Shedge, S. V. (2012) Development and application of noniterative methods for calculation of electric response properties within density functional theory. PhD thesis, CSIRNational Chemical Laboratory, Pune, India.

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Abstract
Abstract ____________________________________________________________ The main objective of this thesis is to develop noniterative method for calculation of electric response properties such as polarizabilities, hyperpolarizabilities within density functional theory (DFT). The effect of a weak external perturbation on the electronic distribution of the molecule is reflected in its response properties. Dipole moment, polarizability and hyperpolarizability are the fundamental electric properties of molecule. These properties are widely studied due to the significance in identifying material with improved nonlinear optical (NLO) properties [1]. For studying properties of large molecular systems, DFT is an obvious choice because of simplicity in applications. However, response properties using DFT have been calculated mainly using finitefield method. Recently, the noniterative approach to response properties using DFT i.e. the noniterative approximation to the coupledperturbed KohnSham (NIACPKS) [24] method has been developed with application to large molecules in mind. The presented work in this thesis focuses on the implementation of NIACPKS, for calculation of dipoledipole polarizabilities and dipolequadrupole polarizabililities. CPKS is a standard method for calculation of the derivatives of the energy such as geometric derivatives, derivative with respect to magnetic field and electric field. Here in this thesis we focus mainly on energy derivative with respect to electric field, i.e. electric response properties. NIACPKS is the noniterative approach developed within CPKS formalism. Here the derivative of the KohnSham matrix is calculated numerically and used in CPKS equation for calculation of response density matrix. The electric polarizabilities can then be calculated as trace of response density with dipole or quadrupole moment integrals depending upon the kind of polarizability we want to calculate. This method has been implemented in deMon2k software which is based on KSDFT [5]. We also present here the new implementation of NIACPKS in self consistent perturbation (SCP) formalism which is more efficient for calculation of polarizabiities [6]. The method has been validated by application to interesting class of systems and its comparison with higher level methods. We have also compared our method with another newly developed analytical noniterative method known as auxiliary density perturbation theory (ADPT)[7,8] implemented in deMon2k software. In this thesis, we present the application of our method for calculation of electric dipoledipole polarizabilities, dipolequadrupole polarizabilities. We have also studied here the frequency dependence and temperature dependence of dipolequdrupole polarizabilities. In one of the chapters we discussed the behaviour of DFT for electric response properties when the molecule is stretched along the bond axis [9]. The dipoledipole and dipolequadrupole polarizabilities calculated with different functional is presented. NIACPKS has been developed only for closed shell systems. In near future we aim to implement this method for application to open shell systems. The methodology for implementation of open shell NIACPKS is presented in this thesis. The geometric derivatives of the polarizabilities are important quantities in calculation of Vabrational Raman Optical Activity (VROA). Thus, we present here the methodology for implementation of geometric derivatives of the dipolequadrupole polarizabilities within ADPT and NIACPKS. The thesis is organized as follows: Chapter 1: General overview and introduction to theoretical method. In chapter one, we briefly review the theoretical methods available for electronic structure calculation. We discuss the wavefunction based methods, HF approximation and methods beyond HatreeFock approximation. This is followed by discussion about the early development of the density matrix theory and KohnSham density functional theory (KSDFT). Then we introduce here electric response properties and different methods available for calculation. We discuss about ADFT and basic structure of the deMon2k programme. We introduce the NIACPKS and ADPT method for calculation of polarizabilities. Chapter 2: Calculation of static dipoledipole polarizability from NIACPKS and its comparison with ADPT. In chapter two, we present a theoretical study of the dipoledipole polarizabilities of free and disubstituted azoarenes employing NIACPKS and its comparison with ADPT. Comparisons are made for disubstituted azoarenes, which shows pushpull mechanism. We study the effect of substitution of electron withdrawing and electron donation group