Anharmonic Downward Distortion Following Research Articles

Geometric analysis of anharmonic downward distortion following paths.

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2f + 1 - 2, where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H2 O molecule in which pitchfork bifurcation is observed.

Crystal Structure Exploration of Boron Nitride Polymorphs Using Anharmonic Downward Distortion Following Method with Potential Energy Surface Modified by the Inverse of Lattice Volume

The boron nitride polymorphs were explored using the anharmonic downward distortion following (ADDF) method with the energy value of the density functional-based tight binding approximation modified by the inverse of the volume of a unit cell. Twelve novel boron nitride polymorphs were discovered. Previously, it has been difficult to search reaction pathways connecting two-dimensional structures such as hexagonal boron nitride to three-dimensional structures using the ADDF method. This problem was partially resolved using this approach.

Exploration of Unimolecular and Bimolecular Pathways for Nitrile N‐Oxide Isomerization to Isocyanate Through Global Reaction Route Mapping Techniques

Mechanisms of the unimolecular and bimolecular isomerization of nitrile N‐oxide to isocyanate were investigated by quantum chemical calculations using the global reaction route mapping (GRRM) technique, which consists of the anharmonic downward distortion following (ADDF) and multi‐component artificial force induced reaction (AFIR) methods, which can exhaustively search reaction paths. In the unimolecular isomerization, isomerization paths of nitrile N‐oxide to isocyanate were exhaustively explored by the ADDF method. The energetically lowest path for 2,6‐dimethoxybenzonitrile oxide (Ar–CNO) isomerization was via oxazirine intermediate formation, which was the rate‐determining step with an activation free energy of 56.8 kcal mol–1. The high activation free energy indicates that the isomerization hardly proceeds as a thermal unimolecular reaction. Next, the bimolecular isomerization paths of Ar–CNO were explored for diradical addition, [3+2] and [3+3] cycloadditions, and self‐catalyzed isomerization through the AFIR method. The diradical addition was the energetically lowest path with an activation free energy of 55.4 kcal mol–1. Although the bimolecular isomerization was energetically favorable than the unimolecular isomerization, its activation free energy was still high for the reaction to proceed under thermal conditions. Exhaustive path searching for these unimolecular and bimolecular isomerizations suggest that these reactions are catalyzed by acid or base.

Isomerization in Gold Clusters upon O2 Adsorption

A systematic investigation is performed on structural transformations in small neutral gold clusters (Au3–Au12) induced by O2 adsorption, with the use of the fully automated reaction path search techniques, i.e., anharmonic downward distortion following (ADDF) and artificial force induced reaction (AFIR) methods, implemented in the global reaction route mapping (GRRM) program. For each size of Au cluster, the most stable structure, low-energy isomers, and a network of isomerization pathways are determined. The located Aun–O2 adsorption forms can be classified into two groups: η1-AunO2, where only one oxygen atom is adsorbed on Aun, and η2-AunO2, where both oxygen atoms are adsorbed on Aun in a bridged manner. These two adsorption forms can be transformed to each other with a low barrier. The isomerization pathways of gold clusters upon O2 adsorption are compared with those obtained for the pure gold clusters without O2. It is demonstrated that O2 adsorption promotes structural transformations in gold clus...

Reactivity of Gold Clusters in the Regime of Structural Fluxionality

This work present results of a systematic investigation of adsorption and dissociation of H2 on the neutral, positively, and negatively charged gold clusters Aunq (n = 2–11; q = 0, ±1) using the global reaction route mapping (GRRM) technique combined with the anharmonic downward distortion following (ADDF) and the artificial force-induced reaction (AFIR) methods. An exhaustive search for H2 dissociation pathways is performed not only on the most stable cluster structures but also on the large number of low-energy isomers, allowing structural transformations between them. The present strategy can automatically identify the structure-dependent lowest transition states (TS) for H2 dissociation with a systematic procedure in the regime of the structural fluxionality of gold clusters at finite temperature. Temperature effects, cluster isomerization, and influence of the charge state of gold clusters on H2 adsorption and dissociation are studied. It is demonstrated that the most stable structures of the gold cl...

