Localized-density-matrix method and its application to nanomaterials

Chen, Guanhua; Yokojima, Satoshi; Liang, WanZhen; Wang, XiuJun

doi:10.1351/pac200072010281

Cited by 3 publications

(4 citation statements)

References 40 publications

(47 reference statements)

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“…This technique has been extensively employed to extract absorption spectroscopy in time-domain methods. 4,6,27 It is an important and complicated problem to choose a proper propagation method in time-domain TDDFT. 5 Here we focus on demonstrating the feasibility and accuracy of our method, and use the 4-order Runge-Kutta method to propagate the equation of motion.…”

Section: B D-perturbation On Mos and Time Propagation Schemementioning

confidence: 99%

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Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cui

Fang

Yang

2010

Phys. Chem. Chem. Phys.

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Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio-and nano-systems.

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Section: B D-perturbation On Mos and Time Propagation Schemementioning

confidence: 99%

“…Its extensive applications are the best examples. 4,6,27,28,32 We here focus on NOLMO, which is the most localized representation of electron because the localized molecular orbitals, which are linear independent, need not be orthogonal. The absence of orthogonality constraints allows the molecular orbitals to be the most localized ones.…”

Section: Introductionmentioning

confidence: 99%

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cui

Fang

Yang

2010

Phys. Chem. Chem. Phys.

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“…Most linear scaling methods have been developed with OLMOs, − e.g. the local space approximation method , and the elongation method. − The applications of these methods to large systems, such as nanomaterials or biological systems, show their success. − Using OLMOs keeps the equations of the wave function and Fock operators almost unchanged compared to ones of CMOs, while OLMOs possess long-range nonlocalized tails, outside the localization center, which is a detriment to computational efficiency and complicates the transferability of the descriptions of LMOs from one system to another.…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Coupled Perturbed Hartree–Fock and Density-Functional-Theory Approach for Calculating Frequency-Dependent (Hyper)Polarizabilities with Nonorthogonal Localized Molecular Orbitals

Peng

et al. 2017

J. Chem. Theory Comput.

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The time-dependent coupled perturbed Hartree-Fock/density-functional-theory (TDHF/TDDFT) approach has been reformulated based on nonorthogonal localized molecular orbitals (NOLMOs). Based on the NOLMO Fock equation, we have derived the corresponding NOLMO-TDHF/TDDFT equations up to the third order, and the formula for the frequency-dependent (hyper)polarizabilities has been given. Our approach has been applied to calculate both static and dynamic (hyper)polarizabilities of molecules varying from small molecules to large molecules. The NOLMO-TDHF/TDDFT approach can reproduce the reference canonical molecular orbital (CMO) results for all of our testing calculations. With the help of ongoing development of optimized local virtual molecular orbitals, the NOLMO-TDHF/TDDFT approach would be a very efficient method for large system calculations and tp achieve linear scaling.

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“…There are two types of LMOs: one is the extensively investigated orthogonal LMOs (OLMOs), and the other is the nonorthogonal LMOs (NOLMOs). As the OLMOs generation from CMOs has been largely explored, − many (nearly) linear-scaling methods have been developed with this basis, e.g., the local space approximation given by Kirtman et al , and the elongation method proposed by Imamura et al − These methods have been widely used on investigating large systems, e.g., nanomaterials or biological systems. − Moreover, another reason for using OLMOs in these methods is that the orthogonal properties among the LMOs keep the equations of the wave function and Fock/KS operators almost unchanged. This results in a relatively convenient implementation of computer code.…”

Section: Introductionmentioning

confidence: 99%

Coupled-Perturbed SCF Approach for Calculating Static Polarizabilities and Hyperpolarizabilities with Nonorthogonal Localized Molecular Orbitals

Peng

et al. 2015

J. Chem. Theory Comput.

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Coupled-perturbed self-consistent-field (CPSCF) approach has been broadly used for polarizabilities and hyperpolarizabilities computation. To extend this application to large systems, we have reformulated the CPSCF equations with nonorthogonal localized molecular orbitals (NOLMOs). NOLMOs are the most localized representation of electronic degrees of freedom. Methods based on NOLMOs are potentially ideal for investigating large systems. In atomic orbital representation, with a static external electric field added, the wave function and SCF operator of unperturbed NOLMO-SCF wave function/orbitals are expanded to different orders of perturbations. We have derived the corresponding equations up to the third order, which are significantly different from those of a conventional CPSCF method because of the release of the orthogonal restrictions on MOs. The solution to these equations has been implemented. Several chemical systems are used to verify our method. This work represents the first step toward efficient calculations of molecular response and excitation properties with NOLMOs.

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Localized-density-matrix method and its application to nanomaterials

Cited by 3 publications

References 40 publications

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Time-Dependent Coupled Perturbed Hartree–Fock and Density-Functional-Theory Approach for Calculating Frequency-Dependent (Hyper)Polarizabilities with Nonorthogonal Localized Molecular Orbitals

Coupled-Perturbed SCF Approach for Calculating Static Polarizabilities and Hyperpolarizabilities with Nonorthogonal Localized Molecular Orbitals

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