We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Chemistry with ADF

Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

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Advanced capabilities for materials modelling with Quantum ESPRESSO.

Gaussian-type orbital and auxiliary basis sets have been optimized for local spin density functional calculations This first paper deals with the atoms boron through neon Subsequent papers will provide a list through xenon The basis sets have been tested for their ability to give equilibrium geometries, bond dissociation energies, hydrogenation energies, and dipole moments These results indicate that the present optimization technique yields reliable basis sets for molecular calculations Keywords: Gaussian basis sets, density functional theory, boron–neon, geometries, energies of reactions

Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation

We report the implementation of time‐dependent density‐functional response theory (TD‐DFRT) for molecules using the time‐dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density‐functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Karna and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency‐dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N2 are found to be in good agreement with experiment and with results from other ab initio methods.

Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N2 as a case study

New algorithm for the optimization of geometries in local density functional theory

As a test of the applicability of the density functional theory to systems containing hydrogen bonds, linear combination of Gaussian type orbitals-local density calculations have been performed on two intermolecular and two intramolecular hydrogen-bonded systems. A comparison is made of results using the local density approximation (LDA) and those including nonlocal density gradient type corrections, using two different nonlocal functionals. The calculated minimum energy structures for the water dimer and the formamid-water complex are presented

Dennis R. Salahub

Papers

Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation

Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N2 as a case study

New algorithm for the optimization of geometries in local density functional theory

Gaussian density functional calculations on hydrogen-bonded systems

Nuclear magnetic resonance shielding tensors calculated with a sum-over-states density functional perturbation theory