No abstract

No abstract

In the field of soft matter research, the characteristic behavior of both nematic-isotropic (N-I) and smectic-A nematic(Sm-A N) phase transitions has gained considerable attention due to their several attractive features. In this work, a high-resolution measurement of optical birefringence (Δn) has been performed to probe the critical behavior at the N-I and Sm-A N phase transitions in a binary system comprising the rodlike octylcyanobiphenyl and a laterally methyl substituted hockey-stick-shaped mesogen, 4-(3-n-decyloxy-2-methyl-phenyliminomethyl)phenyl 4-n-dodecyloxycinnamate. For the investigated mixtures, the critical exponent β related to the limiting behavior of the nematic order parameter close to the N-I phase transition has come out to be in good conformity with the tricritical hypothesis. Moreover, the yielded effective critical exponents (α', β', γ') characterizing the critical fluctuation near the Sm-A N phase transition have appeared to be nonuniversal in nature. With increasing hockey-stick-shaped dopant concentration, the Sm-A N phase transition demonstrates a strong tendency to be driven towards a first-order nature. Such a behavior has been accounted for by considering a modification of the effective intermolecular interactions and hence the related coupling between the nematic and smectic order parameters, caused by the introduction of the angular mesogenic molecules.

In this paper, the iteration scheme associated with single reference coupled cluster theory has been analyzed using nonlinear dynamics. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, that dictate the dynamics, while all other amplitudes are enslaved. Starting with a few initial iterations to establish the inter-relationship among the cluster amplitudes, a supervised machine learning scheme with a polynomial kernel ridge regression model has been employed to express each of the enslaved amplitudes uniquely in terms of the former set of amplitudes. The subsequent coupled cluster iterations are restricted solely to determine those significant excitations, and the enslaved amplitudes are determined through the already established functional mapping. We will show that our hybrid scheme leads to a significant reduction in the computational time without sacrificing the accuracy.

The discrete-time propagation of a double similarity transformed Coupled Cluster theory with input perturbation is studied. The coupled iterative scheme to solve the ground state Schrödinger equation is cast as a multivariate logistic map, the solutions show the universal Feigenbaum dynamics. Using recurrence analysis, it is shown that the dynamics is dictated by a small subgroup of cluster operators, mostly those involving chemically active orbitals, whereas all other cluster operators with smaller amplitudes are enslaved.

Measurements of birefringence (Dn), dielectric permittivity (3 k , 3 t ), elastic moduli (K 11 , K 33 ) and rotational viscosity (g 1 ) have been carried out on the nematic (N) phase of a few hockey stick-shaped compounds 4-(3n-alkyloxy-2-methyl-phenyliminomethyl)phenyl 4-n-alkyloxycinnamates with a lateral methyl group inserted between the m-alkyloxy chain and the azomethine connecting group. Interestingly, a dual characteristic (i.e. partially calamitic like and partially bent-core like) is revealed in the N phase of these compounds. The SmC a -N transition is found to be of first order in nature while the SmC s -N transition is either second order or weakly first order. All the mesogens exhibit a temperature dependent inversion in the static dielectric anisotropy (D3 ¼ 3 k À 3 t ) from positive to negative values on entering the SmC a phase. Remarkably in the entire nematic range, the bend elastic modulus (K 33 ) is substantially lower than the corresponding splay modulus (K 11 ). The rotational viscosity coefficient (g 1 ) as obtained by extracting the relaxation time (s 0 ) values from two precise, independent probing methods, viz. the capacitive decay technique and the optical phase-decay-time measurement method, are slightly higher than those of many known calamitic systems. Moreover, the activation energy (E a ) calculated from the viscosity data is found to be considerably higher in the nematic phase than those obtained for conventional calamitics. The observed behaviours are accounted for by considering the intriguing shape-determined inter-molecular interactions and molecular associations appearing in the mesophase.

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analyzed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree−Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.