I develop an analytically tractable model of dynamic force spectroscopy by considering the forced escape of a Brownian particle out of a potential well, along a one-dimensional reaction pathway. I compute explicit expressions for pertinent experimental observables, such as average bond lifetimes and rupture force distributions. The results generalize conventional quasistatic theories to arbitrary forces and loading rates, thus covering the whole range of conditions found in experiments and all-atom simulations. The theory is extended to so-called catch-slip bonds that play an important role in biology, and to “hidden” degrees of freedom, which may bear significantly on the observed bond kinetics at high loading rates.

The work presented in this thesis is dedicated to developing inexpensive quantum-chemical models that are able to produce smooth and physically correct potential energy curves for the dissociation of single covalent bonds. It is well known that the energies produced by many ab initio theories scaling as the fifth order with the system size (for instance, second-order Moller-Plesset (MP2) and Epstein-Nesbet perturbation theories) diverge at large interatomic separations. We show that the divergent behavior of such perturbation schemes is due to a small number of terms in the energy expressions. Then, we demonstrate that the self-consistent replacement of these terms by their analogs from the coupled cluster theory (such as CCSD) allows one to redress the erroneous behavior of the perturbation theories without the damage to the overall scaling. We also investigate the accuracy of these hybrid perturbation theory-coupled cluster theories near equilibrium geometry. Judging from the computed spectroscopic constants and shapes of the potential energy curves, one such model, denoted MP2-CCSD(II) in this work, performs consistently better than the MP2 theory at essentially the same computational cost.

The site of initial metal-carbonyl bond-breaking during ligand-exchange reactions in a series of octahedral metal carbonyls of the type (L2)M(CO)4 (M = Cr, Mo, W; L2 = diphos, phen, dipy) has been determined employing infrared spectroscopy and Fourier transform nuclear magnetic resonance spectroscopy. The results of this study reveal, for all metal carbonyl complexes of the type mentioned above, that loss of CO occurs exclusively at an axial position (cis to the bidentate ligand, I^)• The dynamic nature of the five-coordinate intermediates, such as (diphos)Mo(CO)3, (phen)M(CO)3 (M = Cr, Mo, W), and (dipy)Cr(CO)3, which are generated in solution upon CO dissociation, is reported and discussed. The results of this investigation confirm that these intermediates are fluxional on the time scale of CO-exchange process. A mechanism which describes the site of initial metal-carbonyl bond-breaking and the fluxionality of the five-coordinate intermediate during ligand-exchange reactions in the complexes (L2)M(CO)4 is proposed. A kinetic study of reactions of W(CO)6 with pseudo-halide anions (NCS-, NCO-, CN-) has been initiated. The results indicate that these reactions proceed via a bimolecular path, which involves initial attack of the pseudo-halide anion at a carbonyl carbon of W(CO)6,

Accurate energetic modeling of large molecular systems is always desired by chemists. For example, ligand-protein binding simulations and enzymatic catalysis studies all involve with a small energy difference. The energetic accuracy depends largely on a proper handling of electronic correlations. Molecular mechanics (MM) methods deliver a parameterized Newtonian treatment to these problems. They show great capability in handling large calculations but give only qualitatively good results. Quantum mechanics (QM) methods solve Schrödinger equations and exhibit much better energy accuracy, though the computational cost can be prohibitive if directly applied to very large systems. Fragment-based methods have been developed to decompose large QM calculations into fragment calculations. However, most current schemes use a self- consistent field (SCF) method on fragments, in which no electronic correlation is accounted for. The super-system energy is computed as a sum of fragment energies plus two-body corrections and, possibly, three-body corrections (a "body" is a fragment). Higher order corrections can be added. Nevertheless, many problems require the treatment of high order electronic correlations. The coupled-cluster (CC) theory is the state-of-the-art QM method for handling electronic correlations. The CC wavefunction contains correlated excitations up to a given truncated level and coincidental excitations for all possible electronic excitations. It is a brilliant way of including more electronic correlations while maintaining a low-order scaling. In the proposed excitonic coupled-cluster (X-CC) theory, substantial modifications have been made to allow CC algorithms to act on the collective coordinates of fragment fluctuations to obtain super-system energy. The X-CC theory is designed to achieve accurate energetic modeling results for large chemical systems with much improved affordability and systematic improvability. The test system used in this work is a chain of beryllium atoms. A 30-fragment X-CCSD(2) calculation delivered matching accuracy with traditional CCSD method. An X-CCSD(2) calculation on a chain of 100 bonded fragments finished in 7 hours on a single 2.2 GHz CPU core. The X-CC scheme also demonstrates the ability in handling charge transfer problems. Due to the use of fluctuation basis in the test cases, the excitonic algorithms can be easily generalized to inhomogeneous systems. This will be investigated in future work.

From a theoretical standpoint, the accurate description of potential energy surfaces for bond breaking and the equilibrium structures of metal-ligand catalysts are distinctly similar problems. Near degeneracies of the bonding and anti-bonding orbitals for the case of bond breaking and of the partially-filled d-orbitals for the case of metal-ligand catalyst systems lead to strong non-dynamical correlation effects. Standard methods of electronic structure theory, as a consequence of the single-reference approximation, are incapable of accurately describing the electronic structure of these seemingly different theoretical problems. The work within highlights the application of multi-reference methods, methods capable of accurately treating these near-degeneracies, for describing the bond-breaking potentials in several small molecular systems and the equilibrium structures of metal-salen catalysts. The central theme of this work is the ability of small, compact reference functions for accurately describing the strong non-dynamical correlation effects in these systems.