One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as 𝑂(N⁷) in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as R⁻⁶ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems. / Ph. D.

Auditory neurons selectively respond to frequency and amplitude of sound. In the auditory midbrain, duration-tuned neurons (DTNs) are subsets of neurons that selectively respond to the duration of sound. DTNs may help further understand the neural mechanism underlying temporal processing in the central nervous system. Temporal processing has been shown to play important roles in speech, discriminating species-specific signals, and echolocation. The goal of this thesis is to explore the role of DTNs through single-unit electrophysiological recordings in the auditory midbrain of the big brown bat (Eptesicus fuscus). Monotic and dichotic paired-tone stimulation was used to evoke excitatory and inhibitory responses from DTNs. Two stimuli consisted of best duration (BD) excitatory and non-excitatory (NE) tones. In the monotic condition, both tones were presented to the contralateral ear, and when they were close in time, the NE tone always suppressed spikes evoked by the BD tone. In the dichotic condition, the BD tone was presented to the contralateral ear. The NE tone was presented to the ipsilateral ear and suppressed BD tone evoked spiking in ~50% of cells. Properties of the ipsilaterally-evoked inhibition were investigated by varying the frequency of the NE tone from the best excitatory frequency (BEF), throughout a cell’s excitatory bandwidth (eBW). We measured the inhibitory frequency response area, best inhibitory frequency (BIF), and inhibitory bandwidth (iBW) of each cell. We found inhibition became weaker as the frequency of the NE tone moved further from the middle of the eBW. We found that a DTN’s BEF and BIF closely matched, but the eBW was broader than the iBW and overlapped the iBW measured from the same cell. This suggests temporal selectivity of midbrain DTNs are created by monaural inputs, with binaural inputs playing a lesser role in shaping duration selectivity. / Thesis / Master of Science (MSc)

This thesis entails the utilisation of ab initio density functional theory (DFT) in conjunction with neutron and synchrotron spectroscopy to study the mechanical, vibrational, and dielectric response of metal-organic framework (MOF) materials at the molecular level. MOFs are crystalline materials with nanoscale porosity, which have garnered immense scientific and technological interest for a wide variety of innovative engineering applications. One part of the thesis involves using low-frequency lattice vibrations to characterise the various physical motions that are possible for framework materials. These collective modes detected at terahertz (THz) frequencies have been used to reveal a broad range of exciting possibilities. New evidence has been established to demonstrate that THz modes are intrinsically linked to anomalous elasticity underpinning gate-opening and pore-breathing mechanisms, and to shear-induced phase transitions and the onset of structural instability. The phenomenon of molecular rotor mechanisms and trampoline-like motions are also observed, along with the first experimental confirmation of coordinated shear dynamics. Additionally, a new method to characterise the effects of temperature, and hence thermally-induced structural amorphisation is reported. Finally, for the first time, the frequency-dependent (dynamic) dielectric response of MOF materials, across the extended infrared (IR) spectral region was reported. The results were obtained from experimental synchrotron radiation IR reflectivity and DFT to reveal the low-к dielectric response of MOFs and established structure-property trends that highlight them as promising systems for microelectronic device applications.