Fast and Accurate Computation of Nonadiabatic Coupling Matrix Elements Using the Truncated Leibniz Formula and Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory.

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 H2 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.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids.

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.

How Beneficial Is the Explicit Account of Doubly-Excited Configurations in Linear Response Theory?

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 1Bu+ state, the DE contribution in MRSF-TDDFT approaches 10% with the increasing system size. For the optically dark 2Ag- 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 1Bu- 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 1Bu+ 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.

Sulfuric Acid Formation via H2SO3 Oxidation by H2O2 in the Atmosphere.

With the help of quantum mechanical methods, the formation of H2SO4 by the oxidation of H2SO3 with H2O2 was studied theoretically. Both stepwise and concerted mechanisms were calculated. It was found that the direct oxidation of H2SO3 by H2O2 alone requires prohibitive activation energies of >38.6 kcal/mol. However, the addition of one water molecule exhibits a strong catalytic effect that dramatically reduces the overall reaction barrier to 6.2 (2.3 with PCM) kcal/mol. The deprotonated HSO3- species also reduces the overall reaction barrier to 5.6 (-5.8 with PCM) kcal/mol. Both of these proceed via concerted pathways. On the other hand, the stepwise mechanisms generally produce intermediates with a hydroperoxy group (-O-O-H), which is a result of a nucleophilic attack by the oxygens of H2O2. While studying the catalytic effect of water, a previously unknown hydroperoxy intermediate (HOO)S(OH)3, where sulfur is coordinated with three OH groups, was found. This work also reveals a rearrangement step of another hydroperoxy intermediate (HOO)SO2- to HSO4- that was found in earlier experimental studies. For all of the mechanisms calculated, the final H2SO4 is formed with a significant exothermicity of >60 kcal/mol. In general, even without sunlight, it was found that the formation of sulfuric acid by hydrogen peroxide can occur in a heterogeneous moisturized environment.

Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet-Triplet Energy Gaps.

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.

Probing Evolution of Twist-Angle-Dependent Interlayer Excitons in MoSe2/WSe2 van der Waals Heterostructures.

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 MoSe2/WSe2 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 MoSe2 and WSe2 layers. Furthermore, the interlayer coupling becomes insignificant, irrespective of twist angles, by the incorporation of a hexagonal boron nitride monolayer between MoSe2 and WSe2.

Si⋠⋠⋠H Interligand Interactions in Cobalt(V) and Iridium(V) Bis(silyl)bis(hydride) Complexes.

A series of bis(silyl)bis(hydride) cobalt complexes [Cp*Co(H)2 (SiR3 )2 ] (Cp*=pentamethylcyclopentadienyl; SiR3 =SiPh2 H, SiMe3 , SiH3 , SiF3 , SiCl3 , SiBr3 , Si(CF3 )3 ; Co1-Co7) as well as the analogous iridium complexes [Cp*Ir(H)2 (SiR3 )2 ] (SiR3 =SiEt3 , SiMe3 , SiH3 , SiF3 , SiCl3 , SiBr3 , Si(CF3 )3 ; Ir1-Ir7) were studied to detect possible residual Si⋅⋅⋅H interactions. Tests of several density functionals by comparison with coupled-cluster results indicate that the TPSSh functional performs better than B3LYP, BP86, M06, M06L, and PBEPBE. Based on molecular structures, as well as Wiberg bond indices and J(Si,H) spin-spin coupling constants as indicators of a possible Si⋅⋅⋅H interaction, at least two residual Si⋅⋅⋅H interactions in Co2, Co5, and all four possible Si⋅⋅⋅H interactions in Co3 and Co4 have been detected. Co6 and Co7 exhibit stronger Si⋅⋅⋅H bonding than the other complexes studied. On the contrary, the iridium complexes Ir1-Ir3 and Ir5-Ir7 are classical iridium(V) bis(silyl)bis(hydride) complexes with only rudimentary Si⋅⋅⋅H interactions, if any.

Hydrogen motion in proton sponge cations: a theoretical study.

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.