T. Yu. Mikhailova

Quantum-chemical modeling of ferroelectric solids with hydrogen-bond networks of different dimensionalities and their deuterated analogs

The application of quantum chemistry methods in the microscopic theory of H/D-bonded ferroelectrics and antiferroelectrics is illustrated using a comparative analysis of low-temperature order-disorder structural phase transitions in zero-dimensional materials of the K3H(SO4)2 family, zero-dimensional crystals of 5-halo derivatives of 9-hydroxyphenalenone (5Hal-9HPO), and three-dimensional crystals of potassium dihydrogen phosphate (KDP) and potassium dideuterium phosphate (DKDP) as examples. In the framework of the Ising model with tunneling, it is demonstrated that (in agreement with experimental data) the transition to the low-temperature ordered phase in zero-dimensional materials is possible only in the case of their deuteration, whereas the quantum paraelectric behavior is characteristic of undeuterated samples. This behavior for KDP crystals is impossible due to the sharp increase in the Ising parameters as compared to zero-dimensional materials. The factors responsible for the increase in these parameters are considered.

Three mechanisms of cooperative coupling of intermolecular H-bond protons in condensed phases

Abstract Three mechanisms of cooperative proton-proton coupling are briefly described for H-bonded crystals (mainly of the “solid acids” class). Direct and indirect electrostatic mechanisms (with the participation of non-hydrogen structural units in the latter case) as well as the indirect non-electrostatic mechanism are considered. Numerical estimations for the efficiency of these mechanisms are presented. The relation of these mechanisms to the observed thermodynamic properties is noted.

Mechanism and energetics of 1,2-addition of dioxygen 1O2(1Δg) to ethylene

The optimal geometry and energy parameters for five electronic states of the {1O2 (1Δg) + C2H4} system that characterize the elementary reactions of two-step 1,2-addition giving the dioxetane molecule were calculated using various quantum chemical methods (RHF, B3LYP, MPn, n = 2–4, QCISD, and CCSD) and basis sets (from 6-31+G(d,p) to 6-311+G(3df,2p) and pVTZ). The first step of the reaction was found to pass through the ethylene perepoxide intermediate. Considering experimental and published calculated data, the dependence of the results on the calculation procedure was exampled. The higher-level methods (QCISD, CCSD, CASSCF) and the standard methods (DFT, MPn) were found to reliably lead to virtually the same description of the energetics of this two-step reaction corresponding to experimental estimates.

Structural phase transition in quasi-one-dimensional H-bonded ferroelectric PbHPO 4 (LHP) crystal: Quantum-chemical analysis

Thermodynamic features of the structural phase transition (SPT) in the H-bonded ferroelectric material PbHPO4 (LHP) have been considered using a pseudo-spin Ising model with inclusion of tunneling and long-range effects. To determine all pseudo-spin Hamiltonian (PSH) parameters necessary for analysis of the SPT—Slater parameters and tunneling integrals, a technique based on an independent quantum-chemical method of their finding was applied. A simplified scheme has been suggested for selecting a model cluster, which makes it possible to use higher-level methods (CCSD and QCISD with the 6-311+G** basis set) in calculations of double-well potential profiles and PSH parameters. The computation results have been discussed in the framework of two statistical models—in the molecular field approximation and using the Bethe cluster method. The critical temperature of the transition of LHP has been evaluated and it has been demonstrated that experimental data can be semiquantitatively reproduced only in the statistical cluster approximation with inclusion of tunneling and long-range effects.

Indirect non-electrostatic mechanism of the proton-proton interaction and proton-lattice coupling in KH2PO4 ferroelectrics

It has been shown that the mechanism previously proposed for the effective interaction of protons in MH2AO4 ferroelectrics, such as KH2PO4 (KDP), is applicable to the description of the proton-lattice coupling. The expression derived for the total Hamiltonian of the coupled proton-lattice system, along with the single-mode approximation, also allows the consideration of several modes involved in the ferroelectric phase transition. The use of the proposed approach is illustrated by the example of the numerical evaluation of the effect of the proton-lattice coupling on the critical temperature Tc of the ferroelectric phase transition in KDP and deuterated KDP.

