Development of Methods for Reducing the Cost of Density Functional Theory and Time-Dependent Density Functional theory (original) (raw)
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Time-dependent density functional theory employing optimized effective potentials
The Journal of Chemical Physics, 2002
Exchange-only ab initio ͑parameter-free͒ time-dependent density functional calculations for the vertical excitation energies of atoms and polyatomic molecules are performed by employing optimized effective potentials ͑OEP's͒ and their corresponding adiabatic exchange kernels for the first time. Accurate OEP's are obtained by a novel linear-combination-of-atomic-orbital ͑LCAO͒ algorithm ͓R. Colle and R. K. Nesbet, J. Phys. B 34, 2475 ͑2001͔͒ in which a potential is represented as a sum of a seed potential having the correct Ϫ1/r asymptotic behavior and a small and rapidly decaying correction, the latter being approximated accurately by a linear combination of Gaussian functions. The time-dependent OEP ͑TDOEP͒ methods with and without the Tamm-Dancoff approximation are implemented by using a trial-vector algorithm, which allows us to avoid the storage or manipulation of transformed two-electron integrals or the diagonalization of large matrices. No approximation is made to TDOEP, besides the adiabatic approximation to the exchange kernel, the LCAO expansion of the orbitals and potentials, and occasionally the Tamm-Dancoff approximation. The vertical excitation energies of the beryllium atom and the nitrogen and water molecules calculated by TDOEP are compared with those obtained from time-dependent density functional theory ͑TDDFT͒ employing conventional local or gradient-corrected functionals, configuration interaction singles ͑CIS͒, time-dependent Hartree-Fock ͑TDHF͒ theory, similarity-transformed equation-of-motion coupled-cluster with single and double substitutions, and experiments. TDOEP, which neglects electron correlation while treating the exchange contribution rigorously within the Kohn-Sham DFT framework, performs equally well as, or even appreciably better than, CIS or TDHF. The slightly better performance of TDOEP might be attributed to the local nature of the exchange potentials that allows the bare orbital energy differences to approximate excitation energies well. Nevertheless, TDDFT employing local or gradient-corrected functionals outperforms TDOEP for low-lying valence excited states, implying that the former somehow accounts for electron correlation effectively, whereas for high-lying and Rydberg excited states, the latter performs better than the former. By combining the desirable features of OEP and local or gradient-corrected exchange-correlation potentials, we arrive at a simple asymptotic correction scheme to the latter. TDDFT with the asymptotic correction yields uniformly accurate excitation energies for both valence and Rydberg excited states.
Multiscale Simulation Methods for Nanomaterials, 2007
Fullerene like cages and naonotubes of carbon and other inorganic materials are currently under intense study due to their possible technological applications. First principle simulations of these materials are computationally challenging due to large number of atoms. We have recently developed a fast, variational and fully analytic density functional theory (ADFT) based model that allows study of systems larger than those that can be studied using existing density functional models. Using polarized Gaussian basis sets (6-311G**) and ADFT, we optimize geometries of large fullerenes, fullerene-like cages and nanotubes of carbon, boron nitride, and aluminum nitride containing more than two thousand atoms. The calculation of C2160 using nearly 39000 orbital basis functions is the largest calculation on any isolated molecule reported to-date at this level of theory, and it includes full geometry optimization. The electronic structure related properties of the inorganic cages and other carbon fullerenes have been studied. Computer simulations are playing increasingly important role in our understanding about materials. Generally, the choice of computational models that are employed in studying the properties of materials depend on the property of interest and the length scale or the size of the system[1]. The latter is the most important factor in the selection of appropriate level of theory. Our interest is in the electronic and structural properties of large carbon fullerenes and fullerene like cages of aluminum and boron nitride containing a few hundred atoms. At these sizes, the current toolbox of methods that are available include semiempirical quantum mechanical models such as ZINDO[2], PM3[3] methods or tight binding approaches[4]. More accurate description of electronic properties require use of more involved meth- * Electronic address: rzope@alchemy.nrl.navy.mil † Electronic address: dunlap@nrl.navy.mil
The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field (CASSCF) methods are deficient in their ability to describe dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we describe the hole-hole Tamm- Dancoff approximated (hh-TDA) density functional theory method, which is closely related to the previously established particle-particle random phase approximation (pp-RPA) and its TDA variant (pp-TDA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical inters...
Progress in Time-Dependent Density-Functional Theory
Annual Review of Physical Chemistry, 2012
The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the...
An efficient hybrid scheme for time dependent density functional theory
The Journal of Chemical Physics, 2020
A hybrid approach able to perform Time Dependent Density Functional Theory (TDDFT) simulations with the same accuracy as that of hybrid exchange-correlation (xc-) functionals but at a fraction of the computational cost is developed, implemented, and validated. The scheme, which we name Hybrid Diagonal Approximation (HDA), consists in employing in the response function a hybrid xc-functional (containing a fraction of the non-local Hartree-Fock exchange) only for the diagonal elements of the omega matrix, while the adiabatic local density approximation is employed for the off-diagonal terms. HDA is especially (but not exclusively) advantageous when using Slater type orbital basis sets and allows one to employ them in a uniquely efficient way, as we demonstrate here by implementing HDA in a local version of the Amsterdam Density Functional code. The new protocol is tested on NH 3 , C 6 H 6 , and the [Au 25 (SCH 3) 18 ] − cluster as prototypical cases ranging from small molecules to ligand-protected metal clusters, finding excellent agreement with respect to both full kernel TDDFT simulations and experimental data. Additionally, a specific comparison test between full kernel and HDA is considered at the Casida level on seven other molecular species, which further confirm the accuracy of the approach for all investigated systems. For the [Au 25 (SCH 3) 18 ] − cluster, a speedup by a factor of seven is obtained with respect to the full kernel. The HDA, therefore, promises to provide a quantitative description of the optical properties of medium-sized systems (nanoclusters) at an affordable cost, thanks to its computational efficiency, especially in combination with a complex polarization algorithm version of TDDFT.
New Orbital-Free Approach for Density Functional Modeling of Large Molecules and
2016
Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms. Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic table rows show a good accordance with the Kohn-Sham DFT results.
A new density functional method for electronic structure calculation of atoms and molecules
arXiv: Chemical Physics, 2019
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradi...
Journal of Chemical Theory and Computation, 2015
During the last two decades density functional based linear response approaches have become the de facto standard for the calculation of optical properties of small and medium-sized molecules. At the heart of these methods is the solution of an eigenvalue equation in the space of single-orbital transitions, whose quickly increasing number makes such calculations costly if not infeasible for larger molecules. This is especially true for time-dependent density functional tight binding (TD-DFTB), where the evaluation of the matrix elements is inexpensive. For the relatively large systems that can be studied the solution of the eigenvalue equation therefore determines the cost of the calculation. We propose to do an oscillator strength based truncation of the single-orbital transition space to reduce the computational effort of TD-DFTB based absorption spectra calculations. We show that even a sizeable truncation does not destroy the principal features of the absorption spectrum, while naturally avoiding the unnecessary calculation of excitations with small oscillator strengths. We argue that the reduced computational cost of intensity-selected TD-DFTB together with its ease of use compared to other methods lowers the barrier of performing optical properties calculations of large molecules, and can serve to make such calculations possible in a wider array of applications.