# Analytic gradients for natural orbital functional theory.

@article{Mitxelena2016AnalyticGF, title={Analytic gradients for natural orbital functional theory.}, author={Ion Mitxelena and Mario Piris}, journal={The Journal of chemical physics}, year={2016}, volume={146 1}, pages={ 014102 } }

The analytic energy gradients with respect to nuclear motion are derived for the natural orbital functional (NOF) theory. The resulting equations do not require resorting to linear-response theory, so the computation of NOF energy gradients is analogous to gradient calculations at the Hartree-Fock level of theory. The structures of 15 spin-compensated systems, composed of first- and second-row atoms, are optimized employing the conjugate gradient algorithm. As functionals, two orbital-pairing…

## 7 Citations

### Analytic gradients for spin multiplets in natural orbital functional theory.

- PhysicsThe Journal of chemical physics
- 2020

A single evaluation is required, so integral derivatives can be computed on-the-fly along the calculation, thus improving the effectiveness of screening by the Schwarz inequality.

### Analytic second-order energy derivatives in natural orbital functional theory

- ChemistryJournal of Mathematical Chemistry
- 2018

The analytic energy gradients in the atomic orbital representation have recently been published (Mitxelena and Piris in J Chem Phys 146:014102, 2017) within the framework of the natural orbital…

### Advances in approximate natural orbital functional theory

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### Analytical nuclear derivatives for the parametric two-electron reduced density matrix method

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### Analytical gradients of variational reduced-density-matrix and wavefunction-based methods from an overlap-reweighted semidefinite program.

- ChemistryThe Journal of chemical physics
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The analytical gradients of variational 2-RDM methods are applied to perform geometry optimizations on several transition metal complexes, octahedral and trigonal prismatic CrF6 as well as the (ethylene-1,2-dithiolato)nickel, or Ni(edt)2, complex.

### Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units

- Computer ScienceJournal of Chemical Theory and Computation
- 2022

Efficient integral-direct methods are derived and benchmarked for various approximate functionals, including improved methods for calculating diagonal elements of the two-electron integral tensor as required in self-interaction-corrected functionals and second derivatives of the energy with respect to the occupation numbers.

### DoNOF: An open-source implementation of natural-orbital-functional-based methods for quantum chemistry

- PhysicsComput. Phys. Commun.
- 2021

## References

SHOWING 1-10 OF 91 REFERENCES

### Spin conserving natural orbital functional theory.

- Physics, ChemistryThe Journal of chemical physics
- 2009

The natural orbital functional theory is considered for spin uncompensated systems, i.e., systems that have one or more unpaired electrons and a new condition to ensure the conservation of the total spin is obtained for the two-particle cumulant matrix.

### Molecular electric moments calculated by using natural orbital functional theory.

- ChemistryThe Journal of chemical physics
- 2016

The calculated PNOF6 electric moments agree satisfactorily with the corresponding experimental data and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles and multi-reference single and double excitation configuration interaction methods.

### Analytic energy gradient for the projected Hartree-Fock method.

- ChemistryThe Journal of chemical physics
- 2014

The analytic energy gradient for the symmetry Projected Hartree-Fock (PHF) method avoiding the solution of coupled-perturbed HF-like equations is derived and implemented, despite the elaborate multi-reference character of the PHF wave function.

### On the evaluation of analytic energy derivatives for correlated wave functions

- Physics
- 1984

It is shown that to obtain the (2n)th and (2n+1)th energy gradients, it is only necessary to solve equations of the difficulty of the nth order coupled perturbed equations for the orbital and…

### Interacting pairs in natural orbital functional theory.

- ChemistryThe Journal of chemical physics
- 2014

An interacting-pair model is considered to attain a new natural orbital functional (NOF) that belongs to the JKL-only family of NOFs, and is superior to its predecessor, PNOF5, which is an independent-pair approach.

### Analytic configuration interaction (CI) gradient techniques for potential energy hypersurfaces. A method for open-shell molecular wave functions

- Chemistry
- 1981

A formalism is presented for the determination of analytic energy first derivatives for the most common types of open‐shell correlated wave functions. These are the cases for which the electronic…

### Natural orbital functional for correlation in polymers

- Physics
- 2005

We extend a natural orbital functional to calculate correlation energies for periodic polymers. We generalize the proposed correlation matrix in a two-particle reduced density matrix to achieve a…

### Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems.

- ChemistryThe Journal of chemical physics
- 2007

We report a method for the efficient evaluation of analytic energy second derivatives with respect to in-phase nuclear coordinate displacements within Hartree-Fock and Kohn-Sham density functional…

### Communication: The role of the positivity N-representability conditions in natural orbital functional theory.

- ChemistryThe Journal of chemical physics
- 2010

The positivity conditions for the N-representability of the reduced density matrices are considered and a new natural orbital functional, Piris Natural Orbital Functional 4 (PNOF4), is proposed, applied to the dissociation of selected diatomic molecules.

### Perspective on natural orbital functional theory

- Chemistry
- 2014

The natural orbital functional (NOF) theory is briefly reviewed. The meaning of the top-down and bottom-up approaches for the construction of a NOF is analyzed. A particular reconstruction of the…