Low-Temperature Phase Transition and Structure of Ordered Phase in K3H(SO4)2 (TKHS)-Family Materials

Abstract Suitability of quantum chemistry to describe the structural phase transitions on the semi-quantitative level in H-bonded ferroelectrics and related materials has been demonstrated. The low-temperature H/D-ordering transitions have been treated for the TKHS-like materials in the scope of the static and dynamic Ising models. Parameters of the Ising-type Hamiltonians are evaluated on the Hartree–Fock/second-order perturbation theory level using the available diffraction data. The type of D-ordering in the low-temperature phase of M 3 D(AO 4 ) 2 specimens, which is debated so far, is proposed in the limits of the static model. As shown this ordering points out the antiferroelectric-type structure with the b -doubling of paraelectric A 2/ a cell and admits the c -doubling of this cell. Estimations of T c in the fully deuterated specimens are obtained by the Bethe cluster approximation using the dynamic model. An absence of such transition for M 3 H(AO 4 ) 2 has been explained by both the proton quantum fluctuations (tunneling effect) and the differences in geometries of H- and D-bonds (geometric isotope effect).

Quantum-chemical analysis of the thermodynamic isotope effect in quasi-one-dimensional H-bonded Pb(H/D)PO4 ferroelectrics

The thermodynamics of the structural phase transition of H-bonded ferroelectric materials, Pb(H/D)PO4, were considered in terms of the pseudo-spin Ising model with inclusion of tunneling and longrange effects. The pseudo-spin Hamiltonian parameters needed for analysis of the transition were determined by a procedure based on an independent quantum chemical method. A simplified scheme for the selection of model clusters was proposed, which allows the application of various quantum chemical methods, including high-level methods (CCSD/6-311+G** and so on), in the calculations of double-well potential profiles and Slater parameters. The calculation results were discussed in terms of two statistic models: molecular field approximation (MFA) and Bethe cluster method (BCM). The theoretical estimates of critical transition temperature for both systems are discussed and it is shown that the (semi)quantitative reproduction of experimental data is possible only in terms of BCM taking into account the tunneling effects. The explanation is given for the observed isotope effect caused by very pronounced increase in the critical transition temperature upon deuteration (ΔTс ≈ 140 K). The crucial role belongs to the difference between tunneling effects in the ferroelectric crystals in question. It is emphasized that the observed differences between the crystal lattice and H/D bond geometries, including the mutual orientation of the bonds, must be accurately included in the calculations.

Quantum-chemical simulation of the elementary step of the oxidation reactions of styrene and its derivatives involving 1О2 (1Δg)

The results of simulation of the oxidation reaction of styrene and its methyl (two isomers) and phenyl derivatives with molecular oxygen in the excited singlet state (1Δg) have enabled the conclusion that the reaction can proceed through several mechanisms. For styrene and its phenyl derivative, three reaction channels are possible, and for the methyl derivative, there are four possible channels. For the first two substrates, the major channel is 1,2-addition to form dioxetane; for the methyl derivatives, an extra channel to give a hydroperoxide species is possible in addition to the above channel. The multichannel reaction character revealed by calculations makes it possible to qualitatively understand the reason behind the moderate selectivity (no more than 70%) of such reactions in the case of styrene and its derivatives.

Quantum-chemical simulation of unit process for the oxidation reactions of ethylene and its derivatives invoving 1O2 (1Δg)

The results of simulation of oxidation reactions of ethylene derivatives with different substituents (F atoms, CH3O and CH3 groups) and butadiene molecule with participation of 1O2 (1Δg) have shown the possibility to realize different routes for the majority of the considered reactions. The largest product variety is obtained for butadiene and CH3 derivatives of ethylene. For butadiene, along with 1,2-cycloaddition reactions resulting in four-membered dioxetane (which is realized in all cases), the possibility to form six-membered cyclic epidioxides (1,4-addition) and diepoxide products with two three-membered rings (epoxidation) has been found. The formation of hydroperoxide forms along with 1,2-addition reactions is also possible for all CH3 derivatives of ethylene. Formation conditions and relative stability of the noted products have been analyzed for each case and certain features of the revealed reaction pathways with the transfer of two oxygen atoms have been discussed.

Effect of the Hydrostatic Pressure on the Thermodynamics of Structural Phase Transition in Quasi-One-Dimensional Ferroelectrics Pb(H/D)PO4: Quantum Chemical Analysis

The change in the structural phase transition thermodynamics of lead hydrogen phosphate (LHP) and lead deuterium phosphate (LDP) depending on the external hydrostatic pressure was studied using the Ising pseudo-spin model taking account of tunneling and long-range effects. The same simplified version of the quantum chemical approach that we proposed for studying these systems at atmospheric pressure was used. The critical transition temperatures Tc were estimated for both systems and the considerable decrease in Tc observed experimentally was explained in each case. The calculations gave an estimate for the width of the barrier in LHP (≈0.35 Å); no experimental neutron diffraction value for this barrier is available from the literature.