Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates.

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation.

In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules (H2O and N2) and calculate the ground and excited state energies of three molecules (LiH, CH+, and H2O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

The Mechanochemistry of Carboranes.

We developed o-carborane as a new mechanophore by showing that the o-carborane cluster is the preferred scission site in chain-centered polymers through ultrasonication mechanochemistry. Mechanistic studies are consistent with a predominately homolytic mechanism of chain scission. The mechanically generated monocarbaborane fragments are highly reactive toward alcohol nucleophiles. By contrast, carborane with a different regiochemistry (m-carborane) maintained its high mechanical stability. DFT simulations provide insights into the origins of carborane's mechanical lability. This fundamental research provides a new stimulus for carborane cage activation.

Distal conformational locks on ferrocene mechanophores guide reaction pathways for increased mechanochemical reactivity.

Mechanophores can be used to produce strain-dependent covalent chemical responses in polymeric materials, including stress strengthening, stress sensing and network remodelling. In general, it is desirable for mechanophores to be inert in the absence of force but highly reactive under applied tension. Metallocenes possess potentially useful combinations of force-free stability and force-coupled reactivity, but the mechanistic basis of this reactivity remains largely unexplored. Here, we have used single-molecule force spectroscopy to show that the mechanical reactivities of a series of ferrocenophanes are not correlated with ring strain in the reactants, but with the extent of rotational alignment of their two cyclopentadienyl ligands. Distal attachments can be used to restrict the mechanism of ferrocene dissociation to proceed through ligand 'peeling', as opposed to the more conventional 'shearing' mechanism of the parent ferrocene, leading the dissociation rate constant to increase by several orders of magnitude at forces of ~1 nN. It also leads to improved macroscopic, multi-responsive behaviour, including mechanochromism and force-induced cross-linking in ferrocenophane-containing polymers.

Towards Near-Exact Solutions of Molecular Electronic Structure: Full Coupled-Cluster Reduction with a Second-Order Perturbative Correction.

We introduce a new augmented adaptation of the recently developed full coupled-cluster reduction (FCCR) with a second-order perturbative correction, abbreviated as FCCR(2). FCCR is a selected coupled-cluster expansion aimed at optimally reducing the excitation manifold and commutator expansions for high-rank excitations for obtaining accurate solutions of the electronic Schödinger equation in a size-extensive manner. The present FCCR(2) enables estimating the residual correlation of FCCR by the second-order perturbative correction E(2) from the complementary space of the FCCR projection manifold. The linear relationship between E(2) and the energy of FCCR(2) allows accurate estimates of near-exact energies for a wide variety of molecules with strong electron correlation. The potential of the method is demonstrated using challenging cases, the ground-state electronic energy of the benzene molecule in equilibrium and stretched geometries, and the isomerization energy of the transition metal complex [Cu(NH3)]2O22+.

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

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.

Generalizing metallocene mechanochemistry to ruthenocene mechanophores.

Recent reports have shown that ferrocene displays an unexpected combination of force-free stability and mechanochemical activity, as it acts as the preferred site of chain scission along the backbone of highly extended polymer chains. This observation raises the tantalizing question as to whether similar mechanochemical activity might be present in other metallocenes, and, if so, what features of metallocenes dictate their relative ability to act as mechanophores. In this work, we elucidate polymerization methodologies towards main-chain ruthenocene-based polymers and explore the mechanochemistry of ruthenocene. We find that ruthenocene, in analogy to ferrocene, acts as a highly selective site of main chain scission despite the fact that it is even more inert. A comparison of ruthenocene and ferrocene reactivity provides insights as to the possible origins of metallocene mechanochemistry, including the relative importance of structural and thermodynamic parameters such as bond length and bond dissociation energy. These results suggest that metallocenes might be privileged mechanophores through which highly inert coordination complexes can be made dynamic in a stimuli-responsive fashion, offering potential opportunities in dynamic metallo-supramolecular materials and in mechanochemical routes to reactive intermediates that are otherwise difficult to obtain.

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.

Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation.

A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster reduction that is capable of providing very accurate solutions of the many-body Schrödinger equation is then initiated employing screenings to the projection manifold and commutator operations. The projection manifold is iteratively updated through the single commutators ⟨κ|[H[over ^],T[over ^]]|0⟩ comprised of the primary clusters T[over ^]_{λ} with a substantial contribution to the connectivity. The operation of the commutators is further reduced by introducing a correction, taking into account the so-called exclusion-principle-violating terms that provides a fast and near-variational convergence in many cases.

Partially linearized external models to active-space coupled-cluster through connected hextuple excitations.

Partially linearized external models to active-space coupled-cluster through hextuple excitations, for example, CC{SDtqph}L , CCSD{tqph}L , and CCSD{tqph}hyb, are implemented and compared with the full active-space CCSDtqph. The computational scaling of CCSDtqph coincides with that for the standard coupled-cluster singles and doubles (CCSD), yet with a much large prefactor. The approximate schemes to linearize the external excitations higher than doubles are significantly cheaper than the full CCSDtqph model. These models are applied to investigate the bond dissociation energies of diatomic molecules (HF, F2 , CuH, and CuF), and the potential energy surfaces of the bond dissociation processes of HF, CuH, H2 O, and C2 H4 . Among the approximate models, CCSD{tqph}hyb provides very accurate descriptions compared with CCSDtqph for all of the tested systems. © 2018 Wiley Periodicals, Inc.

Quantitative and Mechanistic Mechanochemistry in Ferrocene Dissociation.