Anharmonic Downward Distortion Following for Automated Exploration of Quantum Chemical Potential Energy Surfaces

Abstract This article gives a comprehensive review of the anharmonic downward distortion following (ADDF) method. The ADDF method has been developed as an automated reaction path search method. This method follows the anharmonic downward distortion (ADD) toward transition states and dissociation channels starting from a local minimum on the potential energy surface (PES). Systematic applications of the ADDF method to all local minima provide a global network of reaction pathways on the PES of given chemical formulas. Various extensions have been proposed and applied to many interesting chemical problems such as elucidation of photodissociation mechanisms, structure prediction of H-bonded clusters, mechanistic studies of organometallic catalysis, design of generation–conversion routes of amino acid molecules, and so on. It has also been employed in efficient construction of anharmonic PESs for highly accurate vibrational analysis. These developments and applications are illustrated with some representative results.

Application of Automated Reaction Path Search Methods to a Systematic Search of Single-Bond Activation Pathways Catalyzed by Small Metal Clusters: A Case Study on H-H Activation by Gold.

A new theoretical approach to find metal-cluster-catalyzed single bond activation pathways is introduced. The proposed approach combines two automated reaction path search techniques: the anharmonic downward distortion following (ADDF) and the artificial force induced reaction (AFIR) methods, developed in our previous works [Maeda, S.; Ohno, K.; Morokuma, K. Phys. Chem. Chem. Phys. 2013, 15, 3683-3701]. A simple model reaction of the H-H bond activation catalyzed by Aun (n = 7, 8) clusters is considered as an example. We have automatically found 33 and 20 transition-state (TS) structures for H2 dissociation on Au7 and Au8 clusters, respectively, and successfully identified the best dissociation pathways with the lowest barrier. Systematic analysis of the structure-dependent reactivity of small gold clusters is performed. It is demonstrated that the most stable structures of the gold clusters are not always highly reactive and several isomeric structures must be taken into account for adequate description of the reaction rates at finite temperatures. The proposed approach can serve as a promising tool for investigation of the chemical reactions catalyzed by small metal clusters.

Role of Water in Mukaiyama–Aldol Reaction Catalyzed by Lanthanide Lewis Acid: A Computational Study

Carbon-carbon bond formations, such as Kobayashi modification of the Mukaiyama-Aldol reaction, catalyzed by lanthanide (Ln) Lewis acid in aqueous solution comprise one of the most attractive types of reactions in terms of green chemistry. However, their detailed mechanisms and the role of water molecules remained unclear. In order to explore complex potential energy surfaces for the water and substrate coordination around Eu(3+) as well as the detailed mechanism of the Mukaiyama-Aldol reaction between trimethylsilyl (TMS) cylcohexenolate and benzaldehyde (BA) catalyzed by Eu(3+), the recently developed anharmonic downward distortion following (ADDF) and artificial force-induced reaction (AFIR) methods were used with the B3LYP-D3 theory. The most favorable water coordination structures are Eu(3+)(H2O)8 and Eu(3+)(H2O)9; they are comparable in free energy and are likely to coexist, with an effective coordination number of 8.3. Eu(3+)(H2O)8(BA) is the best aldehyde coordinated structure. Starting with this complex, the Mukaiyama-Aldol reaction proceeds via a stepwise mechanism, first C-C bond formation between the substrates, followed by proton transfer from water to BA and then TMS dissociation caused by nucleophilic attack by bulk water molecules. Why did the yield of the Mukaiyama-Aldol reaction catalyzed by Ln(3+) in organic solvent dramatically increase upon addition of water? Without water, the reverse reaction (C-C cleavage) takes place easily. Why did this reaction show syn-preference in water? The anti transition state for C-C formation in water is entropically less favored relative to the syn transition state because of the existence of a rigid hydrogen bond between the TMS part and coordination water around Eu(3+) in the former.

Automated Search for Minimum Energy Conical Intersection Geometries between the Lowest Two Singlet States S0/S1-MECIs by the Spin-Flip TDDFT Method.

Automated search for minimum energy conical intersection geometries between the lowest two singlet states (S0/S1-MECIs) was performed by combining the anharmonic downward distortion following (ADDF) method, the seam model function (SMF) approach, and the spin-flip (SF) TDDFT method. SMF/ADDF has been employed previously in automated searches for MECIs on potential energy surfaces (PESs) with expensive multireference methods. In this work, we adopt the SF-TDDFT method that enables efficient optimization of S0/S1-MECIs in the framework of TDDFT. To evaluate the performance of the present approach, it was applied to ethylene and 1,3-butadiene. The present method automatically gave unknown S0/S1-MECIs as well as all previously reported ones. Therefore, the present hybrid method of SMF/ADDF and SF-TDDFT is shown to be a promising approach to locate S0/S1-MECIs of large systems automatically with modest computational costs.

