We review the methods to preserve the initial state populations in a fast harmonic trap expansion. The design of the time dependence of the frequency using inverse techniques presents advantages over the slow adiabatic approach, band-bang methods, or the non-local "transitionless tracking'' algorithm. Many operations with cold atoms make use of adiabatic expansions and would benefit from such a shortcut to adiabaticity.

A theoretical analysis is presented for the nonadiabatic photodissociation process of hydrogen fluoride and it deuterated species. Four electronic states $X^1\Sigma^+$, $a^3\Pi$, $A^1\Pi$, and $^3\Sigma^+$ are involved in the studies. Based on the accurate ab initio calculations of the potential energy curves, transition dipole moment and spin-orbit couplings among the accessible states, the time dependent quantum wave packet approach with the split-operator scheme is employed to investigate the dissociative dynamics. The dissociative process is analyzed via the evolution of the wave packets. The total cross sections, partial cross sections and branching fractions for both HF and DF initially excited from the vibrational levels $v= 0-3$ of the ground state are evaluated. The calculations are compared with the former investigations and present the prediction for a broad range of the incident photon energies.

Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A 80 (2009) 052705], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the longrange part of the molecular potential.

A simple connection is established between aromaticity and overall stability of five-ring linear polyaromatic hydrocarbon oxyradicals. A chemically intuitive model is developed that exhibits a linear trend between an inexpensive geometric measure of aromaticity and the energetic stability of a model graphene edge with oxygen at different positions. It is believed to be an important step in establishing reaction pathways of soot and graphene oxidation.

We study the field entropy squeezing as a measure of the entanglement in a three-level system interacting with a cavity field. Numerical calculations under current experimental conditions are performed and it is found that the initial state setting and atom-field coupling present changes of the general features of the field entropy squeezing dramatically.

Non-relativistic energies of $1s^22s$ and $1s^2np$ $(\leq 9)$ states for $Cu^{26+}$ ion are calculated by using the full-core plus correlation method. For $1s^22s$ and $1s^22p$ states, relative discrepancies between our results and high precision results of Yan et al. are within 0.1 ppm. By taking account of the first-order corrections to the energy from relativistic and mass-polarization effects, the higher-order relativistic contribution and QED correction to the energy are estimated under a hydrogen-like approximation. The transition energies, wavelengths and oscillator strengths for the $1s^22s-1s^2np$ transitions of the ion are calculated. The results obtained by the three forms are in good agreement with each other.

Murine epidermal growth factor (mEGF) is a single polypeptide of fifty-three amino acid residues containing three intramolecular disulfide bonds, widely found in body fluids like milk. We performed semi-empirical quantum chemistry calculations on sixteen mEGF molecules at level of PM3 to investigate the electronic properties of these molecules. The equilibrium structure, heats of formation, molecular orbitals, polarizability, and dipole moment were computed in vacuum and in solvents (carbon tetrachloride, ethanol, and water). Electronic structure calculations in vacuum show that the highest occupied molecular orbital (HOMO) of all mEGF molecules distributes on five C-terminal residues (Tyr49/Tyr50 and Arg48/Arg53 residues), while the lowest unoccupied molecular orbital (LUMO) locates on the disulfide bonds, indicating that the disulfide bridges and C-terminus are important for the biological activity of EGF. The locations of LUMO and HOMO show almost no solvent effects. In the solvent of relative larger dielectric constant, the heat of formation and mean polarizability of the mEGF molecules become lower while the dipole moment is enhanced. Examination of the locations of hydrogen bonds demonstrates that the B loop (residues 14-31) is crucial for the conformational stability and biological activity of EGF. All these theoretical results are in general agreement with experiments. We suspect that the N- and C-terminal residues play some roles in stabilizing the molecular conformation of EGF, probably associated with the orientation of EGF binding to EGFR (epidermal growth factor receptor).

Plane-wave ultrasoft pseudopotential calculations are performed to study the structural stability and the electronic structure of N- or C-monodoped $TiO_2$. Firstly, various models of nonmetal doped $TiO_2$ are optimized to calculate the defect formation energy of different dopants. It is found that the Ti-rich condition facilitates N- or C-doping. The nonmetallic oxide of C and N in high valence facilitates doping under the Ti-rich condition. The element and the oxide of C and N in low valence facilitate doping under the O-rich condition. Secondly, the energy band structure of doped $TiO_2$ is analyzed. The results show that N-doping generates a semi-filled shallow impurity energy level near the top of the valence band. C-doping generates three deep impurity energy levels within the band gap which easily become the recombination centers of electrons and holes. Finally, the bonds between atoms are analyzed using the electron density map and the bond population. It is found that the electronegativity of impurities determines the position of the impurity energy level. These results help to understand the effects of nonmetal doping on the photocatalytic properties of $TiO_2$.

A primary theory for the cold fusion mechanism is proposed early in 1989 by us based on atomic, molecular, nuclear and crystal physics. According to this theory, the cold fusion of deuterons may be raised in crystal with produce of excess heat and fusion products $^4He.$ After this theory, the remarkable effects of excess heat and fusion products $^4He$ were observed during the electrolysis of heavy water with Pd or Ti electrodes in our experimental researches. These results indicate that the prediction in our theory is valid. In order to get more clear understanding for the cold fusion, the further theoretical and experimental research had been studied repeatedly by us in the past twenty years. Through a deep analysis, we find that the cold fusion is arised from the interaction of two adjacent full atoms (contain nucleus and valence electrons) of heavy hydrogen in the interstitial position of crystal. This full atomic theory will be discussed in detail in this paper. According to this theory, we find out that $^3He$ may be made from the cold fusion of heavy hydrogen and hydrogen atoms.