DFT Variants for Mixed-Metal Oxides. Benchmarks Using Multi-Center Cluster Models

Mixed-metal
oxides, e.g., V–Mo and Bi–Mo, are promising selective
oxidation catalysts. Yet, their intricate chemical composition and
electronic structure often confound DFT methods. This study addresses
problems arising from the simultaneous presence of two kinds of transition
metals, by probing eight functionals–five hybrid functionals
(MN15, M06, PBE0-D3, B3LYP-D3, and TPSSh-D3), the meta-GGA functional
M06-L-D3, the range-separated functional ωB97XD, and the GGA
functional PBE-D3. We examine the ability of these functionals to
localize reducing electrons, and to reproduce reaction energies from
CCSD­(T) calculations. Accordingly, hybrid functionals containing 20%
or more exact exchange perform considerably better in both tests.
The B3LYP-D3 approach exhibits the lowest overall mean absolute deviation
of reaction energies (OMAD), 21 kJ mol–1, and gave
electron distributions as expected from the local lattice structure
according to the pseudo-Jahn–Teller effect. MN15 and PBE0-D3
reproduced the electron distributions, but bore slightly higher OMAD
values, at 31 and 32 kJ mol–1. Despite acceptable
OMAD values, M06 (28 kJ mol–1) and TPSSh (23 kJ
mol–1) in some cases did not yield the expected
electron distributions. The range-separated functional ωB97XD
experienced the opposite problem, yielding correct electron distributions
but a poor OMAD of 41 kJ mol–1. M06-L-D3 and PBE-D3
performed relatively poorly, regarding the electron distribution and
the OMAD values, 39 and 65 kJ mol–1, respectively.

混合金属氧化物，例如V-Mo和Bi-Mo，在选择性氧化催化方面展现出巨大的潜力。然而，其复杂的化学组成和电子结构往往令DFT方法难以捉摸。本研究旨在解决两种过渡金属同时存在时产生的问题，通过探究八种泛函——五种混合泛函（MN15、M06、PBE0-D3、B3LYP-D3和TPSSh-D3），元-GGA泛函M06-L-D3，范围分离泛函ωB97XD以及GGA泛函PBE-D3——的能力。我们评估了这些泛函在局部化还原电子以及再现CCSD(T)计算反应能方面的能力。据此，含有20%或以上精确交换的混合泛函在两项测试中均表现出显著优异的性能。B3LYP-D3方法展现出最低的总平均绝对偏差（OMAD）21 kJ mol–1，并给出了符合从局域晶格结构出发，依据伪Jahn-Teller效应预期的电子分布。MN15和PBE0-D3能够再现电子分布，但其OMAD值分别为31和32 kJ mol–1，略高。尽管OMAD值尚可接受，但M06（28 kJ mol–1）和TPSSh（23 kJ mol–1）在某些情况下并未产生预期的电子分布。范围分离泛函ωB97XD则遭遇了相反的问题，其电子分布正确，但OMAD值高达41 kJ mol–1。M06-L-D3和PBE-D3在电子分布及OMAD值方面表现相对较差，分别达到39和65 kJ mol–1。