The century old [2+2] photocycloaddition reaction appeared as the most synthetically useful reaction amongst all photochemical reactions. It provides not only cyclobutane ring systems, but at the same time it provides access to medium rings through facile ring expansion/fragmentation of the strained cyclobutane ring. The high regio‐and stereoselectivity observed during cycloaddition has made it an attractive tool for synthesis of multicyclic structurally complex natural products. The vast majority of [2+2] photocycloaddition reactions involves enone–alkene cycloaddition which is conveniently achieved through direct excitation or sensitization by UV irradiation. Substantial progress has also been made in [2+2] cycloaddition between two unactivated alkenes using transition metal salts especially copper(I) salts. Sometimes Cu(I)‐catalyzed cycloaddition is advantageous over enone–alkene photocycloaddition. Search for an alternative source to environmentally harmful high energy UV light has led to the discovery of transition metal salts which can be used to excite alkenes by visible light. This causes alkenes to undergo [2+2] cycloaddition and has been used for synthesis of cyclobutane derivatives. This review aims to give an overview about different aspects of [2+2] photocycloaddition reaction with an emphasis in the stereoselective synthesis of selected complex natural products and related molecules where cycloaddition has been used as the key step.

We present a brief description of a valence-universal multireference coupled cluster (VU-MRCC) theory that can handle completely general incomplete model spaces, remaining close to the intermediate normalization (IN) condition for omega as much as possible without violating extensivity and without the use of a post facto correction. In this formalism, the connectedness of the cluster operators as well as effective Hamiltonian and hence the extensivity of the corresponding roots is achieved by invoking appropriate decoupling conditions on the special type of wave operator omega = {exp(S + X(cl))} satisfying the Bloch equations in the Fock-space S in an excitation operator and X is a closed operator (denoted by cl). This special type of wave-operator leads to a unique partition of the excitations from the model space into those generated by the cluster operators (open and quasi-open) and those generated by the effective Hamiltonian (closed). In this formulation, for every X(cl), there is a counterterm from {exp(S)}(cl) canceling each other. This leads to a connected expressions for cluster amplitudes, using the constraint omega(cl) = 1. The new form of the effective Hamiltonian preserves the extensivity of the target energies. Our analysis implies that IN for omega is a valid size-extensive normalization for certain special IMS such as the quasi-complete model space and the isolated incomplete model space.

Spontaneous symmetry breakdown in non-relativistic quantum mechanics Am. J. Phys. 80, 891 (2012) Understanding the damping of a quantum harmonic oscillator coupled to a two-level system using analogies to classical friction Am. J. Phys. 80, 810 (2012) Relation between Poisson and Schrödinger equations Am. J. Phys. 80, 715 (2012) Comment on "Exactly solvable models to illustrate supersymmetry and test approximation methods in quantum mechanics," Am. J. Phys. 79, 755-761 (2011) Am. J. Phys. 80, 734 (2012) The uncertainty product of position and momentum in classical dynamics Am.We show that the ␦-function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential, if coupled with a ␦ function potential, remains exactly soluble. We use the strength of the ␦ function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.

Finite size effects on classical ideal gas are revisited. The micro-canonical partition function for a collection of ideal particles confined in a box is evaluated using Euler-Maclaurin's as well as Poissonʼs summation formula. In Poissonʼs summation formula there are some exponential terms which are absent in Euler-Maclaurin's formula. In the thermodynamic limit the exponential correction is negligibly small but in the macro/nano dimensions and at low temperatures they may have a great significance. The consequences of finite size effects have been illustrated by redoing the calculations in one and three dimensions keeping the exponential corrections. Global and local thermodynamic properties, diffusion driven by the finite size effect, and effect on speed of sound have been discussed. Thermo-size effects, similar to thermoelectric effects, have been described in detail and may be a theoretical basis with which to design nano-scaled devices. This paper can also be very helpful for undergraduate and graduate students in physics and chemistry as an instructive exercise for a good course in statistical mechanics.

An efficient atom-economic coupling of 1,5-amino alcohols and Michael acceptors has been developed employing [CpRu(MeCN) 3 ]PF 6 as a key catalyst to synthesize α,β-unsaturated ketones with exclusive generation of E-geometrical isomers at room temperature without any co-catalyst and additives. A base catalysed 6-endo-trig cyclization of the α,β-unsaturated ketone delivers a direct access to tri-substituted piperidones.