Interlayer excitons were observed at the heterojunctions in van der Waals heterostructures (vdW HSs). However, it is not known how the excitonic phenomena are affected by the stacking order. Here, we report twist-angle-dependent interlayer excitons in MoSe/WSe vdW HSs based on photoluminescence (PL) and vdW-corrected density functional theory calculations. The PL intensity of the interlayer excitons depends primarily on the twist angle: It is enhanced at coherently stacked angles of 0° and 60° (owing to strong interlayer coupling) but disappears at incoherent intermediate angles. The calculations confirm twist-angle-dependent interlayer coupling: The states at the edges of the valence band exhibit a long tail that stretches over the other layer for coherently stacked angles; however, the states are largely confined in the respective layers for intermediate angles. This interlayer hybridization of the band edge states also correlates with the interlayer separation between MoSe and WSe layers. Furthermore, the interlayer coupling becomes insignificant, irrespective of twist angles, by the incorporation of a hexagonal boron nitride monolayer between MoSe and WSe.

Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet–triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn–Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.

The mixed-reference spin-flip (MRSF) time-dependent density functional theory (TDDFT) method eliminates the notorious spin contamination of SF-TDDFT, thus enabling identification of states of proper spin-symmetry for automatic geometry optimization and molecular dynamics simulations. Here, we analyze and optimize the MRSF-TDDFT in the calculations of the vertical excitation energies (VEEs) and the singlet−triplet (ST) gaps. The dependence of the obtained VEEs and ST gaps on the intrinsic parameters of the MRSF-TDDFT method is investigated, and prescriptions for the proper use of the method are formulated. For VEEs, MRSF-TDDFT displays similar or better accuracy than SF-TDDFT (ca. 0.5 eV), while considerably outperforming the LR-TDDFT for the ST gaps. As a result, a new functional of STG1X (dubbed here), especially for ST gaps is suggested on the basis of splitting between the components of the atomic multiplets.

This work presents a study of intramolecular NHN hydrogen bonds in cations of the following proton sponges: 2,7-bis(trimethylsilyl)-1,8-bis(dimethylamino)naphthalene (1), 1,6-diazabicyclo[4.4.4.]tetradecane (2), 1,9-bis(dimethylamino)dibenzoselenophene (3), 1,9-bis(dimethylamino)dibenzothiophene (4), 4,5-bis(dimethylamino)fluorene (5), quino[7,8-h]quinoline (6) 1,2-bis(dimethylamino)benzene (7), and 1,12-bis(dimethylamino)benzo[c]phenantrene (8). Three different patterns were found for proton motion: systems with a single-well potential (cations 1-2), systems with a double-well potential and low proton transfer barrier, ΔEe (cations 3-5), and those with a double-well potential and a high barrier (cations 6-8). Tests of several density functionals indicate that the PBEPBE functional reproduces the potential-energy surface (PES) obtained at the MP2 level well, whereas the B3LYP, MPWB1K, and MPW1B95 functionals overestimate the barrier. Three-dimensional PESs were constructed and the vibrational Schrödinger equation was solved for selected cases of cation 1 (with a single-well potential), cation 4 (with a ΔEe value of 0.1 kcal mol(-1) at the MP2 level), and cations 6 (ΔEe = 2.4 kcal mol(-1)) and 7 (ΔEe=3.4 kcal mol(-1)). The PES is highly anharmonic in all of these cases. The analysis of the three-dimensional ground-state vibrational wave function shows that the proton is delocalized in cations 1 and 4, but is rather localized around the energy minima for cation 7. Cation 6 is an intermediate case, with two weakly pronounced maxima and substantial tunneling. This allows for classification of proton sponge cations into those with localized and those with delocalized proton behavior, with the borderline between them at ΔEe values of about 1.5 kcal mol(-1). The excited vibrational states of proton sponge cations with a low barrier can be described within the framework of a simple particle-in-a-box model. Each cation can be assigned an effective box width.

