| Molecular spectroscopy,a robust tool to characterize molecular structure and properties,is a bridge between the microscopic states and the macroscopic phenomena,which thus has a wide applicability in chemistry,physics,and biology.During the past decades,many progress has been made in the theoretical and computational community in elucidating the structures and dynamics complementary to experimental spectra for small-and medium-sized molecular systems.Nevertheless,for macromolecular,supramolecular,and condensed-phase systems,it is still a formidable challenge for conventional quantum mechanics methods because the computational cost skyrockets(at least the fourth power)with molecular size.The well-established quantum mechanics/molecular mechanics(QM/MM)approach is one of the widely used methods to address this issue.Despite of its tremendous success,there exists a frequently asked question "How large should a QM region be?" To treat a sufficiently large QM region with hundreds or thousands of atoms and to obtain a converged result,lower and linear-scaling methods should be employed.Among which,fragment-based methods have spurred a surge of interests.The core idea lies in the locality of density matrix and electron correlation.Specifically,the total energy of a large system is evaluated as a linear combination of a series of small "electrostatically embedded"subsystems according to a fragmentation strategy.Likewise,with first-,second-or higher energy derivatives,structure optimization and various molecular spectra could be obtained as well.The main part of this dissertation is to implement the calculation of some molecular spectra within the generalized energy-based fragmentation(GEBF)method to allow molecular spectra of macromolecular,supramolecular and condensed-phase systems computationally tractable.To be specific,vibrational circular dichroism(VCD)and chemical shielding constants in nuclear magnetic resonance(NMR)have been implemented within the framework of GEBF and applied to various systems.The main findings and innovations are summarized as follows:In Chapter 3,we implemented the calculation of the vibrational circular dichroism(VCD)spectra within the GEBF framework(denoted as GEBF-VCD thereafter).Based on the fact that atomic axial tensors(AATs)pertinent to the rotational strengths as well as atomic polar tensors(APTs),the most important two quantities for the vibrational intensities,are both transferrable,the VCD spectra of a large system could be calculated by carrying out corresponding calculations on a series of subsystems.The accuracy of GEBF-VCD is first evaluated in comparison to full ab initio calculations and further against experimental VCD spectra with inclusion of a 310-helix peptide,an a-helix peptide,and a double a-helix gramicidin D.The mean signed error(MSE)and mean absolute error(MAE)are 0.7 and 13.4 cm-1,respectively.Simultaneously,we have assigned all the prominent peaks.We highly recommend GEBF-M06-2X/6-311+G(d,p)for small systems with 150 atoms or so and GEBF-M06-2X/6-31G(d,p)for large systems with more than 500 atoms.The computational timings demonstrated the linear/low-scaling efficiency of the approach.In Chapter 4,we extended the GEBF approach to investigate nuclear magnetic resonance(NMR)chemical shift of macromolecular and condensed-phase systems.The method is named GEBF-NMR thereafter.Our method can well reproduce the results of the calculated NMR by using conventional quantum chemistry method.Therefore,we further applied GEBF-NMR to compute the 1H or 15N shielding constants of a large foldamer,a supramolecular aggregate,and a system of CH3CN in the CHCl3 solvent.For the former two systems,the predicted 1H chemical shifts are in good agreement with the experimental data.For the CH3CN/CHC13 solution,the 15N shielding constant of CH3CN is evaluated as the ensemble average of up to 200 sufficiently large CH3CN/CHCl3 clusters from either classical or QM/MM MD simulations.Our results reveal that the gas-to-solution shift of 15N based on PM6-DH+/MM MD simulations is in good accord with the experimental value,outperforming those based on classical MD simulations and the previous IEF-PCM study.The mean error is only 2.2 ppm to the experimental data.This study unravels that the generation of representative liquid structures is critical in evaluating the NMR shielding constants of condensed phase systems.Furthermore,we have found that for various CH3CN/CHCl3 clusters accurate predictions of NMR shielding constants with the GEBF-NMR method require an ultrafine integration grid in DFT calculations.In Chapter 5,the GEBF-NMR method was further extended to the treatment of condensed-phase systems under periodic boundary conditions.The method is named PBC-GEBF-NMR thereafter.In this approach,NMR shielding constants in a unit cell or supercell are evaluated as a linear combination of the corresponding quantities from a series of small embedded subsystems.First,we validated the PBC-GEBF-NMR method for a bunch of molecular crystals with experimental data.The mean absolute errors of 1H,13C,15N,and 170 are 0.5,1.7,3.0,and 5.0 ppm,respectively.Further applications include the calculation of chemical shielding constants of 1H and 17O in hexagonal ice Ih and liquid water.Based on structures generated from ab initio molecular dynamics simulations,we reproduced the experimental shielding constants accurately and efficiently.Again,our results reveal that quality of the representative structures generated from MD simulations are critical in reproducing the experimental chemical shieldings.In contrast,calculations on those generated from classical force fields show large deviations from the experimental data.In addition,averaging(of chemical shieldings)over the number of monomers in a unit cell can sharply reduce the number of MD snapshots to obtain the convergent results.In Chapter 6,combined with classical molecular dynamics(MD)simulations,we applied the GEBF method to investigate the thermodynamic and dynamic process as well as spectra of self-assembly of a double-stranded foldamer from two monomers in solution.Calculations based GEBF show that the driving forces for the aggregation are extensive ?-?*interactions,while the MD simulations on a couple of homologs show that this spontaneous self-assembly takes place at microsecond time-scale,and proceeds through an "unwinding-threading-rewinding" mechanism.The detailed mechanisms about folding and self-assembly in aromatic oligoamide foldamer we present here disclose how the sequence is associated with a well-ordered three-dimensional structure at atomic level,and therefore may have implications for designing new foldamers with versatile functions. |
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