Molecular Electronic‐Structure Theory

Helgaker, Trygve; Jørgensen, Poul; Olsen, Jeppe

doi:10.1002/9781119019572

Cited by 2,671 publications

(3,425 citation statements)

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“…ERKALE operates with a basis set consisting of segmented contractions of GTOs [20,23] in either cartesian [Eqs.…”

Section: Basis Setmentioning

confidence: 99%

“…(3) are spherical harmonics in the real form,r denoting the unit vector in the direction of r. The functions Y LM can be expressed as a sum of the cartesian functions of the same shell. [23] All operations with basis functions, such as evaluation of the basis functions at a point, are performed on a shell basis in ERKALE.…”

Section: Basis Setmentioning

confidence: 99%

“…[21,22] The main drawback of the Gaussian basis set is its incorrect asymptotic behavior, notably the violation of the nuclear cusp condition and the asymptotic decay that is too fast. [23] Slatertype orbital (STO) basis sets do not have these shortcomings and can also be used to perform HF and hybrid DFT calculations when suitable fitting algorithms are used, [24,25] but a greater number of integrals need to be performed using purely numerical quadrature. This approach has been chosen in the commercial ADF code.…”

Section: Introductionmentioning

confidence: 99%

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ERKALE—A flexible program package for X‐ray properties of atoms and molecules

et al. 2012

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ERKALE is a novel software program for computing X-ray properties, such as ground-state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree-Fock or density-functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange-correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes.

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“…ERKALE operates with a basis set consisting of segmented contractions of GTOs [20,23] in either cartesian [Eqs.…”

Section: Basis Setmentioning

confidence: 99%

Section: Basis Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ERKALE—A flexible program package for X‐ray properties of atoms and molecules

et al. 2012

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“…The full configuration interaction (FCI) method [16] diagonalizes the molecular Hamiltonian to provide solutions to the electronic structure problem that are exact within this basis. FCI scales exponentially with respect to the size of the molecular system studied and therefore is restricted to the treatment of small diatomic and triatomic systems [17].…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for obtaining the energy spectrum of molecular systems

Wang

Kais

Aspuru‐Guzik

et al. 2008

Phys. Chem. Chem. Phys.

119

143

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Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the wellknown result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multi-configurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible; Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

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“…It is well-known, however, that DFT with standard functionals frequently fail to accurately describe noncovalent interactions, especially dispersion. 35 Though many dispersion-related DFT methods 4,[36][37][38][39][40][41][42][43][44][45] have been exploited and successfully applied recently to typical noncovalent systems, 46 it has been shown that the predictive power strongly depends on the target system. That is, a DFT functional which works well for some specific noncovalent system does not necessarily give good results in another.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

Hongo

Watson

Iitaka

et al. 2015

J. Chem. Theory Comput.

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We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of p-DIB molecular crystal polymorphism. [J. Phys. Chem. Lett. 2010Lett. , 1, 1789Lett. -1794 We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest which are currently feasible using the resources of the K computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1×1×1) simulation cell considerably. We therefore repeated our DMC simulations with a 1×3×3 simulation cell, which is the largest such calculation to date. We used a DFT nodal surface generated with the PBE functional and we accumulated statistical samples with ∼ 6.4 × 10 5 core-hours for each polymorph. Our final results predict a polymorph stability consistent with experiment, but indicate that results in our previous paper were somewhat fortuitous.We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are far larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T -move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.

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Molecular Electronic‐Structure Theory

Cited by 2,671 publications

References 0 publications

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

Quantum algorithm for obtaining the energy spectrum of molecular systems

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

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