We present a fast and accurate numerical algorithm for computing the first-order nonadiabatic coupling matrix element (NACME). The algorithm employs the truncated Leibniz formula (TLF) approximation within the finite-difference method, which makes it easily applicable in connection with any wave function-based methodology. In this work, we used the algorithm in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT, MRSF for brevity). The accuracy is assessed for NACME between the singlet electronic states of a dissociating hydrogen molecule. It is demonstrated that an intermediate approximation, TLF(1), affords a negligible numeric error on the order of ∼10 −10 a.u. while enabling a fast computation of NACME. As the MRSF method yields the correct description of the dissociation curves of H 2 for all the electronic states involved, the numeric TLF(1)/MRSF NACME values are in excellent agreement with the reference analytical values obtained by the full configuration interaction. For polyatomic molecules, the MRSF NAC vectors agree very closely with the MRCISD NAC vectors. Hence, the proposed protocol is a promising tool for the evaluation of NACMEs.

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In different branches of time-dependent density functional theory (TDDFT), the static and dynamic electron correlation enters in different ways. The standard spin-conserving linear response (LR-TDDFT) methodology includes explicitly the contributions of the singly-excited configurations; however, it relies on an implicit account of the electron correlation through an (approximate) exchange-correlation (XC) functional. In the mixed-reference spin-flip TDDFT (MRSF-TDDFT), a number of doubly-excited (DE) configurations are explicitly included in the description of their response states. Here, the importance of the explicit account of DE is investigated for the lowest four excited singlet states of all-trans-polyenes up to C24H26. For the optically bright 1B u + state, the DE contribution in MRSF-TDDFT approaches 10% with the increasing system size. For the optically dark 2A g – state, the DE contribution increases from ca. 13% (C4H6) to nearly 30% (C24H26). An even more considerable DE contribution (∼50%) is observed in the higher 1B u – states. As LR-TDDFT misses these contributions entirely, its ability to accurately describe the excited states is limited by the XC functional. The hybrid XC functionals with a small fraction of the exact exchange, e.g., B3LYP, may mimic certain effects of DE through the self-interaction error (SIE). However, the description of the 1B u + state by LR-TDDFT remains poor. On the other hand, MRSF-TDDFT can flexibly take an implicit (through the XC functional) and an explicit (through DE) account of the electron correlation, which enables a more balanced description of various types of the excited states regardless of their character, thus reducing the chances of failure.

Stepwise and concerted mechanisms for the formation of mono-and dipropylene glycol over ZSM-5 zeolite were investigated. For the calculations, a T128 cluster model of zeolite was used with a QM/QM scheme to investigate the reaction mechanism. The active inner part of zeolite was represented by a T8 model and was treated at the DFT (BP86) level, including D3 Grimme dispersion, and the outer part of the zeolite was treated at the DFTB level. The solvent effects were taken into account by including explicitly water molecules in the cavity of the zeolite. The Gibbs energies were calculated for both mechanisms at 70 °C. In the case of the stepwise mechanism for the monopropylene glycol formation, the ratelimiting step is the opening of the epoxide ring. The activation energy for this process is 35.5 kcal mol −1 , while in the case of the concerted mechanism the rate-limiting step is the simultaneous ring opening of the epoxide and the attack by a water molecule. This process has an activation energy of 27.4 kcal mol −1 . In the case of the stepwise mechanism of the dipropylene glycol formation, the activation energy for the rate-limiting step is the same as for the monopropylene glycol formation, and in the case of the concerted mechanism, the activation energy for the rate-limiting step is 30.8 kcal mol −1 . In both cases (mono-and dipropylene glycol formation), the concerted mechanism should be dominant over the stepwise one. The barrier for monopropylene glycol formation is lower than that for dipropylene glycol formation. Consequently, our results show that the formation of the monopropylene glycol is faster, although the formation of dipropylene glycol as a byproduct cannot be avoided using this zeolite.