Fragment Molecular Orbital Scheme Research Articles

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme.

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH) and (FH) -H O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) -H O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

RI-MP3 calculations of biomolecules based on the fragment molecular orbital method.

In this study, the third-order Møller-Plesset perturbation (MP3) theory using the resolution of the identity (RI) approximation was combined with the fragment molecular orbital (FMO) method to efficiently calculate a high-order electron correlation energy of biomolecular systems. We developed a new algorithm for the RI-MP3 calculation, which can be used with the FMO scheme. After test calculations using a small molecule, the FMO-RI-MP3 calculations were performed for two biomolecular systems comprising a protein and a ligand. The computational cost of these calculations was only around 5 and 4 times higher than those of the FMO-RHF calculations. The error associated with the RI approximation was around 2.0% of the third-order correlation contribution to the total energy. However, the RI approximation error in the interaction energy between the protein and ligand molecule was insignificantly small, which reflected the negligible error in the inter fragment interaction energy. © 2018 Wiley Periodicals, Inc.

Ab initio quantum chemical calculation of electron density, electrostatic potential, and electric field of biomolecule based on fragment molecular orbital method

AbstractEfficient quantum chemical calculations of electrostatic properties, namely, the electron density (EDN), electrostatic potential (ESP), and electric field (EFL), were performed using the fragment molecular orbital (FMO) method. The numerical errors associated with the FMO scheme were examined at the HF, MP2, and RI‐MP2 levels of theory using 4 small peptides. As a result, the FMO errors in the EDN, ESP, and EFL were significantly smaller than the magnitude of the electron correlation effects, which indicated that the FMO method provides sufficiently accurate values of electrostatic properties. In addition, an attempt to reduce the computational effort was proposed by combining the FMO scheme and a point charge approximation. The error due to this approximation was examined using 2 proteins, prion protein and human immunodeficiency virus type 1 protease. As illustrative examples, the ESP values at the molecular surface of these proteins were calculated at the MP2 level of theory.

Fragment Model Study of Molecular Multiorbital System X[Pd(dmit)2]2

Electronic properties of quasi-two-dimensional molecular conductors $X$[Pd(dmit)$_2$]$_2$ are studied theoretically. We construct an effective model based on the fragment molecular orbital scheme developed recently, which can describe the multi-orbital degree of freedom in this system. The tight-binding parameters for a series of $\beta'$-type compounds with different cations $X$ are evaluated by fitting to first-principles band calculations. We find that the transfer integrals within the dimers of Pd(dmit)$_2$ molecules, along the intramolecular and intermolecular bonds including the diagonal ones, are the same order, leading to hybridization between different molecular orbitals. This results in charge disproportionation within each molecule, as seen in our previous ab initio study [T. Tsumuraya et al, J. Phys. Soc. Jpn. 82, 033709 (2013)], and also to a revised picture of an effective dimer model. Furthermore, we discuss broken-symmetry insulating states triggered by interaction effects, which show characteristic features owing to the multi-orbital nature. The on-site Coulomb interaction induces antiferromagnetic states with intramolecular antiparallel spin pattern, while electron-lattice couplings stabilize non-magnetic charge-lattice ordered states where two kinds of dimers with different charge occupation arrange periodically. These states showing different spatial patterns compete with each other as well as with the paramagnetic metallic state.

RI-MP2 Gradient Calculation of Large Molecules Using the Fragment Molecular Orbital Method.

The second-order Møller-Plesset perturbation theory (MP2) gradient using resolution of the identity approximation (RI-MP2 gradient) was combined with the fragment molecular orbital (FMO) method to evaluate the gradient including electron correlation for large molecules. In this study, we adopted a direct implementation of the RI-MP2 gradient, in which a characteristic feature of the FMO scheme was utilized. Test calculations with a small peptide presented a computational advantage of the RI-MP2 gradient over the canonical MP2 gradient. In addition, it was shown that the error of the RI-MP2 gradient, caused by RI approximation, was negligible. As an illustrative example, we performed gradient calculations for two biomolecules-a prion protein with GN8 and a human immunodeficiency virus type 1 (HIV1) protease with lopinavir (LPV). These calculations demonstrated that the gradient including the correlation effect could be evaluated with only about twice the computational effort of the Hartree-Fock (HF) gradient.

Higher-order correlated calculations based on fragment molecular orbital scheme

We have developed a new module for higher-order correlated methods up to coupled-cluster singles and doubles with perturbative triples (CCSD(T)). The matrix-matrix operations through the DGEMM routine were pursued for a number of contractions. This code was then incorporated into the ABINIT-MPX program for the fragment molecular orbital (FMO) calculations. Intra-fragment processings were parallelized with OpenMP in a node-wise fashion, whereas the message passing interface (MPI) was used for the fragment-wise parallelization over nodes. Our new implementation made the FMO-based higher-order calculations applicable to realistic proteins. We have performed several benchmark tests on the Earth Simulator (ES2), a massively parallel computer. For example, the FMO-CCSD(T)/6-31G job for the HIV-1 protease (198 amino acid residues)–lopinavir complex was completed in 9.8 h with 512 processors (or 64 nodes). Another example was the influenza neuraminidase (386 residues) with oseltamivir calculated at the full fourth-order Moller–Plesset perturbation level (MP4), of which job timing was 10.3 h with 1024 processors. The applicability of the methods to commodity cluster computers was tested as well.

Counterpoise-corrected interaction energy analysis based on the fragment molecular orbital scheme

Basis set superposition error (BSSE) correction with counterpoise (CP) procedure under the environmental electrostatic potential is newly introduced to interfragment interaction energy (IFIE), which is important for interaction analysis in the fragment molecular orbital method. The CP correction for IFIE is applied to a stacked dimer of base pair and a protein–ligand complex of estrogen receptor and 17β-estradiol with scaled third-order Møller–Plesset perturbation theory. The BSSEs amount to about quarter of IFIE for hydrogen-bonding and electrostatic interactions and half or even more for dispersion interactions. Estimation of IFIE with the CP correction is therefore preferred for the quantitative discussion.

