First-principles linear combination of atomic orbitals method for the cohesive and structural properties of solids: Application to diamond

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Abstract
We present a new method for the ab initio calculation of the cohesive and structural properties of solids. The method is based upon a linear combination of atomiclike orbitals (LCAO). Thus it possesses the physical appeal of traditional LCAO approaches. The method is a "first principles" one in the sense that no adjustable parameters enter the calculation. The required overlap integrals are calculated directly in real space. The one-electron potentials are derived from atomic properties and correspond to "ab initio" pseudopotentials. Another aspect of the method is that it does not involve a fully-self-consistent-field solution of the Schrödinger equation. Rather, the total energy of the system is obtained by using a noniterative approach based explicitly on the variational principle in the density-functional formalism. The method is applied to an archtypical covalent system: the diamond crystal. Several ground-state properties—including the cohesive energy, lattice constant, the bulk modulus, and the derivative of the bulk modulus with pressure—are computed. The computed lattice constant and bulk modulus are within 1-2% of the experimental values and the computed cohesive energy is within 10% of the experimental value. Also, we present a frozen-phonon calculation for the optical phonons at the Brillouin-zone center and obtain agreement to within 1% of the experimental value.