Emergence in Practice: Case Studies Using Density Functional Theory

Abstract

Emergence is a philsophical concept that has proved to be attractive
and long lasting. However in some forms, theories of emergence can be at odds with
the process of deductive scientific research. Here I develop a theory of historical
emergence based on our inability to describe, and therefore explain highly complex
physical systems. To provide evidence for this hypothesis, I perform electronic struc-
ture calculations on cyclobutadiene, iron arsenide, elemental iron, and manganese
oxide using DFT. I find that only in the iron calculations was historical emergence
found. I conclude that historical emergence is an effective definition of emergence,
as only the iron calculations exhibited all the behaviour expected in a system that
hosts emergence, namely dependent novelty, irreducibility, and unpredictability.
Further, I propose a general theory that is able to calculate the wavefunction of
the nuclei in an effective potential. I use this to calculate the Raman spectrum of
cyclobutadiene, in which an energy splitting of vibrational energy levels is found
due to tunnelling between two chemically equivalent rectangular configurations. I
find that the structure of this spectrum, including the tunnelling splitting, can be
explained by recourse to the typical motions predicted from a semiclassical model.
I conclude that the properties different isomers cannot be calculated using a single
generalised quantum calculation, even though isomers are composed of the same
particles and have the same Hamiltonian. Therefore chemical systems are likely to
host historically emergent explanations.
From the analysis of single-crystal XRES measurements on FeAs, and symmetry
considerations I propose a new canted magnetic structure commensurate with the
incommensurate elliptical helical magnetic order. I justify this with an orbital
projection method that is able to calculate the susceptibilities of the material to
spin-orbit interactions.
I also detail a spin initialisation procedure based on rotations of the exchange-
correlation potential, that aims to reduce bias towards undesired density config-
urations by the density search algorithms in noncollinear systems. I present its
application to symmetry unconstrained, noncollinear calculations of manganese ox-
ide and elemental iron. I conclude that this procedure is not suitable for systems
with magnetic configurations robust to changes in their exchange and correlation
potentials. Additionally symmetry unconstrained calculations are nontrivial, and
future calculations will require modified density search algorithms to deal with sym-
metry unconstrained calculations on many conductors due to complex interactions
at the Fermi surface.