Ferrocene is classically regarded as being highly inert owing to the large dissociation energy of metal-cyclopentadienyl (Cp) bonds. We show that the Fe-Cp bond in ferrocene is the preferential site of mechanochemical scission in the pulsed ultrasonication of main-chain ferrocene-containing polybutadiene-derived polymers. Quantitative studies reveal that the Fe-Cp bond is similar in strength to the carbon-nitrogen bond of an azobisdialkylnitrile (bond dissociation energy < -0 kcal/mol), despite the significantly higher Fe-Cp bond dissociation energy (approximately 90 kcal/mol). Mechanistic studies are consistent with a predominately heterolytic mechanism of chain scission. DFT calculations provide insights into the origins of ferrocene's mechanical lability.

Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function.

An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.

Block correlated second order perturbation theory with a generalized valence bond reference function.

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Hybrid coupled cluster methods based on the split virtual orbitals: barrier heights of reactions and spectroscopic constants of open-shell diatomic molecules.

We report an efficient implementation of the coupled cluster (CC) singles, doubles, and a hybrid treatment of triples based on the split virtual orbitals (SVO-CCSD(T)-h) method [J. Chem. Phys.2012, 136, 044101]. In this approach, virtual orbitals are split into two subsets, and correspondingly triple excitations are divided into active and inactive subsets. The active triple excitations are treated with the CCSDt (CC singles, doubles, and active triples) method, while the inactive triple excitations are treated with the CCSD(T) (CC singles, doubles, and perturbative triples) method. In the present work, the use of semicanonical molecular orbitals allows the CCSD(T)-like equations in SVO-CCSD(T)-h to be solved without iteration. As a result, the present SVO-CCSD(T)-h scheme does not need a large disk space to store the large number of triple excitation amplitudes, which is required by the original scheme. Test applications indicate that the present method can give results almost identical to those of the original scheme. The present method is then applied to investigate the reaction barriers for a number of simple reactions and spectroscopic constants including the equilibrium bond lengths and vibrational frequencies in several open-shell diatomic molecules. The SVO-CCSD(T)-h method is demonstrated to provide a significant improvement upon the CCSD(T) method in many cases.

Hybrid coupled cluster methods: combining active space coupled cluster methods with coupled cluster singles, doubles, and perturbative triples.

Based on the coupled-cluster singles, doubles, and a hybrid treatment of triples (CCSD(T)-h) method developed by us [J. Shen, E. Xu, Z. Kou, and S. Li, J. Chem. Phys. 132, 114115 (2010); and ibid. 133, 234106 (2010); and ibid. 134, 044134 (2011)], we developed and implemented a new hybrid coupled cluster (CC) method, named CCSD(T)q-h, by combining CC singles and doubles, and active triples and quadruples (CCSDtq) with CCSD(T) to deal with the electronic structures of molecules with significant multireference character. These two hybrid CC methods can be solved with non-canonical and canonical MOs. With canonical MOs, the CCSD(T)-like equations in these two methods can be solved directly without iteration so that the storage of all triple excitation amplitudes can be avoided. A practical procedure to divide canonical MOs into active and inactive subsets is proposed. Numerical calculations demonstrated that CCSD(T)-h with canonical MOs can well reproduce the corresponding results obtained with non-canonical MOs. For three atom exchange reactions, we found that CCSD(T)-h can offer a significant improvement over the popular CCSD(T) method in describing the reaction barriers. For the bond-breaking processes in F(2) and H(2)O, our calculations demonstrated that CCSD(T)q-h is a good approximation to CCSDTQ over the entire bond dissociation processes.

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals.

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).

A coupled cluster approach with excitations up to six orbital pairs: the formulation and test applications for bond breaking processes.

The formalism of the coupled cluster (CC) method with excitations up to six orbital pairs (CC6P) and its illustrative applications are presented. By definition, CC6P includes connected excitations from full singles, doubles, triples, and partial quadruples, pentuples, and hextuples. CC6P and its approximate variants (CC6P-4, CC6P-5, and CC6P-6a) have the similar computational cost as the CC singles, doubles, and triples (CCSDT). They have been applied to investigate the potential energy surfaces for bond dissociation processes in four small molecules (F(2), H(2)O, N(2), and F(2)(+)). In comparison with full configuration interaction results, CC6P and its approximate variants are demonstrated to provide very accurate descriptions for the single-bond breaking process in F(2). While for multi-bond breaking processes, these methods provide considerable improvement over CCSDT.

New coupled cluster approaches based on the unrestricted Hartree-Fock reference for treating molecules with multireference character.

Here we review the basic formalism, implementation details, and performance of two newly developed coupled cluster (CC) methods based on the unrestricted Hartree-Fock (UHF) reference for treating molecules with multireference character. These two approaches can be considered to be approximations to the CC singles, doubles, and triples (CCSDT) method. The key concept of these two approaches is the corresponding orbitals, which are unitary transformations of canonical UHF molecular orbitals so that all spin orbitals are grouped into unique orbital pairs. In one approach called CCSDT(5P), a subset of triple excitations involving up to five-pair indices is included. In another approach called CCSD(T)-h, the contribution of connected triple excitations is treated in a hybrid way. With the concept of active corresponding orbitals, triple excitations can be automatically partitioned into two subsets, and the amplitudes of these two subsets are determined via solving different equations. Both CCSD(T)-h and CCSDT(5P) computationally scale as the seventh power of the system size. A survey of a number of applications demonstrates that CCSD(T)-h is an excellent approximation to the full CCSDT method, and CCSDT(5P) provides a good approximation to CCSDT for single-bond breaking processes. The overall performance of CCSDT(5P) is less accurate than that of CCSD(T)-h, but significantly better than that of the widely used CCSD(T).