Theoretical insights into C–H bond activation of methane by transition metal clusters: the role of anharmonic effects

Bhumla, Preeti; Kumar, Manish; Bhattacharya, Saswata

doi:10.1039/d0na00669f

Cited by 9 publications

(8 citation statements)

References 79 publications

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“…Here, ZPE is the zero-point energy correction;

is the electronic energy; E Rot + E Trans + E Vib are the contributions to energy due to translation, rotation, and vibration as function of temperature, respectively. In order to compute the probability of the occurrence of one particular cluster in an ensemble of Be 4 B 8 clusters (Boltzmann ensemble at thermal equilibrium) as a function of temperature, we employed the probability of occurrence [ 33 , 76 , 80 , 81 , 135 , 136 , 137 , 138 , 139 , 140 ] given in Equation (6):

where

is the Boltzmann constant, T is the temperature, and

k is the Gibbs free energy of the k th isomer. Any molecular properties observed are statistical averages over a Boltzmann ensemble of clusters.…”

Section: Theoretical Methods and Computational Detailsmentioning

confidence: 99%

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

et al. 2021

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Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer’s probability of occurrence in a Boltzmann-weighted superposition of each isomer’s spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer–enantiomer and enantiomer–achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

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“…Here, ZPE is the zero-point energy correction;

where

is the Boltzmann constant, T is the temperature, and

k is the Gibbs free energy of the k th isomer. Any molecular properties observed are statistical averages over a Boltzmann ensemble of clusters.…”

Section: Theoretical Methods and Computational Detailsmentioning

confidence: 99%

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

et al. 2021

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“…To compute the probability of the occurrence of one particular Cu 38 cluster in a Boltzmann ensemble at thermal equilibrium as a function of temperature, we employed the probability of occurrence ( Shortle, 2003 ; Li et al, 2007 ; Grimme, 2012 ; Bhattacharya et al, 2017 ; Schebarchov et al, 2018 ; Dzib et al, 2019 ; Goldsmith et al, 2019 ; Grigoryan and Springborg, 2019 ; Mendoza-Wilson et al, 2020 ; Bhumla et al, 2021 ; Buelna-Garcia et al, 2021 ; Buelna-Garcia et al, 2021 ) given by Eq. 5 :

where

is the Boltzmann constant, T is the temperature, and

k is the Gibbs free energy of the k th isomer.…”

Section: Free Energy Surface Exploration Methods and Computational De...mentioning

confidence: 99%

Relative Populations and IR Spectra of Cu38 Cluster at Finite Temperature Based on DFT and Statistical Thermodynamics Calculations

et al. 2022

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The relative populations of Cu38 isomers depend to a great extent on the temperature. Density functional theory and nanothermodynamics can be combined to compute the geometrical optimization of isomers and their spectroscopic properties in an approximate manner. In this article, we investigate entropy-driven isomer distributions of Cu38 clusters and the effect of temperature on their IR spectra. An extensive, systematic global search is performed on the potential and free energy surfaces of Cu38 using a two-stage strategy to identify the lowest-energy structure and its low-energy neighbors. The effects of temperature on the populations and IR spectra are considered via Boltzmann factors. The computed IR spectrum of each isomer is multiplied by its corresponding Boltzmann weight at finite temperature. Then, they are summed together to produce a final temperature-dependent, Boltzmann-weighted spectrum. Our results show that the disordered structure dominates at high temperatures and the overall Boltzmann-weighted spectrum is composed of a mixture of spectra from several individual isomers.

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“…The detail of the AIMD simulations is plotted in The incorporation of anharmonic effects helps to further understand the potential catalyst for C-O bond activation. 69 For this, we plotted the infrared spectra (harmonic vs. anharmonic) of (AuLi)-CO and (AuLi) 4 -CO, and compared them in Fig. 6.…”

Section: Adsorption Characteristics and Stability Of (Auli) N -Co (N ...mentioning

confidence: 99%

“…5. It can be seen that the adsorption structure maintains integrity with only slight disturbances of individual atoms at a temperature of 500 K, suggesting its good thermal stability in a high temperature environment.The incorporation of anharmonic effects helps to further understand the potential catalyst for C-O bond activation 69. For this, we plotted the infrared spectra (harmonic vs. anharmonic) of (AuLi)-CO and (AuLi) 4 -CO, and compared them in Fig.6.…”

mentioning

confidence: 99%

The nature of stability and adsorption interactions of binary Au–Li clusters with bridge adsorption structures

Zhang

Zhu

Liu

et al. 2023

Phys. Chem. Chem. Phys.

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Theoretical insights into C–H bond activation of methane by transition metal clusters: the role of anharmonic effects

Abstract: In heterogeneous catalysis, the determination of active phases has been a long-standing challenge, as materials’ property changes under operational conditions (i.e. temperature (T ) and pressure (p) in an atmosphere...

Cited by 9 publications

References 79 publications

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Relative Populations and IR Spectra of Cu38 Cluster at Finite Temperature Based on DFT and Statistical Thermodynamics Calculations

The nature of stability and adsorption interactions of binary Au–Li clusters with bridge adsorption structures

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