We describe a first-principles method to calculate scanning tunneling microscopy (STM) images, and compare the results to well-characterized experiments combining STM with atomic force microscopy (AFM). The theory is based on density functional theory with a localized basis set, where the wave functions in the vacuum gap are computed by propagating the localized-basis wave functions into the gap using a real-space grid. Constant-height STM images are computed using Bardeen's approximation method, including averaging over the reciprocal space. We consider copper adatoms and single CO molecules adsorbed on Cu(111), scanned with a single-atom copper tip with and without CO functionalization. The calculated images agree with state-of-the-art experiments, where the atomic structure of the tip apex is determined by AFM. The comparison further allows for detailed interpretation of the STM images.

We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

The main body of this thesis describes how to calculate scanning tunneling microscopy (STM) images from first-principles methods. The theory is based on localized orbital density functional theory (DFT), whose limitations for large-vacuum STM models are resolved by propagating localized-basis wave functions close to the surface into the vacuum region in real space. A finite difference approximation is used to define the vacuum Hamiltonian, from which accurate vacuum wave functions are calculated using equations based on standard single-particle Green’s function techniques, and ultimately used to compute the conductance. By averaging over the lateral reciprocal space, the theory is compared to a series of high-quality experiments in the low- bias limit, concerning copper surfaces with adsorbed carbon monoxide (CO) species and adsorbate atoms, scanned by pure and CO-functionalized copper tips. The theory compares well to the experiments, and allows for further insights into the elastic tunneling regime.

A second significant project in this thesis concerns first-principles calculations of a simple chemical reaction of a hydroxyl (oxygen-deuterium) monomer adsorbed on a copper surface. The reaction mechanism is provided by tunneling electrons that, via a finite electron-vibration coupling, trigger the deuterium atom to flip between two nearly identical configurational states along a frustrated rotational motion. The theory suggests that the reaction primarily occurs via nuclear tunneling for the deuterium atom through the estimated reaction barrier, and that over-barrier ladder climbing processes are unlikely. 

Achieving a high intensity in inelastic scanning tunneling spectroscopy (IETS) is important for precise measurements. The intensity of the IETS signal can vary by up to a factor of 3 for various tips without an apparent reason accessible by scanning tunneling microscopy (STM) alone. Here, we show that combining STM and IETS with atomic force microscopy enables carbon monoxide front-atom identification, revealing that high IETS intensities for CO/Cu(111) are obtained for single-atom tips, while the intensity drops sharply for multiatom tips. Adsorption of the CO molecule on a Cu adatom [CO/Cu/Cu(111)] such that the molecule is elevated over the substrate strongly diminishes the tip dependence of IETS intensity, showing that an elevated position channels most of the tunneling current through the CO molecule even for multiatom tips, while a large fraction of the tunneling current bypasses the CO molecule in the case of CO/Cu(111).

We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal/CO-functionalized STM tips. The theory furthermore allows us to discuss the significance of s- and p-wave tips.

The work in this thesis is basically divided into two related but separate investigations.

The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces.

The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.

An electromagnetic analysis is presented for experiments with strong permanent disc magnets. The analysis is based on the well known experiment that demonstrates the effect of circulating eddy currents by dropping a strong magnet through a vertically placed metal cylinder and observing how the magnet is slowly falling through the cylinder with a constant velocity. This experiment is quite spectacular with a super strong neodymium magnet and a thick metal cylinder made of copper or aluminum. A rigorous theory for this experiment is provided based on the quasi-static approximation of the Maxwell equations, an infinitely long cylinder (no edge effects) and a homogeneous magnetization of the disc magnet. The results are useful for teachers and students in electromagnetics who wish to obtain a deeper insight into the analysis and experiments regarding this phenomenon, or with industrial applications such as the grading and calibration of strong permanent magnets or with measurements of the conductivity of various metals, etc.. Several experiments and numerical computations are included to validate and to illustrate the theory.

To describe vibrationally mediated configuration changes of adsorbates on surfaces we have developed a theory to calculate both reaction rates and pathways. The method uses the T-matrix to describe excitations of vibrational states by the electrons of the substrate, adsorbate, and tunneling electrons from a scanning tunneling probe. In addition to reaction rates, the theory also provides the reaction pathways by going beyond the harmonic approximation and using the full potential energy surface of the adsorbate which contains local minima corresponding to the adsorbates different configurations. To describe the theory, we reproduce the experimental results in [T. Kumagai et al., Phys. Rev. B 79, 035423 (2009)], where the hydrogen/deuterium atom of an adsorbed hydroxyl (OH/OD) exhibits back and forth flipping between two equivalent configurations on a Cu(110) surface at T = 6 K. We estimate the potential energy surface and the reaction barrier, similar to 160 meV, from DFT calculations. The calculated flipping processes arise from (i) at low bias, tunneling of the hydrogen through the barrier, (ii) intermediate bias, tunneling electrons excite the vibrations increasing the reaction rate although over the barrier processes are rare, and (iii) higher bias, overtone excitations increase the reaction rate further.