Theoretical study of the prion protein based on the fragment molecular orbital method

We performed fragment molecular orbital (FMO) calculations to examine the molecular interactions between the prion protein (PrP) and GN8, which is a potential curative agent for prion diseases. This study has the following novel aspects: we introduced the counterpoise method into the FMO scheme to eliminate the basis set superposition error and examined the influence of geometrical fluctuation on the interaction energies, thereby enabling rigorous analysis of the molecular interaction between PrP and GN8. This analysis could provide information on key amino acid residues of PrP as well as key units of GN8 involved in the molecular interaction between the two molecules. The present FMO calculations were performed using an original program developed in our laboratory, called "Parallelized ab initio calculation system based on FMO (PAICS)".

Fragment molecular orbital calculation using the RI-MP2 method

The resolution of the identity second-order Møller–Plesset perturbation theory (RI-MP2) was introduced into the fragment molecular orbital (FMO) method, where the program of the RI-MP2 method was newly developed. After some test calculations with a small peptide, the performance of the RI-MP2 method with the FMO scheme was demonstrated for two biomolecular systems: the human immunodeficiency virus type 1 protease with the lopinavir molecule, and the prion protein with the GN8 molecule. These calculations showed the great advantage of FMO calculations using the RI-MP2 method over ordinary FMO calculations.

Parallelized integral-direct CIS(D) calculations with multilayer fragment molecular orbital scheme

We have developed a parallelized integral-direct code of the perturbative doubles correction for configuration interaction with singles, proposed as CIS(D) by Head-Gordon et al. (Chem Phys Lett 219:21, 1994). The CIS(D) method provides the energy corrections both of the relaxation and differential correlation for the respective CIS excited states. The implementation of CIS(D) is based on our original algorithm for the second-order Moller–Plesset perturbation (MP2) calculations (Mochizuki et al. in Theor Chem Acc 112:442, 2004). There is no need to communicate bulky intermediate data among worker processes of the parallelized execution. This CIS(D) code is then incorporated into a developer version of ABINIT-MP program, in order to improve the overestimation in excitation energies calculated by the CIS method in conjunction with the multilayer fragment molecular orbital scheme (MLFMO-CIS) (Mochizuki et al. in Chem Phys Lett 406:283, 2005). The MLFMO-CIS(D) method is first used in evaluating the lowest n\(\pi^{*}\) excitation energy of the hydrated formaldehyde. The photoactive yellow protein (PYP) is the second target of MLFMO-CIS(D) calculation. Through these applications, it is shown that the CIS(D) correction improves the CIS results favorably.

Application of fragment molecular orbital scheme to silicon-containing systems

The fragment molecular orbital (FMO) scheme has been successfully used for a variety of large-scale molecules such as proteins and nucleic acids so far. We have applied the FMO calculations to the silicon-containing systems like polysilanes. The error caused by the fragmentation was examined by the Hartree–Fock method and the second-order Møller-Plesset (MP2) perturbation method for the ground state energy. The dynamic polarizability as a linear response property was also evaluated with and without the fragmentation. A series of numerical comparisons showed that the FMO scheme is applicable to silicon-based molecules with reasonable accuracy. This implied a potential availability of FMO calculations for the issues relevant to nanoscience and nanotechnology.

Dynamic polarizability calculation with fragment molecular orbital scheme

We have developed a linear response module to evaluate the dynamic polarizability, by accepting the fragment molecular orbital (FMO) scheme proposed by Kitaura. The module is parallelized in an integral-driven fashion with atomic-orbital indices in a local version of abinit-mp program. The error caused by fragmentation was checked through test calculations on the water pentamer and the glycine pentamer. The error is shown to be small even under nonzero frequency, indicating the potential applicability of the FMO-based polarizability evaluation for large molecules.

Configuration interaction singles method with multilayer fragment molecular orbital scheme

We have developed a parallelized integral-direct solver for configuration interaction singles (CIS) in the A binit-mp program, by accepting the recently proposed multilayer fragment molecular orbital (MLFMO) method. In the MLFMO–CIS scheme, the region of interest in photoactive issues can be treated with the environmental potential at the Hartree–Fock (HF) level. The parallel efficiency is observed to be reasonable for the formaldehyde hydration system. A realistic applicability of the method is demonstrated for the photoactive yellow protein (PYP) including 125 amino acid residues.

Large scale MP2 calculations with fragment molecular orbital scheme

We have recently developed a parallelized integral-direct algorithm for the second-order Møller–Plesset perturbation theory (MP2) and implemented it into the ABINIT-MP program of the fragment molecular orbital (FMO) scheme. A flexible parallelization is possible by combining the fragment indices (upper level) and the two-electron integral indices (lower level) on distributed computational resources, leading to an enhancement of in-core processings. In this Letter, we carry out a series of benchmark FMO–MP2 calculations of realistic proteins consisting of the tens of thousands of basis functions. The performance is shown to be high, indicating that the ABINIT-MP program is easily applicable to the realistic systems.

Molecular orbital analysis based on fragment molecular orbital scheme

Dipole and quadrupole moments computed in the fragment molecular orbital (FMO) scheme reproduce the results from the full molecular orbital (MO) theory within a few percent error. It is also shown that the FMO molecular orbitals for creating the FMO density matrix of each fragment provide qualitatively correct information on the chemical active sites of molecular aggregates in comparison with the full MO counterpart. The FMO also provides correct HOMO for single strand DNA, while the ordering of the LUMO among the fragments is not correct.