Monthly Archives: June 2022

Percentage of Molecular Orbital Composition – G09,G16

Canonical Molecular Orbitals are–by construction–delocalized over the various atoms making up a molecule. In some contexts it is important to know how much of any given orbital is made up by a particular atom or group of atoms, and while you could calculate it by hand given the coefficients of each MO in terms of every AO (or basis set function) centered on each atom there is a straightforward way to do it in Gaussian.

If we’re talking about ‘dividing’ a molecular orbital into atomic components, we’re most definitely talking about population analysis calculations, so we’ll resort to the pop keyword and the orbitals option in the standard syntax:

#p M052x/cc-pVDZ pop=orbitals

This will produce the following output right after the Mulliken population analysis section:

Atomic contributions to Alpha molecular orbitals:
 Alpha occ 140 OE=-0.314 is Pt1-d=0.23 C38-p=0.16 C31-p=0.16 C36-p=0.16 C33-p=0.15
 Alpha occ 141 OE=-0.313 is Pt1-d=0.41
 Alpha occ 142 OE=-0.308 is Cl2-p=0.25
 Alpha occ 143 OE=-0.302 is Cl2-p=0.72 Pt1-d=0.18
 Alpha occ 144 OE=-0.299 is Cl2-p=0.11
 Alpha occ 145 OE=-0.298 is C65-p=0.11 C58-p=0.11 C35-p=0.11 C30-p=0.11
 Alpha occ 146 OE=-0.293 is C58-p=0.10
 Alpha occ 147 OE=-0.291 is C22-p=0.09
 Alpha occ 148 OE=-0.273 is Pt1-d=0.18 C11-p=0.12 C7-p=0.11
 Alpha occ 149 OE=-0.273 is Pt1-d=0.18
 Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18
 Alpha vir 151 OE=-0.028 is C7-p=0.25 C16-p=0.11 C44-p=0.11
 Alpha vir 152 OE=0.017 is Pt1-p=0.10
 Alpha vir 153 OE=0.021 is C36-p=0.15 C31-p=0.14 C63-p=0.12 C59-p=0.12 C38-p=0.11 C33-p=0.11
 Alpha vir 154 OE=0.023 is C36-p=0.13 C31-p=0.13 C63-p=0.11 C59-p=0.11
 Alpha vir 155 OE=0.027 is C65-p=0.11 C58-p=0.10
 Alpha vir 156 OE=0.029 is C35-p=0.14 C30-p=0.14 C65-p=0.12 C58-p=0.11
 Alpha vir 157 OE=0.032 is C52-p=0.09
 Alpha vir 158 OE=0.040 is C50-p=0.14 C22-p=0.13 C45-p=0.12 C17-p=0.11
 Alpha vir 159 OE=0.044 is C20-p=0.15 C48-p=0.14 C26-p=0.12 C54-p=0.11

Alpha and Beta densities are listed separately only in unrestricted calculations, otherwise only the first is printed. Each orbital is listed sequentially (occ = occupied; vir = virtual) with their energy value (OE = orbital energy) in atomic units following and then the fraction with which each atom contributes to each MO.

By default only the ten highest occupied orbitals and ten lowest virtual orbitals will be assessed, but the number of MOs to be analyzed can be modified with orbitals=N, if you want to have all orbitals analyzed then use the option AllOrbitals instead of just orbitals. Also, the threshold used for printing the composition is set to 10% but it can be modified with the option ThreshOrbitals=N, for the same compound as before here’s the output lines for HOMO and LUMO (MOs 149, 150) with ThreshOrbitals set to N=1, i.e. 1% as occupation threshold (ThreshOrbitals=1):

Alpha occ 149 OE=-0.273 is Pt1-d=0.18 N4-p=0.08 N6-p=0.08 C20-p=0.06 C13-p=0.06 C48-p=0.06 C9-p=0.06 C24-p=0.05 C52-p=0.05 C16-p=0.04 C44-p=0.04 C8-p=0.03 C15-p=0.03 C17-p=0.03 C45-p=0.02 C46-p=0.02 C18-p=0.02 C26-p=0.02 C54-p=0.02 N5-p=0.01 N3-p=0.01
Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18 C44-p=0.08 C16-p=0.08 C15-p=0.06 C8-p=0.06 N6-p=0.04 N4-p=0.04 C52-p=0.04 C24-p=0.04 N5-p=0.03 N3-p=0.03 C46-p=0.03 C18-p=0.03 C48-p=0.02 C20-p=0.02

The fragment=n label in the coordinates can be used as in BSSE Counterpoise calculations and the output will show the orbital composition by fragments with the label "Fr", grouping all contributions to the MO by the AOs centered on the atoms in that fragment.

As always, thanks for reading, sharing, and rating. I hope someone finds this useful.

Au(I) Chemistry No.3 – New paper in Dalton Transactions

Stabilizing Gold in low oxidation states is a longstanding challenge of organometallic chemistry. To do so, a fine tuning of the electron density provided to an Au atom by a ligand via the formation of a σ bond. The group of Professor Rong Shang at the University of Nagasaki has accomplished the stabilization of an aurate complex through the use of a boron, nitrogen-containing heterocyclic carbene; DFT calculations at the wB97XD/(LANL2TZ(f),6-311G(d)) level of theory revealed that this ligand exhibits a high π-withdrawing character of the neutral 4π B,N-heterocyclic carbene (BNC) moiety and a 6π weakly aromatic character with π-donating properties, implying that this is the first cyclic carbene ligand that is able to be tuned between π-withdrawing (Fischer-type)- and π-donating (Schrock-type) kinds.

A π-withdrawing character on part of the ligand is important to allow the electron-rich gold center back donate some of its excess electron density, this way preventing its oxidation. A modification of Bertrand’s cyclic (alkyl)(amino)carbene (CAAC) has allowed Shang and co-workers to perform the two electrons Au(I) reduction to form the aurate shown in figure 1 (CCDC 2109027). This work also reports on the modular synthesis of the BNC-1 ligand and the mechanism was calculated once again by Leonardo “Leo” Lugo.

Figure 1. Compound 4a (H atoms omitted for clarity)

The ability of the BNC-1 ligand to accept gold’s back donation is reflected on the HOMO/LUMO gap as shown in Figure 2; while BNC-1 has a gap of 7.14 eV, the classic NHC carbene has a gap of 11.28 eV, furthermore, in the case of NHC the accepting orbital is not LUMO but LUMO+1. Additionally, the NBO delocalization energies show that the back donation from Au 5d orbital to the C-N antibonding π* orbital is about half that expected for a Fischer type carbene, suggesting an intermediate character between π accepting and π donating carbene. On the other hand, the largest interaction corresponds to the carbanion density donated to Au vacant p orbital (ca. 45 kcal/mol). All these observations reveal the successful tuning of the electron density on BNC-1.

Figure 2. Frontier Molecular Orbitals for the ligand BNC-1 and a comparison to similar carbenes used elsewhere

This study is available in Dalton Transactions. As usual, I’m honored to be a part of this international collaboration, and I’m deeply thankful to the amazing Prof. José Oscar Carlos Jiménez-Halla for inviting me to be a part of it.

Yoshitaka Kimura, Leonardo I. Lugo-Fuentes, Souta Saito, J. Oscar C. Jimenez-HallaJoaquín Barroso-FloresYohsuke YamamotoMasaaki Nakamoto and Rong Shang* “A boron, nitrogen-containing heterocyclic carbene (BNC) as a redox active ligand: synthesis and characterization of a lithium BNC-aurate complex”, Dalton Trans., 2022,51, 7899-7906

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