Abstract
The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation.
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André JM, Moseley DH, Champagne B, Delhalle J, Fripiat JG, Brédas JL, Vanderveken DJ, Vercauteren DP (1993) Methods and techniques in computational chemistry: METECC-94. In: Clementi E (eds) STEF, Cagliari, pp 423–480
Ewald PP (1921) Ann Phys Leipzig 64:253
Flamant I (1998) Fourier space restricted Hartree-Fock method for the electronic structure calculation of stereoregular polymers. Ph.D. dissertation, Facultés Universitaires Notre-Dame de la Paix
Flamant I, Fripiat JG, Delhalle J, Harris FE (2000) Theor Chem Acc 104:350
Ambrosiano J, Greengard L, Rokhlin V (1988) Comput Phys Commun 48:117
Lambert CG, Darden TA, Board JA Jr. (1996) J Comput Phys 126:274
Strain MC, Scuseria GE, Frisch MJ (1996) Science 271:51
Pisani C, Dovesi R, Roetti C, Causà M, Orlando R, Casassa S, Saunders VR (2000) Int J Quantum Chem 77:1032
Saunders VR, Freyria-Fava C, Dovesi R, Roetti C (1994) Comput Phys Commun 84:156
Fripiat JG, Delhalle J, Flamant I, Harris FE (2010) J Chem Phys 132:044108
Terras R (1991) J Comput Phys 39:233
Harris FE (2008) J Comput Appl Math 215:260
Harris FE, Fripiat JG (2009) Int J Quantum Chem 109:1728
Abramowitz, M, Stegun, I (eds) (1964) Handbook of mathematical functions. Dover, New York
Acknowledgments
FEH was supported by US National Science Foundation Grant PHY-0601758. JGF is grateful to Professors J. M. André and B. Champagne for their support. JGF thanks the FNRS for financial support making possible his visits to QTP at the University of Florida during these last years. We thank Professor Joseph Delhalle for his continuing interest in this work and for many fruitful discussions. Part of this research has been funded by BELSPO (IAP P6/27 network “Functional Supramolecular Systems”).
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Published as part of the special collection of articles celebrating theoretical and computational chemistry in Belgium.
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Fripiat, J.G., Harris, F.E. Ewald-type formulas for Gaussian-basis studies of one-dimensionally periodic systems. Theor Chem Acc 131, 1257 (2012). https://doi.org/10.1007/s00214-012-1257-0
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DOI: https://doi.org/10.1007/s00214-012-1257-0