on dipoledipole polarizabilities of azoarene molecules. We present the dipoledipole polarizabilities of these molecules calculated with three different exchangecorrelation functionals and two different auxiliary function sets. The computational advantages of both these methods are discussed here. Chapter 3: Technical details of implementation NIACPKS version of SCP Earlier implementation of NIACPKS was based on CPKS equation system. Here we present the technical details about new implantation of our approach in the framework of SCP method. This implementation is done for calculation of dipoledipole and dipolequadrupole polarizability. The advantages of implementation are discussed here. We briefly discuss the self consistent perturbation theory and ADPT implementation for calculation of perturbed density matrix. The chapter ends with the comparison of NIACPKS and ADPT. Chapter 4: Calculation of dipolequadrupole polarizabilities of tetrahedral molecules. To validate the implementation of newer version of NIACPKS for calculation of dipolequadrupole polarizabilities three tetrahedral molecules have been selected. The comparison between NIACPKS and ADPT results is presented for P4, CH4 and adamantane. We also report MP2 and CCSD results for comparison with our results to validate the methodology of our implementation. We study the basis set dependence of the dipolequadrupole polarizability for selected set of molecules. Chapter 5: Ab initio MD simulation of static and dynamic dipolequadrupole polarizability. The experimental values of dipolequadrupole polarizabilities are measured at higher temperature and frequencies used for calculation. Therefore it is not always feasible to compare static polarizabilities obtained from theoretical methods with experimental results. In our earlier study we have observed the discrepancy between experimental and theoretical values of dipolequadrupole polarizability of adamantane molecule. In this chapter we present the dipolequadrupole polarizabilitie for different frequencies calculated with ADPT method. Molecular dynamic simulation will allow us to study the temperature dependence of these polarizabilities and find the reason of discrepancy of our results from experimental values. Chapter 6: Behaviour of DFT for electric response properties at distorted geometries of molecules. We present here the rigorous calculation of electric response properties at distorted geometries of the molecules. We study here dipoledipole polarizability and dipolequadrupole polarizability for description of role of static and dynamic correlation for electric response properties. The calculations are performed with our new approach, noniterative approximation to coupledperturbed KohnSham method (NIACPKS). These DFT results are compared with higher level ab initio such as CCSD and fully correlated full CI. We report here the dipoledipole polarizability and dipolequadrupole polarizability of HF, BH, H2CO, CO and NO+. We also present the effect of basis and functional on polarizability and dipolequadrupole polarizability. Chapter 7: Conclusions and future tasks This chapter is based on final conclusion of the work presented in this thesis and discussion about the future work. The NIACPKS has been developed only for closed shell systems the extension of this approach for open shell system will facilitate in extending the scope of our method. Thus, the methodology of NIACPKS for UKS and ROKS is presented in this chapter. We also present the methodology to calculate dipoledipole polarizability, dipolequadrupole polarizability and electric–magnetic dipole polarizability derivatives with respect to nuclear coordinate’s to simulation a VROA spectra. References 1. Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. Rev. 1994, 94, 195. 2. Sophy, K.B.; Pal, S. J. Chem. Phys. 2003 118, 10861. 3. Sophy, K.B.; Shedge, S.V.; Pal, S. J. Phys. Chem. A 2008, 112, 11266. 4. Shedge, S. V.; CarmonaEspíndola, J.; Pal, S.; Kӧster, A. M. J. Phys. Chem. A, 2010, 114, 2357. 5. Köster, A. M.; Calaminici, P.; Casida, M. E.; Flores, R.; Geudtner, G.; Goursot, A.; Heine, T.; Janetzko, F. M.; del Campo, J.; Patchkovskii, S.; Reveles, J. U.; Salahub, D. R.; Vela, A. deMon2k, The deMon developers; Cinvestav: Mexico City, Mexico, 2006. See http://www.demonsoftware.com 6. Shedge S. V.; Pal S.; Kӧster A. M. Chem Phys Lett. 2011, 510, 185. 7. FloresMoreno, R.; Köster, A.M. J. Chem. Phys. 2008, 128, 134015. 8. FloresMoreno, R. Ph.D. Thesis, Cinvestav, Mexico City, Mexico, 2006. 9. Shedge, S. V.; Joshi, S. P.; Pal, S. Theor. Chem. Acc. 2011 , 131, 1094
Item Type:  Thesis (PhD) 

Subjects:  Theory and Computational Science Physical Chemistry 
Divisions:  UNSPECIFIED 
Depositing User:  Shedge Sapana Shedge 
Date Deposited:  22 May 2012 06:05 
Last Modified:  26 Jul 2017 09:10 
URI:  http://ncl.csircentral.net/id/eprint/1016 
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