A Thermosensitive polymers exhibiting a lower critical solution temperature (LCST) can be made responsive to pH change by introducing acid or base comonomer units, and the LCST can be switched between higher and lower temperatures as a result of the polarity change of the comonomer units upon their pH--induced protonation or deprotonation. In the present study, we describe a new comonomer design that aims at increasing the magnitude of the pH--triggered LCST shift.Random copolymers of N--isopropylacrylamide and 4--((2--carboxyallyl)oxy)benzoic acid, denoted as P(NIPAM--co--CBA), were synthesized, in which each CBA comonomer unit bears an acrylic acid and a benzoic acid group of similar pKa. With respect to comonomers containing a single acid group, this particular comonomer structure makes it more hydrophobic in the protonated state (pHpKa) due to the doubled charge, which results in larger pH--triggered LCST shift based on the comonomer effect. The demonstrated comonomer design principle, which is general and can also be applied to base comonomers, represents a useful strategy for enhancing the efficiency and sensitivity of the pH--responsiveness of LCST polymers. 15 A rational comonomer design leads to large pH-induced LCST shift.

Several of the limitations of approximate exchange–correlation functionals within Kohn–Sham density functional theory can be eliminated by extending the single-determinant reference system to a multi-determinant one. Here, we employ the correlation factor ansatz to combine multi-configurational, self-consistent field (MCSCF) with approximate density functionals. In the proposed correlation factor approach, the exchange–correlation hole ρXC(r, u), a function of the reference point r and the electron–electron separation u, is written as a product of the correlation factor fC(r, u) and an exchange plus static-correlation hole ρXS(r, u), i.e., ρXCCFXS(r, u) = fC(r, u)ρXS(r, u). ρXS(r, u) is constructed to reproduce the exchange–correlation energy of an MCSCF reference wave function. The correlation factor fC(r, u) is designed to account for dynamic correlation effects that are absent in ρXS(r, u). The resulting approximation to the exchange–correlation energy, which we refer to as CFXStatic, is free of empirical parameters, and it combines the qualitatively correct description of the electronic structure obtainable with MCSCF with the advantages of approximate density functionals in accounting for dynamic correlation.

One strategy to construct approximations to the exchange–correlation (XC) energy EXC of Kohn–Sham density functional theory relies on physical constraints satisfied by the XC hole ρXC(r, u). In the XC hole, the reference charge is located at r and u is the electron–electron separation. With mathematical intuition, a given set of physical constraints can be expressed in a formula, yielding an approximation to ρXC(r, u) and the corresponding EXC. Here, we adapt machine learning algorithms to partially automate the construction of X and XC holes. While machine learning usually relies on finding patterns in datasets and does not require physical insight, we focus entirely on the latter and develop a tool (ExMachina), consisting of the basic equations and their implementation, for the machine generation of approximations. To illustrate ExMachina, we apply it to calculate various model holes and show how to go beyond existing approximations.

We focus on the spherically averaged exchange–correlation hole ρXC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρX model(r, u) is multiplied by a CF (f C(r, u)) to yield an approximation to the exchange–correlation hole ρXC(r, u) = f C(r, u) ρX model(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.