We anticipate that future research on quantum-sized nanoclusters will stimulate broad scientific and technological interests in this special type of metal nanomaterial.”
“Just as Newtonian law governs classical physics, the Schrodinger equation Nilotinib mw (SE) and the relativistic Dirac equation (DE) rule the world of chemistry. So, if we can solve these equations accurately, we can use computation to predict chemistry precisely. However, for approximately 80 years after the discovery of these equations, chemists believed that they could not solve SE and DE for atoms and molecules that included many electrons. This Account reviews ideas developed over the past decade to further the goal of predictive quantum chemistry.
Between 2000 and 2005, I discovered a general method of solving the SE and DE accurately.
As a first inspiration, I formulated the structure Inhibitors,Modulators,Libraries of the exact wave function of the SE in a compact mathematical form. The explicit inclusion of the exact wave function’s structure within the variational space allows for the calculation of the exact wave function as a solution of the variational method. Although this process sounds almost impossible, it is indeed possible, and I have published several formulations and applied them to solve the full configuration interaction (CI) with a very small number of variables. However, when I examined analytical solutions for atoms and molecules, the Hamiltonian integrals in their secular equations diverged. This singularity problem occurred in all atoms and molecules because it originates from the singularity of the Coulomb potential in their Hamiltonians.
Inhibitors,Modulators,Libraries Inhibitors,Modulators,Libraries To overcome this problem, I first introduced the inverse SE and then the scaled SE. The latter simpler idea led to immediate and surprisingly accurate solution for the SEs of the hydrogen atom, helium atom, and hydrogen molecule.
The free complement (FC) method, also called the free iterative CI (free ICI) method, was efficient for solving the SEs. In the FC method, the basis functions that Inhibitors,Modulators,Libraries span the exact wave function are produced by the Hamiltonian of the system and the zeroth-order wave function. Anacetrapib These basis functions are called complement functions because they are the elements of the complete functions for the system under consideration. We extended this idea to solve the relativistic DE and applied it to the hydrogen and helium atoms, without observing any problems such as variational collapse.
Thereafter, we obtained very accurate solutions of the SE for the ground and excited states of the Born-Oppenheimer (BO) and non-BO states of very small systems like He, H-2(+), H-2, and their analogues. For larger systems, however, the overlap and Hamiltonian integrals over the complement functions are sellekchem not always known mathematically (integration difficulty); therefore we formulated the local SE (LSE) method as an integral-free method.