Generalized Energy-Based Fragmentation Approach for Localized

Subscriber access provided by TUFTS UNIV

Article

Generalized Energy-Based Fragmentation Approach for Localized Excited States of Large Systems Wei Li, Yunzhi Li, Ruochen Lin, and Shuhua Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b11193 • Publication Date (Web): 15 Nov 2016 Downloaded from http://pubs.acs.org on November 19, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Generalized Energy-Based Fragmentation Approach for Localized Excited States of Large Systems Wei Li, Yunzhi Li, Ruochen Lin, and Shuhua Li∗ Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210023, People’s Repubic of China E-mail: [email protected]

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We have extended the generalized energy-based fragmentation (GEBF) approach to localized excited states of large systems. In this approach, the excited-state energy of a large system could be expressed as the combination of the excited-state energies of “active subsystems”, which contains the chromophore center, and the gound-state energies of “inactive subsystems”. The GEBF approach has been implemented at the levels of time-dependent density functional theory (TDDFT) and approximate coupled cluster singles and doubles (CC2) method. Our results show that GEBF-TDDFT can reproduce the TDDFT excitation energies and solvatochromic shifts for large systems and GEBF-CC2 could be used to validate GEBF-TDDFT result (with different functionals). The GEBF-TDDFT method is found to be able to provide satisfactory or reasonable descriptions on the experimental solvatochromic shifts for the n → π ∗ transitions of acetone in various solutions, and the lowest π → π ∗ transitions of pyridine and uracil in aqueous solutions.

Introduction Electronic excited-state calculations for large systems are challenges in quantum chemistry. A number of excited-state methods have been developed for small and medium-sized systems, which include, for example, symmetry adapted cluster configuration interaction (SAC-CI), 1 equation-of-motion coupled cluster single and doubles (EOM-CCSD), 2,3 approximate CCSD model (CC2), 4 and complete acetive space second-order perturbation theory (CASPT2). 5 The configuration interaction singles (CIS), 6 time-dependent Hartree-Fock (TDHF) 7 and time-dependent density functional theory (TDDFT) 8,9 can be used for medium-sized or relatively large systems. However, it is still very difficult to apply these methods to large or very large systems due to their steep scalings with the number of electrons. However, for some large systems with localized excitations, such as solutions and luminescent proteins, five categories of simplified methods have been developed, based on the fact that the 2 ACS Paragon Plus Environment

Page 2 of 50

Page 3 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


excitations in such systems are localized only in a small part of the system. The first category is the continuum solvent model (for solutions only), such as polarizable continuum model (PCM), 10,11 in which the solute is placed in a cavity within the continuous dielectric field. The model can only used for solutions with very weak solute-solvent interactions. The second category is the combined quantum mechanics and molecular mechanics (QM/MM) method, 12–17 in which the excitation center is treated by QM methods, including TDDFT, EOM-CCSD, and etc., and the remaining part is treated by force fields (FFs). In QM/MM calculations on solutions, usually only the solute is treated by QM. Such QM/MM methods have been quite successful for those solutions with weak solute-solvent interactions, but they are less accurate for solutions with strong solute-solvent interactions. 18 Due to the flexibility of solute/solvent configurations in solutions, incorporation of the solvent molecules in the QM region is not easy in practice. The third category is localized molecular orbital (LMO) based approach, 19–28 including local-EOM-CC method, 19–21 localized excitation approximation (LEA) approach, 22–25 fragment localized molecular orbital (FLMO) approach, 26 renormalized excitonic method (REM), 27,28 and etc. In these approaches, only the local excitations within the localized excitation center are taken into account in the TDDFT (or TDHF or CIS) calculations. The LMO-based approaches have been shown to provide satisfactory descriptions on the blue shift in the n → π ∗ transition of acetone in aqueous solution. 25 However, the gradients and second-order energy derivatives are not yet available for these approaches. Another category is the embedding theory for localized excited state, 29–31 including DFT-in-DFT and wave function theory in DFT (WFT-in-DFT). In these approaches, the accurate TDDFT or linear response WFT methods for the local excitations are embedded in the DFT calculations of large systems. The last category is fragment-based approach, including the fragment molecular orbital (FMO) approach by Chiba and coworkers, 32 divideand-conquer (D&C) approach by Nakai and coworkers. 33 The basis idea of these approaches is that the excitation energy of a large systems can be obtained from excited-state calculations on some subsystems. The applications of these two methods to some systems have



