Wave function based electronic structure methods have became a robust and reliable tool for the prediction and interpretation of the results of chemical experiments. However, they suffer from very steep scaling behavior with respect to an increase in the size of the system as well as very slow convergence of the correlation energy with respect to the basis set size. Thus these methods are limited to small systems of up to a dozen atoms. The first of these issues can be efficiently resolved by exploiting the local nature of electron correlation effects while the second problem is alleviated by the use of explicitly correlated R12/F12 methods. Since R12/F12 methods are central to this work, we start by reviewing their modern formulation.
Next, we present the explicitly correlated second-order Mo ller-Plesset (MP2-F12) method in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 144}, 144109 (2016)]. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the DLPNO-MP2 method by Neese, Valeev and co-workers [Pinski et al., {em J. Chem. Phys.} {bf 143}, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes) the bigO{N} DLPNO-MP2-F12 method becomes less expensive than the conventional bigO{N^{5}} MP2-F12 for $n$ between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C$_{200}$H$_{402}$, in def2-TZVP basis the observed computational complexity is $N^{sim1.6}$, largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.
We extend this formalism to develop a linear-scaling coupled-cluster singles and doubles with perturbative inclusion of triples and explicitly correlated geminals [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 146}, 174108 (2017)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets; e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster ($sim$186 kcal/mol) is affected by the reduced-scaling approximations by only $sim$0.4 kcal/mol. The reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions.
Additionally, we discuss a massively parallel implementation of the Laplace transform perturbative triple correction (T) to the DF-CCSD energy within density fitting framework. This work is closely related to the work by Scuseria and co-workers [Constans et al., {em J. Chem. Phys.} {bf 113}, 10451 (2000)]. The accuracy of quadrature with respect to the number of quadrature points has been investigated on systems of the 18-water cluster, uracil dimer and pentacene dimer. In the case of the 18-water cluster, the $mu text{E}_{text{h}}$ accuracy is achieved with only 3 quadrature points. For the uracil dimer and pentacene dimer, 6 or more quadrature points are required to achieve $mu text{E}_{text{h}}$ accuracy; however, binding energy of $<$1 kcal/mol is obtained with 4 quadrature points. We observe an excellent strong scaling behavior on distributed-memory commodity cluster for the 18-water cluster. Furthermore, the Laplace transform formulation of (T) performs faster than the canonical (T) in the case of studied systems. The efficiency of the method has been furthermore tested on a DNA base-pair, a system with more than one thousand basis functions.
Lastly, we discuss an explicitly correlated formalism for the second-order single-particle Green's function method (GF2-F12) that does not assume the popular diagonal approximation, and describes the energy dependence of the explicitly correlated terms [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 147}, 121101 (2017)]. For small and medium organic molecules the basis set errors of ionization potentials of GF2-F12 are radically improved relative to GF2: the performance of GF2-F12/aug-cc-pVDZ is better than that of GF2/aug-cc-pVQZ, at a significantly lower cost. / Ph. D. / Chemistry has traditionally been considered an experimental science; however, since the dawn of quantum mechanics, scientists have investigated the possibility of predicting the outcomes of chemical experiments via the use of mathematical models. All molecular properties are encoded in the motion of the electrons, which can be quantitatively described by the many-body Schrödinger equation. However, the Schrödinger equation is too complicated to be solved exactly for realistic molecular systems, and so we must rely on approximations. The most popular way to solve the Schrödinger equation when high accuracy is required are the coupled-cluster (CC) family of methods. These methods can provide unsurpassed accuracy; one particularly accurate and popular method is the coupled-cluster singles and doubles with perturbative inclusion of triples (CCSD(T)) method. The CCSD(T) method is known as the “gold standard” of quantum chemistry, and, when combined with a high quality basis set, it gives highly accurate predictions (that is, close to the experimental results) for a variety of chemical properties. However, this method has a very steep scaling behavior with a computational cost of N⁷ , where N is the measure of the system size. This means that if we double the size of the system, the computation time will increase by roughly two orders of magnitude. Another problem is that this method shows very slow convergence to the complete basis set (CBS) limit. Thus, in order to reduce the basis set error caused by the incompleteness of the basis set, more than 100 basis functions per atom should be used, limiting this method to small systems of up to a dozen atoms. These two issues can be efficiently resolved by exploiting the local nature of electron correlation effects (reduced-scaling techniques) and by using explicitly correlated R12/F12 methods. The main focus of this thesis is to bridge the gap between reduced-scaling techniques and the explicit correlation formalism and to allow highly accurate calculations on large molecular systems with several hundred of atoms. As our first contribution to this field, we present a linear-scaling formulation of the explicitly correlated second-order Møller-Plesset method (MP2-F12) [Pavoŝević et al., J. Chem. Phys. 144, 144109 (2016)]. This is achieved by the use of pair-natural orbitals (PNOs) for the compact representation of the unoccupied space. The method shows near-linear scaling behavior on the linear alkane chains with a computational scaling of N<sup>1.6</sup> for the largest alkane, C₂₀₀H₄₀₂, recovering more than 99.9% of correlation energy. The MP2-F12 method is intrinsically inadequate if high accuracy is required, but our formulation of the linear-scaling MP2-F12 method lays a solid foundation for the accurate linear-scaling explicitly correlated coupled-cluster singles and doubles method with perturbative inclusion of triples (PNO-CCSD(T)-F12) [Pavoŝević et al., J. Chem. Phys. 146, 174108 (2017)]. We have demonstrated that the PNO-CCSD(T)-F12 method shows a near-linear scaling behavior of N<sup>1.5</sup> . The error introduced by reduce-scaling approximations is only 0.4 kcal/mol of the binding energy with respect to the canonical result in the case of a 20-water cluster which is much lower than the required chemical accuracy defined as 1 kcal/mol. Furthermore, the reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding ener- gies of large molecular systems that are far beyond the reach of the conventional CCSD(T) method. Our prediction of the binding energy for of the coronene dimer is the most accurate theoretical estimate of binding energy of the coronene dimer to this date. Such a system is an example of an organic semiconductor used for light conversion. However, the modeling of light harvesting materials requires an accurate knowledge of ionization potentials (IP) and electron affinities (EA). We describe [Pavoŝević et al., J. Chem. Phys. 147, 121101 (2017)] how to incorporate an explicit correlation correction into the Green’s function formalism (GF2) that is used for the calculation of IPs. We show that the GF2-F12 method removes errors associated with the basis sets, allowing extremely accurate predictions of IPs to be made at a significantly lower cost than the parent GF2 method. The work presented in this thesis will set a stage for further developments in reduced-scaling explicitly correlated methods. Furthermore it will be a useful benchmarking method for parametrizing the popular DFT functionals making accurate predictions of the relative stability of different forms of pharmaceuticals. Due to the simplicity and generality of the GF2-F12 method, it has the potential to be used to augment more accurate Green’s function methods, such as NR2, allowing for the accurate prediction of IPs and EAs of large molecular and periodic systems.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/82000 |
| Date | 02 February 2018 |
| Creators | Pavosevic, Fabijan |
| Contributors | Chemistry, Valeyev, Eduard Faritovich, Madsen, Louis A., Troya, Diego, Crawford, T. Daniel |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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