Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations. I
15 Aug 1968-Journal of Chemical Physics (American Institute of Physics)-Vol. 49, Iss: 4, pp 1719-1729
TL;DR: In this article, the Hartree-Fock wave function was used as an approximate wave function for the direct calculation of force constants and dipole-moment derivatives from SCF-MO wavefunctions.
Abstract: General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂φi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.
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TL;DR: In this paper, the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method, is reviewed.
Abstract: This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.
6,917 citations
Cites methods from "Force Constants and Dipole-Moment D..."
...In the specific context of the Hartree-Fock approximation, the resulting algorithm is called the coupled Hartree-Fock method (Gerratt and Mills, 1968)....
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...Similar methods are known in the quantum chemistry literature under the generic name of analytic evaluation of second-order energy derivatives (Gerratt and Mills, 1968; Amos, 1987)....
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TL;DR: In this paper, a modified conjugate gradient algorithm for geometry optimization is presented for use with ab initio MO methods, where the second derivative matrix rather than its inverse is updated employing the gradients.
Abstract: A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initioSCF–MO calculations.
3,373 citations
TL;DR: The construction of transferable, hierarchical basis sets are demonstrated, allowing the calculation to range from qualitative tight-binding like accuracy to meV-level total energy convergence with the basis set, since all basis functions are strictly localized.
2,178 citations
TL;DR: In this article, it is suggested that force constants should be calculated by differentiating the forces numerically, which is numerically more accurate and requires less computation than the customary one of differentiating energy numerically twice.
Abstract: The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested that force constants should be calculated by differentiating the forces numerically. This method, called the force method, is numerically more accurate and requires less computation than the customary one of differentiating the energy numerically twice. It permits the quick determination of the equilibrium geometry by relaxing the nuclear coordinates until the forces vanish. The unreliability of the methods using the Hellmann-Feynman forces is re-emphasized. The question of which force constants can be best calculated ab initio is discussed.
2,106 citations
TL;DR: In this paper, a noniterative triples correction to the coupled-cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non-Hartree-Fock (non-HF) reference functions.
Abstract: A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...
1,812 citations
References
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Book•
01 Jan 1954
TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.
Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.
7,756 citations
4,691 citations
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TL;DR: In this article, it was shown that the force on a nucleus in an atomic system is just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution.
Abstract: Formulas have been developed to calculate the forces in a molecular system directly, rather than indirectly through the agency of energy. This permits an independent calculation of the slope of the curves of energy vs. position of the nuclei, and may thus increase the accuracy, or decrease the labor involved in the calculation of these curves. The force on a nucleus in an atomic system is shown to be just the classical electrostatic force that would be exerted on this nucleus by other nuclei and by the electrons' charge distribution. Qualitative implications of this are discussed.
2,832 citations
1,673 citations