Reply to the Comments of M. S. Sodha and C. J. Palumbo

Mapping between local potentials and ground state densities

“…To make further progress, we specialize our consideration to a finite-dimensional vector space. The discrete matrix version of the Hohenberg-Kohn theorem can be formulated as follows [6,7]. We consider a Hamiltonian matrix of the form Assuming a Pauli-like single occupancy restriction for each orbital, we obtain for the ground state of n (noninteracting) particles the density p = (Pk), where n pk = C C ; k ,…”

From Proteins and Protein Models to Their Use in Immunology and Immunotherapy

“…Poly-DL-alanyl trypsin, with an average polyalanine chain length of 6 -9 residues, was resistant to autolysis at temperatures up to 38°C and reacted normally with soybean and serum inhibitors. Poly-DL-alanyl chymotrypsin had similar stability and activity properties (18). Several years later, Roger Acher visited us from Paris and investigated poly-DL-alanyl Kunitz trypsin inhibitor (19).…”

“…During my second stay at the NIH (1960 -1961), I continued studies on oxidation of reduced ribonuclease (15) and started investigating the enzymatic properties of poly-DL-alanyl derivatives of ribonuclease (16,17), trypsin, and chymotrypsin (18). Alanylated ribonuclease with as many as 4 or 5 alanine residues per chain kept its enzymatic activity and regenerated its full activity after reduction of its disulfide bridges and subsequent reoxidation (16).…”

Stability of finite subspaces in density functional theory: Application to simple atoms

“…It must be mentioned that the latter is not to be considered merely an academic question since the validity of the first HK theorem in finite subspaces is of paramount importance in two particular aspects related to the development and practical application of DFT: (1) it has to be acknowledged, on the one hand, that most DFT approaches (eg, electronic structure calculations) are usually performed in a subspace of the Hilbert space that emerges because the Kohn-Sham N-particle wave function is constructed from Kohn-Sham orbitals, which in turn, are expanded in terms of a finite basis set of well-defined single-particle functions; and, on the other hand, (2) the fulfillment of the first HK theorem is a fundamental requirement for the formulation of the second HK theorem, which states that the exact ground-state energy of an N-Fermion system can be computed by minimizing a universal energy functional solely expressed in terms of 1-electron density, an idea that allows the design and implementation of computational algorithms.When extending the HK first theorem to finite subspaces, particular attention must be paid to the stability conditions that the subspace must satisfy in order to guarantee the fulfillment of this theorem. Some of these restrictions have been given by Epstein et al, [35] Katriel et al, [36] Harriman, [37] and more recently by Pino et al [38,39] According to Pino et al, one way to satisfy these conditions in a finite subspace is to have DV, defined asĤ v 0 2Ĥ v V 0 2V, equal to a constant. However, it must be considered that there may be instability potentials (ie, DV 6 ¼ constant) that violate the subspace stability conditions, meaning that in a finite subspace, one can have external potentials V 0 and V that differ from each other by more than a constant and which still lead to the same 1-particle density.…”