An efficient hybrid scheme for time dependent density functional theory (original) (raw)
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The Journal of Chemical Physics, 2001
An extensive benchmarking of exchange-correlation functionals, pseudopotentials, and basis sets on real X-ray resolved nanoclusters has been carried out and reported here for the first time. The systems investigated and used for the tests are two undecagold and one Au + 24 -based nanoparticles stabilized by thiol and phosphine ligands. Time-dependent density-functional calculations have been performed for comparing results with experimental data on optical gaps. It has been observed that GGA functionals employing PBE-like correlation (viz. PBE itself, BPBE, BP86, and BPW91) coupled with an improved version of the LANL2DZ pseudopotential and basis set provide fairly accurate results for both structure and optical gaps of gold nanoparticles, at a reasonable computational cost. Good geometries have been also obtained using some global hybrid (e.g. PBE0, B3P86, B3PW91) and range separated hybrid (e.g. HSE06, LC-BLYP) functionals, even though they yield optical gaps that constantly overestimate the experimental findings. To probe the effect of the stabilizing organic ligands on the structural and electronic properties of the metal core, we have simulated the full metalorganic nanoparticles (whose diameter exceed the 2 nm threshold) with an ONIOM QM/QM' approach and at the density-functional level of theory. This work represents a first step toward the simulations of structural and opto-electronic properties of larger metal-organic particles suitable for a wide range of nanotechnological applications.
2015
Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) are powerful methods for solving a variety of problems, including ground state electronic structure, electron dynamics, and the absorbance cross section of molecules and materials. DFT is used to calculate the ground state electron configuration, whereas TDDFT is used to solve for the absorption cross section of excited systems. These techniques are not without their challenges. DFT requires the solution of Kohn-Sham orbitals through the diagonalization of the one electron Hamiltonian, which scales as O(N^3) where N signifies the number of orbitals in a simulation. TDDFT has its challenges as well. Each orbital must be propagated every time step, but since a single TDDFT simulation requires thousands of time steps, it is very costly. In this dissertation, we present methods that were developed to circumvent the limitations of DFT and TDDFT.One method for decreasing the cost of DFT and TDDFT is direc...
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.
Chemical Physics, 2010
Almost all time-dependent density-functional theory (TDDFT) calculations of excited states make use of the adiabatic approximation, which implies a frequency-independent exchange-correlation kernel that limits applications to one-hole/one-particle states. To remedy this problem, Maitra et al.[J.Chem.Phys. 120, 5932 (2004)] proposed dressed TDDFT (D-TDDFT), which includes explicit two-hole/two-particle states by adding a frequency-dependent term to adiabatic TDDFT. This paper offers the first extensive test of D-TDDFT, and its ability to represent excitation energies in a general fashion. We present D-TDDFT excited states for 28 chromophores and compare them with the benchmark results of Schreiber et al. [J.Chem.Phys. 128, 134110 (2008).] We find the choice of functional used for the A-TDDFT step to be critical for positioning the 1h1p states with respect to the 2h2p states. We observe that D-TDDFT without HF exchange increases the error in excitations already underestimated by A-TDDFT. This problem is largely remedied by implementation of D-TDDFT including Hartree-Fock exchange.
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...
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
We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4964319\]
A density difference based analysis of orbital-dependent exchange-correlation functionals
Molecular Physics, 2014
We present a density difference based analysis for a range of orbital-dependent Kohn-Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave-function calculations. Particular attention is paid to the quality of approximations to the exchange-only optimized effective potential (OEP) approach: we consider both the Localized Hartree Fock as well as the Krieger-Li-Iafrate methods. Analysis of density differences at the exchange-only level reveals the impact the approximations have on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level an OEP approach based on a perturbative second-order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density-functional approximations.
Efficient computation of the coupling matrix in time-dependent density functional theory
Computer Physics Communications, 2005
We present an efficient implementation of the computation of the coupling matrix arising in time-dependent density functional theory. The two important aspects involved, solution of Poisson's equation and the assembly of the coupling matrix, are investigated in detail and proper approximations are used. Poisson's equation is solved in the reciprocal space and bounded support of the wave functions are exploited in the numerical integration. Experiments show the new implementation is more efficient by an order of magnitude when compared with a standard real-space code. The method is tested to compute optical spectra of realistic systems with hundreds of atoms from first principles. Details of the formalism and implementation are provided and comparisons with a standard real-space code are reported.