Response to Comment on "Reversible disorder-order transitions in atomic crystal nucleation".

Yu et al. suggested calculating precisely the size ranges of the three parts of our figure 3A, adjusting the free-energy levels in figure 3B, and considering the shape effect in the first-principles calculation. The first and second suggestions raise strong concerns for misinterpretation and overinterpretation of our experiments. The original calculation is sufficient to support our claim about crystalline-to-disordered transformations.

Infiltrated thin film structure with hydrogel-mediated precursor ink for durable SOFCs.

The hydrogel of biomolecule-assisted metal/organic complex has the superior ability to form a uniform, continuous, and densely integrated structure, which is necessary for fine thin film fabrication. As a representative of nature-originated polymers with abundant reactive side chains, we select the gelatin molecule as an element for weaving the metal cations. Here, we demonstrate the interaction between the metal cation and gelatin molecules, and associate it with coating quality. We investigate the rheological property of gelatin solutions interacting with metal cation from the view of cross-linking and denaturing of gelatin molecules. Also, we quantitatively compare the corresponding interactions by monitoring the absorbance spectrum of the cation. The coated porous structure is systematically investigated from the infiltration of gelatin-mediated Gd0.2Ce0.8O2-δ (GDC) precursor into Sm0.5Sr0.5CoO3-δ (SSC) porous scaffold. By applying the actively interacting gelatin-GDC system, we achieve a thin film of GDC on SSC with excellent uniformity. Compare to the discrete coating from the typical infiltration process, the optimized thin film coated structure shows enhanced performance and stability.

Reversible disorder-order transitions in atomic crystal nucleation.

Nucleation in atomic crystallization remains poorly understood, despite advances in classical nucleation theory. The nucleation process has been described to involve a nonclassical mechanism that includes a spontaneous transition from disordered to crystalline states, but a detailed understanding of dynamics requires further investigation. In situ electron microscopy of heterogeneous nucleation of individual gold nanocrystals with millisecond temporal resolution shows that the early stage of atomic crystallization proceeds through dynamic structural fluctuations between disordered and crystalline states, rather than through a single irreversible transition. Our experimental and theoretical analyses support the idea that structural fluctuations originate from size-dependent thermodynamic stability of the two states in atomic clusters. These findings, based on dynamics in a real atomic system, reshape and improve our understanding of nucleation mechanisms in atomic crystallization.

Scaffold-based molecular design with a graph generative model.

Searching for new molecules in areas like drug discovery often starts from the core structures of known molecules. Such a method has called for a strategy of designing derivative compounds retaining a particular scaffold as a substructure. On this account, our present work proposes a graph generative model that targets its use in scaffold-based molecular design. Our model accepts a molecular scaffold as input and extends it by sequentially adding atoms and bonds. The generated molecules are then guaranteed to contain the scaffold with certainty, and their properties can be controlled by conditioning the generation process on desired properties. The learned rule of extending molecules can well generalize to arbitrary kinds of scaffolds, including those unseen during learning. In the conditional generation of molecules, our model can simultaneously control multiple chemical properties despite the search space constrained by fixing the substructure. As a demonstration, we applied our model to designing inhibitors of the epidermal growth factor receptor and show that our model can employ a simple semi-supervised extension to broaden its applicability to situations where only a small amount of data is available.

Fragment-orbital tunneling currents and electronic couplings for analysis of molecular charge-transfer systems.

In theoretical charge-transfer research, calculation of the electronic coupling element is crucial for examining the degree of the electronic donor-acceptor interaction. The tunneling current (TC), representing the magnitudes and directions of electron flow, provides a way of evaluating electronic couplings, along with the ability of visualizing how electrons flow in systems. Here, we applied the TC theory to π-conjugated organic dimer systems, in the form of our fragment-orbital tunneling current (FOTC) method, which uses the frontier molecular-orbitals of system fragments as diabatic states. For a comprehensive test of FOTC, we assessed how reasonable the computed electronic couplings and the corresponding TC densities are for the hole- and electron-transfer databases HAB11 and HAB7. FOTC gave 12.5% mean relative unsigned error with regard to the high-level ab initio reference. The shown performance is comparable with that of fragment-orbital density functional theory, which gave the same error by 20.6% or 13.9% depending on the formulation. In the test of a set of nucleobase π stacks, we showed that the original TC expression is also applicable to nondegenerate cases under the condition that the overlap between the charge distributions of diabatic states is small enough to offset the energy difference. Lastly, we carried out visual analysis on the FOTC densities of thiophene dimers with different intermolecular alignments. The result depicts an intimate topological connection between the system geometry and electron flow. Our work provides quantitative and qualitative grounds for FOTC, showing it to be a versatile tool in characterization of molecular charge-transfer systems.

Effects of the locality of a potential derived from hybrid density functionals on Kohn-Sham orbitals and excited states.

Density functional theory (DFT) has been an essential tool for electronic structure calculations in various fields. In particular, its hybrid method including the Hartree-Fock (HF) exchange term remarkably improves the reliability of DFT for chemical applications and computational material design. There are two different types of exchange-correlation potential that can be derived from hybrid functionals. The conventional approach adopts a non-multiplicative potential including the non-local HF exchange operator. Herein, we propose to use a local multiplicative potential as an alternative for accurate excited state calculations. We show that such a local potential can be derived from existing global hybrid functionals using the optimized effective potential method. As a proof-of-concept, we chose PBE0 and investigated its performance for the Caricato benchmark set. Unlike the conventional one, the local potential produced orbital energy gaps with no strong dependence on the mixing ratio as a good approximation for optical excitations. Furthermore, its time-dependent DFT resulted in a surprisingly small mean absolute error even with a local density approximation kernel, surpassing all reported values with various popular functionals. In particular, most excitations were dictated by single orbital transitions due to physically meaningful virtual orbitals, which is beneficial to clear interpretations in the molecular orbital picture.

Configuration interaction singles based on the real-space numerical grid method: Kohn-Sham versus Hartree-Fock orbitals.

We developed a program code of configuration interaction singles (CIS) based on a numerical grid method. We used Kohn-Sham (KS) as well as Hartree-Fock (HF) orbitals as a reference configuration and Lagrange-sinc functions as a basis set. Our calculations show that KS-CIS is more cost-effective and more accurate than HF-CIS. The former is due to the fact that the non-local HF exchange potential greatly reduces the sparsity of the Hamiltonian matrix in grid-based methods. The latter is because the energy gaps between KS occupied and virtual orbitals are already closer to vertical excitation energies and thus KS-CIS needs small corrections, whereas HF results in much larger energy gaps and more diffuse virtual orbitals. KS-CIS using the Lagrange-sinc basis set also shows a better or a similar accuracy to smaller orbital space compared to the standard HF-CIS using Gaussian basis sets. In particular, KS orbitals from an exact exchange potential by the Krieger-Li-Iafrate approximation lead to more accurate excitation energies than those from conventional (semi-) local exchange-correlation potentials.