Polarized atomic orbitals for linear scaling methods

Self Cite

3,439

2,672

(2007). Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. The Journal of Chemical Physics, 127 (11) Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases AbstractWe present a library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory. It targets a wide range of chemical environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition number of the overlap matrix for a set of molecules with respect to the exponents and contraction coefficients of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations. We present a library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory. It targets a wide range of chemical environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition number of the overlap matrix for a set of molecules with respect to the exponents and contraction coefficients of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small ͑down to 0.2 kcal/ mol͒ basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations. Gaus...

Section: Introductionsupporting

confidence: 73%

Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases

VandeVondele

Hutter

2007

Self Cite

3,439

2,672

“…The scaling of cost vs. basis size is largely independent of the development of linear scaling (with system size) Fock build algorithms [39][40][41][42][43][44][45] and many diagonalization replacements 46,47 . Moreover, near-complete basis sets are not favored by linear-scaling algorithms, especially when diffuse functions are included, since matrix element sparsity is diminished and the overlap matrix starts to be ill-conditioned, which in turn destroys the sparsity of the density matrix 48,49 . One successful strategy to make large basis KS-DFT calculations more tractable is to compute the full Coulomb (J) and exchange (K) matrices more efficiently by approximating two-electron repulsion integrals (ERIs) with the aid of auxiliary basis functions or grid points.…”

Section: Kohn-sham Density Functional Theorymentioning

confidence: 99%

“…The PAO-SCF energy can be improved using perturbation theory 86 , similar to the dual basis approaches discussed above. The minimal rank of the PAO basis and its atomic locality makes it promising for linearscaling algorithms 49 , but the "double" optimization problem is challenging.…”

Section: Kohn-sham Density Functional Theorymentioning

confidence: 99%

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Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

Mao

Horn

Mardirossian

et al. 2016

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large basis sets are used. To approach the basis set limit with potentially lower costs, a new SCF scheme with minimal adaptive basis (MAB) functions variationally optimized on each atomic site is presented, and the desired accuracy can be obtained by applying a perturbative correction (PC). Compared to exact SCF results, using this MAB-SCF (PC) approach with the same target basis set produces < 0.15 kcal/mol RMS errors for most of the tested TC datasets, and < 0.1 kcal/mol for most of the NCs. The performance of density functionals near the basis set limit can be well reproduced with slight discrepancies. With further improvement to its implementation, MAB-SCF (PC) could be a promising substitute for its conventional counterpart to viably approach the basis set limit of modern density functionals.

“…͑18͒. Although these basis sets have mainly been used in linearscaling calculations in extended molecules, 23,30 as minimal basis sets, they function in this work primarily as a nonorthogonal basis for the and active spaces in the polyenes. Now, the PAOs are only defined up to a unitary transformation that mixes the orbitals on a given atom.…”

Section: The Polyene Seriesmentioning

confidence: 99%

Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes

Chan

Voorhis

2005

We describe the theory and implementation of two extensions to the density-matrix renormalization-group ͑DMRG͒ algorithm in quantum chemistry: ͑i͒ to work with an underlying nonorthogonal one-particle basis ͑using a biorthogonal formulation͒ and ͑ii͒ to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.