Can chemistry be derived from quantum mechanics? Chemical dynamics and structure

Abstract

Following an early suggestion by Dirac, contemporary quantum mechanics (QM) and measurement theory are used to stepwise construct a conceptual framework to chemistry. In QM arbitrary physical quantum states are represented by linear superpositions. Base sets and quantum states are clearly distinguished; the latter are sets of ordered complex numbers. The generator of time evolution $$\fancyscript{H}$$ is shown to have besides the molecular hamiltonian H=H C+K N, the electron–phonon and spin–orbit operators.H is shown diagonal in a product base set formed with generalized electronic diabatic (GED) and nuclear wave functions; the latter represented in a plane wave base set and unique inertial frame; these functions form the GEDM base set. Chemical species are assigned to particular GED base functions and a chemical quantum state is given as a linear superposition in the GEDM base set. Thus, given a fixed number of electrons and nuclei, the GEDM base set includes all electronuclear quantum states from clusters, supermolecule, molecular aggregates, asymptotic states, and ionized states (continuum electron states) to all plasma states. Experimentally measurable quantum states are given by linear superpositions. A chemical process is sensed by amplitude changes involving different electronic states in the linear superposition; vibration states intervene in excitation–relaxation processes; a time evolution of a global quantum 1-system is the feature. If sufficient time is allowed to an isolated system, with a given total energy E, unitary time evolution with $$\fancyscript{H}$$ (but not H) ensures that the system will evolve from the initial state to get amplitudes different from zero for all energy conserving final states. Response towards external dynamic couplings, e.g. electromagnetic fields, is given by changes of amplitudes and expressed in correlation functions. For a quantum state, the amplitude at a given base function reflects the possibility for the system submitted to excitation sources to respond with its spectral signatures; if the experiment is done, and the amplitude is different from zero, then, there will be a response. Algorithms permitting to relate Hilbert space to real space events are discussed. A chemical compound (analyte) is identified to (i) a fixed electronic quantum state; (ii) linear nuclear base states superpositions; (iii) zero amplitude for all other electronic base states. To get this implies either the action of a chemist introducing constraints to bottle the analyte or an accidental change of external (to the box) conditions producing spontaneous separations.