SCF convergence for several of the globular proteins, where the SAD initial guess was unable to yield a converged wave function.

Acknowledgment. WethanktheNIH(GMGM044974) for financial support of this research. Computing support from the Universityof Florida High PerformanceComputing Center is gratefully acknowledged.

References

(1) Szabo, A.; Ostlund, N. S. Modern quantum chemistry: introduction to adVanced electronic structure theory, 1st ed.; McGraw-Hill: New York, 1989.

(2) Parr, R. G.; Yang, W. T. Annu. ReV. Phys. Chem. 1995, 46, 701.

(6) Crawford, T. D.; Schaefer, H. F. ReV. Comput. Chem. 2000, 14, 3.

(7) Kallay, M.; Gauss, J. J. Chem. Phys. 2005, 123, 214105. (8) Kallay, M.; Surjan,P .R . J. Chem. Phys. 2001, 115, 2945.

(9) Bomble, Y. J.; Stanton, J. F.; Kallay, M.; Gauss, J. J. Chem. Phys. 2005, 123, 054101.

(10) Strout, D. L.; Scuseria,G. E. J. Chem. Phys. 1995, 102, 8448.

(1) Schwegler, E.; Challacombe, M. J. Chem. Phys. 1996, 105, 2726.

(13) Fedorov, D. G.; Kitaura, K. J. Phys. Chem. A 2007, 1, 6904.

(14) Challacombe, M.; Schwegler, E. J. Chem. Phys. 1997, 106, 5526.

(15) Friesner, R. A.; Murphy, R. B.; Beachy, M. D.; Ringnalda,

M. N.; Pollard, W. T.; Dunietz, B. D.; Cao, Y. X. J. Phys. Chem. A 1999, 103, 1913.

(16) White, C. A.; Johnson, B. G.; Gill, P. M. W.; Head-Gordon, M. Chem. Phys. Lett. 1994, 230,8 .

(17) White, C. A.; Johnson, B. G.; Gill, P. M. W.; Head-Gordon, M. Chem. Phys. Lett. 1996, 253, 268.

(19) Korchowiec, J.; Lewandowski, J.; Makowski, M.; Gu, F. L.; Aoki, Y. J. Comput. Chem. 2009, 30, 2515.

(20) Jiang, N.; Ma, J.; Jiang, Y. S. J. Chem. Phys. 2006, 124, 114112.

(21) Daniels, A. D.; Scuseria, G. E. J. Chem. Phys. 1999, 110, 1321.

(25) Strain, M. C.; Scuseria, G. E.; Frisch, M. J. Science 1996, 271, 51.

(26) Exner, T. E.; Mezey, P. G. J. Phys. Chem. A 2002, 106, 11791.

(27) Fusti-Molnar, L. J. Chem. Phys. 2003, 119, 11080. (28) Fusti-Molnar, L.; Pulay, P. J. Chem. Phys. 2002, 117, 7827.

(29) Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld,

C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O’Neill, D. P.; DiStasio, R. A.; Lochan, R. C.; Wang, T.; Beran, G. J. O.; Besley,N. A.; Herbert,J. M.; Lin, C. Y.; Van Voorhis, T.; Chien, S. H.; Sodt, A.; Steele, R. P.; Rassolov, V. A.; Maslen, P. E.; Korambath, P. P.; Adamson,R. D.; Austin,B.; Baker,J.; Byrd, E. F. C.; Dachsel, H.; Doerksen, R. J.; Dreuw, A.; Dunietz, B. D.; Dutoi, A. D.; Furlani, T. R.; Gwaltney, S. R.; Heyden, A.; Hirata, S.; Hsu, C. P.; Kedziora, G.; Khalliulin, R. Z.; Klunzinger, P.; Lee, A. M.; Lee, M. S.; Liang, W.; Lotan, I.; Nair, N.; Peters, B.; Proynov, E. I.; Pieniazek, P. A.; Rhee, Y. M.; Ritchie, J.; Rosta, E.; Sherrill, C. D.; Simmonett, A. C.; Subotnik, J. E.; Woodcock,H. L.; Zhang, W.; Bell, A. T.; Chakraborty,A. K.; Chipman, D. M.; Keil, F. J.; Warshel, A.; Hehre, W. J.; Schaefer, H. F.; Kong, J.; Krylov, A. I.; Gill, P. M. W.; Head- Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 3172.

(30) Dixon, S. L.; Merz, K. M. J. Chem. Phys. 1996, 104, 6643.

(31) Gogonea, V.; Westerhoff,L. M.; Merz, K. M. J. Chem. Phys. 2000, 113, 5604.

(32) Shaw, D. M.; St-Amant, A. J. Theor. Comput. Chem. 2004, 3, 419.

(3) Kobayashi, M.; Nakai, H. Int. J. Quantum Chem. 2009, 109, 2227.

(34) Akama, T.; Fujii, A.; Kobayashi, M.; Nakai, H. Mol. Phys. 2007, 105, 2799.

(35) Akama, T.; Kobayashi, M.; Nakai, H. J. Comput. Chem. 2007, 28, 2003.

(36) Kobayashi, M.; Akama, T.; Nakai, H. J. Chem. Phys. 2006, 125, 204106.

F J. Chem. Theory Comput., Vol. x, No. x, X He and Merz

(39) Exner, T. E.; Mezey, P. G. Phys. Chem. Chem. Phys. 2005, 7, 4061.

(40) Nakano, T.; Kaminuma,T.; Sato, T.; Fukuzawa,K.; Akiyama,

Y.; Uebayasi, M.; Kitaura, K. Chem. Phys. Lett. 2002, 351, 475.

(41) Fedorov, D. G.; Kitaura, K. Chem. Phys. Lett. 2006, 433, 182.

(42) Zhang, D. W.; Zhang, J. Z. H. J. Chem. Phys. 2003, 119, 3599.

(43) He, X.; Zhang, J. Z. H. J. Chem. Phys. 2005, 122, 031103.

(4) Fedorov, D. G.; Ishimura, K.; Ishida, T.; Kitaura, K.; Pulay, P.; Nagase, S. J. Comput. Chem. 2007, 28, 1476.

(45) Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2005, 123, 134103.

(Parte 2 de 3)

Comentários