Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems.

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1-4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems.

An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems.

An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu2O2]2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C-C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.

B(C6F5)3-Catalyzed Sequential Additions of Terminal Alkynes to para-Substituted Phenols: Selective Construction of Congested Phenol-Substituted Quaternary Carbons.

We have developed a borane-catalyzed sequential addition of terminal alkynes to para-substituted phenols, which affords a wide range of ortho-propargylic alkylated phenols bearing congested quaternary carbons. Control experiments combined with DFT calculations suggest that the reaction undergoes a sequential phenol alkenylation/hydroalkynylation process. Further extension of this strategy to the construction of triaryl-substituted quaternary carbons demonstrates the broad utility of this method.

Automatic Selection of Active Orbitals from Generalized Valence Bond Orbitals.

The accurate multireference (MR) calculation of a strongly correlated chemical system usually relies on a correct preselection of a small number of active orbitals from numerous molecular orbitals. Currently, the active orbitals are generally determined by using a trial-and-error method. Such a preselection by chemical intuition and personal experience may be tedious or unreliable, especially for large complicated systems, and accordingly, the construction of active space becomes a bottleneck for large-scale MR calculations. In this work, we propose to automatically select the active orbitals according to the natural orbital occupation numbers by performing black box generalized valence bond calculations. We demonstrate the accuracy of this method through testing calculations of the ground states in various systems, ranging from bond dissociation of diatomic molecules (N2, C2, Cr2) to conjugated molecules (pentacene, hexacene, and heptacene) as well as a binuclear transition-metal complex [Mn2O2(H2O)2(terpy)2]3+ (terpy = 2,2':6,2″-terpyridine) with active spaces up to (30e, 30o) and comparing with the complete active space self-consistent field (CASSCF), density matrix renormalization group (DMRG)-CASSCF references, and other recently proposed inexpensive strategies for constructing active spaces. The results indicate that our method is among the most successful ones within our comparison, providing high-quality initial active orbitals very close to the finally optimized (DMRG-)CASSCF orbitals. The method proposed here is expected to greatly benefit the practical implementation of large active space ground-state MR calculations, for example, large-scale DMRG calculations.

Describing Strong Correlation with Block-Correlated Coupled Cluster Theory.

A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide satisfactory descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single C-C bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all C-C bonds.

Mechanistic Insight Into the AuCN Catalyzed Annulation Reaction of Salicylaldehyde and Aryl Acetylene: Cyanide Ion Promoted Umpolung Hydroacylation/Intramolecular Oxa-Michael Addition Mechanism.

The detailed mechanism of the AuCN-catalyzed annulation of salicylaldehyde (SA) and phenyl acetylene leading to isoflavanone-type complexes has been investigated via density functional theory (DFT) calculations. Reaction pathways and possible stationary points are obtained with the combined molecular dynamics and coordinate driving (MD/CD) method. Our calculations reveal that the cyanide ion promoted umpolung hydroacylation/intramolecular oxa-Michael addition mechanism is more favorable than the Au(I)/Au(III) redox mechanism proposed previously. In the umpolung mechanism, the hydroxyl of SA is found to strongly stabilize the cyanide ion involved intermediates and transition states via hydrogen bond interactions, while the Au(I) ion always acts as a counter cation. The overall reaction is exergonic by 41.8 kcal/mol. The hydroacylation of phenyl acetylene is the rate-determining step and responsible for the regioselectivity with a free energy barrier of 27.3 kcal/mol. These calculated results are in qualitative accord with the experimental findings.

Automatic Construction of the Initial Orbitals for Efficient Generalized Valence Bond Calculations of Large Systems.

We propose an efficient general strategy for generating initial orbitals for generalized valence bond (GVB) calculations which makes routine black-box GVB calculations on large systems feasible. Two schemes are proposed, depending on whether the restricted Hartree-Fock (RHF) wave function is stable (scheme I) or not (scheme II). In both schemes, the first step is the construction of active occupied orbitals and active virtual orbitals. In scheme I, active occupied orbitals are composed of the valence orbitals (the inner core orbitals are excluded), and the active virtual orbitals are obtained from the original virtual space by requiring its maximum overlap with the virtual orbital space of the same system at a minimal basis set. In scheme II, active occupied orbitals and active virtual orbitals are obtained from the set of unrestricted natural orbitals (UNOs), which are transformed from two sets of unrestricted HF spatial orbitals. In the next step, the active occupied orbitals and active virtual ones are separately transformed to localized orbitals. Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres (KM) algorithm and are used as the initial guess for the GVB orbitals. The optimized GVB wave function is obtained using the second-order self-consistent-field algorithm in the GAMESS program. With this procedure, GVB energies have been obtained for the lowest singlet and triplet states of polyacenes (up to decacene with 96 pairs) and the singlet ground state of two di-copper-oxygen-ammonia complexes. We have also calculated the singlet-triplet gaps for some polyacenes and the relative energy between two di-copper-oxygen-ammonia complexes with the block-correlated second-order perturbation theory based on the GVB reference.

Adsorption Mechanism of 4-Amino-5-mercapto-1,2,4-triazole as Flotation Reagent on Chalcopyrite.

A novel compound 4-amino-5-mercapto-1,2,4-triazole was first synthesized, and its selective adsorption mechanism on the surface of chalcopyrite was comprehensively investigated using UV-vis spectra, zeta-potential, Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy measurements (XPS), time-of-flight secondary ion mass spectrometry (ToF-SIMS), and first principles calculations. The experimental and computational results consistently demonstrated that AMT would chemisorb onto the chalcopyrite surface by the formation of a five-membered chelate ring. The first principles periodic calculations further indicated that AMT would prefer to adsorb onto Cu rather than Fe due to the more negative adsorption energy of AMT on Cu in the chalcopyrite (001) surface, which was further confirmed by the coordination reaction energies of AMT-Cu and AMT-Fe based on the simplified cluster models at a higher accuracy level (UB3LYP/Def2-TZVP). The bench-scale results indicated that the selective index improved significantly when using AMT as a chalcopyrite depressant in Cu-Mo flotation separation.

Automatic Reaction Pathway Search via Combined Molecular Dynamics and Coordinate Driving Method.

We proposed and implemented a combined molecular dynamics and coordinate driving (MD/CD) method for automatically searching multistep reaction pathways of chemical reactions. In this approach, the molecular dynamic (MD) method at the molecular mechanics (MM) or semiempirical quantum mechanical (QM) level is employed to explore the conformational space of the minimum structures, and the modified coordinate driving (CD) method is used to build reaction pathways for representative conformers. The MD/CD method is first applied to two model reactions (the Claisen rearrangement and the intermolecular aldol reaction). By comparing the obtained results with those of the existing methods, we found that the MD/CD method has a comparable performance in searching low-energy reaction pathways. Then, the MD/CD method is further applied to investigate two reactions: the electrocyclic reaction of benzocyclobutene-7-carboxaldehyde and the intramolecular Diels-Alder reaction of ketothioester with 11 effectively rotatable single bonds. For the first reaction, our results can correctly account for its torquoselectivity. For the second one, our method predicts eight reaction channels, leading to eight different stereo- and regioselective products. The MD/CD method is expected to become an efficient and cost-effective theoretical tool for automatically searching low-energy reaction pathways for relatively complex chemical reactions.