Theoretical Study on the Photodissociation of Methylamine Involving S1, T1, and S0 States

Various photodissociation pathways of methylamine involving the three lowest electronic states, namely, singlet ground S0 state, singlet first excited S1 state, and triplet ground T1 state, were studied by the (MS-)CAS(8e,8o)PT2/6-31++G** method. All critical points, i.e., minima, transition states, minimum energy conical intersections, and minima on the seam of crossing, were explored systematically by the global reaction route mapping (GRRM) strategy utilizing the anharmonic downward distortion following (ADDF) and artificial force induced reaction (AFIR) methods. On the basis of obtained structures, we discuss the photodissociation mechanism of methylamine in the experimental excitation wavelength range 222-240 nm in detail. Especially, the T1 potential energy surface was explored systematically for the first time. The N-H bond rupture is a primary channel on the S1 state. Along the N-H dissociation path on S1, there is a low-energy conical intersection (CI), and through this CI the system can go back to the S0 state; from the CI the system can directly dissociate to CH3NH + H or reproduce the original CH3NH2 on S0. There is a seam of crossing between S0 and T1 in a partially dissociated CH3---NH2 geometry, and through this seam the system may go up to the T1. On the T1 state, a roaming-like pathway giving CH4 + NH (X(3)Σ(-)) products was found, which would explain the recently proposed intersystem crossing mediated roaming dynamics.

Systematic exploration of the mechanism of chemical reactions: the global reaction route mapping (GRRM) strategy using the ADDF and AFIR methods

Global reaction route mapping (GRRM), a fully-automated search for all important reaction pathways relevant to a given purpose, on the basis of quantum chemical calculations enables systematic elucidation of complex chemical reaction mechanisms. However, GRRM had previously been limited to very simple systems. This is mainly because such calculations are highly demanding even in small systems when a brute-force sampling is considered. Hence, we have developed two independent but complementary methods: anharmonic downward distortion following (ADDF) and artificial force induced reaction (AFIR) methods. ADDF can follow reaction pathways starting from local minima on the potential energy surface (PES) toward transition structures (TSs) and dissociation channels. AFIR can find pathways starting from two or more reactants toward TSs for their associative reactions. In other words, ADDF searches for A → X type isomerization and A → X + Y type dissociation pathways, whereas AFIR finds A + B → X (+ Y) type associative pathways. Both follow special paths called the ADDF path and the AFIR path, and these tend to pass through near TSs of corresponding reaction pathways, giving approximate TSs. Such approximate TSs can easily be re-optimized to corresponding true TSs by standard geometry optimizations. On the basis of these two methods, we have proposed practical strategies of GRRM. The GRRM strategies have been applied to a variety of chemical systems ranging from thermal- and photochemical-reactions in small systems to organometallic- and enzyme-catalysis, on the basis of quantum chemical calculations. In this perspective, we present an overview of the GRRM strategies and some results of applications. Their practical usage for systematic prediction is also discussed.

An Automated and Systematic Transition Structure Explorer in Large Flexible Molecular Systems Based on Combined Global Reaction Route Mapping and Microiteration Methods.

The global reaction route mapping (GRRM) method enabled an automated and a systematic search for routes of chemical reactions on a potential energy surface based on the anharmonic downward distortion following (ADDF) approach [Chem. Phys. Lett. 2004, 384, 277]. On the other hand, the microiteration technique [Mol. Phys. 2006, 104, 701] has been developed for full optimizations of transition state (TS) structures for reactions/transformations in large flexible molecular systems and successfully used in ONIOM(QM:MM) calculations. In the present paper, combining the GRRM method with the microiteration technique, we developed a microiteration-ADDF (μ-ADDF) method for automated and systematic TS exploration of large flexible molecular systems. We showed that the method works well with two test systems, (H2CO)(H2O)100 and Si6(C12H17)6, in the ONIOM(QM:MM) framework. It is noted that the present μ-ADDF method can be used for pure quantum mechanics (QM) or molecular mechanics (MM) systems (without ONIOM) and has been tested successfully in C6H10O pure QM calculations.