Linear Scaling Methodology

Recent progress in developing linear scaUng electronic stmcture methods has lead to the development of a variety of 0(N) techniques [6, 7]. The Fermi operator 

Loboda, Quantum-Chemical Studies on Porphyrins, Fullerenes and Carbon Nanostructures, Carbon Nanostrucmres, DOI 10.1007/978-3-642-31845-0 6, Springer-Verlag Berlin Heidelberg 2013 

In last decade, the elongation finite-field (elongation-FF) method has been developed in the theoretical chemistry laboratory [36-42]. In this approach, molecular (hyper)polarizabilities are obtained by numerically differentiating the total energy with respect to electric fields. This mefhod has been applied to many quasi-one- 

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However, ideas from linear scaling methodologies can be used to develop ad hoc methods that are able to compute in a more approximate fashion the wavefunctimi for large systems. Essentially, aU linear scaling methods are based on the definitimi of a very localized basis set that reduces the number of matrix elements to be... 

Kobayashi, M.,Imamura, Y, Nakai, H. Alternative linear-scaling methodology for the second-order MpUer-Plesset perturbation calculation based on the divide-and-conquer method. J. Chem. Phys. 127, 074103 (2007)... 

Johnson, B. G., White, C. A., Zhang, Q., Chen, B., Graham, R. L., Gill, P. M. W., Head-Gordon M., 1996, Advances in Methodologies for Linear-Scaling Density Functional Calculations , in Recent Developments and Applications of Modem Density Functional Theory, J. M. Seminario, (ed.), Elsevier, Amsterdam. 

This section describes the main methodological advances that will be used in subsequent selected applications, including (1) Development of fast semiempirical methods for multiscale quantum simulations, (2) Directions for development of next-generation QM/MM models, and (3) Linear-scaling electrostatic and generalized solvent boundary methods. 

Gogonea V, Merz KM. Fully quantum mechanical description of proteins in solution. Combining linear scaling quantum mechanical methodologies with the Poisson-Boltzmann equation. J Phys Chem A 1999 103 5171-5188. 

This review of semiempirical quantum-chemical methods outlines their development over the past 40 years. After a survey of the established methods such as MNDO, AMI, and PM3, recent methodological advances are described including the development of improved semiempirical models, new general-purpose and special-purpose parametriza-tions, and linear scaling approaches. Selected recent applications are presented covering examples from biochemistry, medicinal chemistry, and nanochemistry as well as direct reaction dynamics and electronically excited states. The concluding remarks address the current and future role of semiempirical methods in computational chemistry. 

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