Two algorithms for calculating overlaps between CIS (or TDDFT) type excited state wave functions are presented, one based on expansion of overlap determinants into level 2 minors (OL2M) and the other based on an expansion of the wave functions into natural transition orbitals (ONTO). Both are significantly faster than previously available algorithms, with the ONTO algorithm reducing the cost of a single overlap element calculation by a factor of the square of the number of occupied orbitals in the system, resulting in orders of magnitude faster calculations for large systems and significantly increasing the size of systems for which TDDFT based nonadiabatic dynamics simulations can be performed. The OL2M algorithm is significantly slower for a single overlap matrix element, but becomes preferred when overlaps between large numbers of states are required. Additionally, we test the accuracy of approximate overlaps calculated using truncated wave functions and show that truncation can lead to very large errors in the overlaps. Lastly, we provide examples of applications for wave function overlaps outside the context of nonadiabatic dynamics.
In order to test
metal diketonates as potential acceptors of bifurcated
halogen bonds, the series of acetylacetonates (acac)
of divalent cations Cu(acac)2 (1), Pd(acac)2 (2), VO(acac)2 (3), Ni(acac)2(H2O)2 (4), Co(acac)2(H2O)2 (5), and Zn
(acac)2(H2O) (6) were
cocrystallized with 1,4-diiodotetrafluorobenzene (tfib) and 1,4-dibromotetrafluorobenzene (tfbb) as halogen
donors. This has yielded a series of 10 cocrystals, tfib having formed cocrystals with all six acceptors and tfbb with all except for 4 and 5. In eight
cocrystals a pair of acac oxygen atoms acts as a bifurcated
halogen bond acceptor, the bond being symmetric in cocrystals of 1 and 2 and asymmetric in cocrystals of 3 and 6. The only cocrystals in which a halogen
bond was formed with alternative acceptor sites were cocrystals of tfib with 4 and 5, where coordinated
water molecules form hydrogen bonds with all available acac oxygen atoms, leaving only the water molecules themselves as halogen
bond acceptors. The favorability of the bifurcated halogen bond was
also confirmed by QM computations, which have shown the bifurcated
bonds to be the most favorable interactions in vacuo, with bond energies
in the range of 29–37 kJ mol–1 for tfib and 20–25 kJ mol–1 for tfbb. This also reflects on the thermal stability of the cocrystals
of 1–3 (which do not contain coordinated
water) with tfib, which melt/decompose between ca. 180
and 220 °C.
To investigate influences on the topicity of perfluorinated halobenzenes as halogen bond (XB) donors in the solid state, we have conducted a database survey and prepared 18 novel cocrystals of potentially ditopic (13ditfb, 14ditfb) and tritopic (135titfb) XB donors with 15 monotopic pyridines. 135titfb shows high tendency to be mono-or ditopic, but with strong bases it can act as a tritopic XB donor. DFT calculations have shown that binding of a single acceptor molecule on one of the iodine atoms of the XB donor reduces the ESP max on the remaining iodine atoms and dramatically decreases their potential for forming further halogen bonds, which explains both the high occurrence of crystal structures where the donors do not achieve their maximal topicity and the observed differences in halogen bond lengths. Despite the fact that this effect increases with the basicity of the acceptor, when the increase of halogen bond energy due to the basicity of the acceptor compensates its decrease due to the reduction of the acidity of the donor, it enables strong bases to form cocrystals in which a potentially polytopic XB donor achieves its maximal topicity.
Although diazoalkanes are important carbene precursors in organic synthesis, a comprehensive mechanism of photochemical formation of carbenes from diazoalkanes has not been proposed. Synergy of experiments and computations demonstrates the involvement of higher excited singlet states in the photochemistry of diazoalkanes. In all investigated diazoalkanes, excitation to S1 results in nonreactive internal conversion to S0. On the contrary, excitation to higher-lying singlet states (Sn, n > 1), drives the reaction toward a different segment of the S1/S0 conical intersection seam and results in nitrogen elimination and formation of carbenes.
A computational protocol for simulating
time-resolved photoelectron
signals of medium-sized molecules is presented. The procedure is based
on a trajectory surface-hopping description of the excited-state dynamics
and a combined Dyson orbital and multicenter B-spline approach for
the computation of cross sections and asymmetry parameters. The accuracy
of the procedure has been illustrated for the case of ultrafast internal
conversion of gas-phase pyrazine excited to the 1
B
2u
(ππ*) state.
The simulated spectra and the asymmetry map are compared to the experimental
data, and a very good agreement was obtained without applying any
energy-dependent rescaling or broadening. An interesting side result
of this work is the finding that the signature of the 1
A
u
(nπ*) state is indistinguishable from that of the 1
B
3u
(nπ*) state in the time-resolved photoelectron spectrum. By locating
four symmetrically equivalent minima on the lowest-excited (S1) adiabatic potential energy surface of pyrazine, we revealed
the strong vibronic coupling of the 1
A
u
(nπ*) and 1
B
3u
(nπ*) states near the S1 ← S0 band
origin.
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