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

been reported. 32,33 In 2005, our group proposed an energy-based fragmentation approach 34 for neutral systems, and then developed a generalized energy-based fragmentation (GEBF) approach 35 in 2007 for general large systems. In the GEBF approach, 35–42 the ground-state energy (or energy derivatives) of a large system can be approximately computed from the corresponding quantities of a series of electrostatically embedded subsystems. It should be mentioned that the GEBF method is implemented to reproduce the full QM calculations of a large system, 41 which is different from the electrostically-embeded model, where the QM calculations is only appled to the active center of large system and the point charges are employed for the remaining part. The GEBF approach has been applied to compute the ground-state energies, molecular geometries, vibrational frequencies, and other molecular properties for large molecules and molecular crystals at the levels of various QM methods. 35–49 Recently, it has been extended to the ab inito molecular dynamics (AIMD) simulations for polypeptides. 41,50 In the present work, we have extended the GEBF approach to excited-state calculations of large systems with localized excited states (such as molecules in solutions). In this implementation, the excited-state energy of a target system can also be obtained from excitedstate or ground-state calculations on a series of electrostatically embedded subsystems, including “active subsystems” and “inactive subsystems”. Only for those “active subsystems”, which contains the chromophore unit, their excited-state energies are required. The localized excited-state GEBF approach has been implemented at the levels of CC2 and TDDFT methods. It is straightforward to implement this approach at other levels, such as SACCI, EOM-CCSD, and approximate coupled cluster triples model (CC3) 51 methods. Then we have applied the GEBF-TDDFT (or GEBF-CC2) method to calculate the n → π ∗ excitation energies of a conjugated aldehyde, C16 H17 CHO, the excitation energies and solvatochromic shifts for the n → π ∗ transitions of acetone in various solutions and the π → π ∗ transition of pyridine and uracil in aqueous solutions. For acetone, pyridine, and uracil in solutions, the statistical average results are obtained from a number of large solute-solvent clusters,


Page 4 of 50

Page 5 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


which are taken from QM/MM molecular dynamics (MD) simulations. The GEBF approach is found to be able to reproduce the corresponding excitation energies and solvatochromic shifts from full system calculations. By statistically averaging the results on 100 configurations of solutions, the GEBF-TDDFT approach with the ωB97XD 52 functional could give reasonably accurate results on the experimental solvatochromic shifts for both the n → π ∗ and π → π ∗ transitions. However, the QM/MM method noticeably underestimates the red shift for the π → π ∗ transition of pyridine and uracil in aqueous solutions. We expect that the GEBF approach can become a practical tool for the absorption spectra of large systems. This paper is organized as follows. In section 2, the GEBF approach for localized excitedstates and the computational details are described. Then the GEBF-CC2 or GEBF-TDDFT results for C16 H17 CHO, and acetone, pyridine, and uracil in solutions are shown and discussed in section 3. Finally, a brief summary is given in section 4.

Methodology and Computational Details GEBF Approach for Localized Excited States In the GEBF approach for the ground state, the total ground-state energy of a target system can be approximately expressed as the combination of the ground-state energies of N electrostatically-embedded subsystems as, 35,41

ETot =

N ∑ i

( ei − Ci E

N ∑ i

) Ci − 1

∑ QA QB RAB AA

(2)

e ∗ is the excited-state energy (including the self-energy of point charges) of the ith where E i active subsystem, and the natural charges are obtained from the exited-state calculations on active primitive subsystems and ground-state calculations on inactive primitive subsystems. The construction of GEBF subsystems for localized excited states is similar to that described previously for the ground state. 35,37,41 Here we give a very brief description on the procedure. First, a target system is divided into various fragments (including an active fragment). For each fragment, a primitive subsystem centered on this fragment (with its coefficient being one) is constructed by adding its neighboring fragments with a distance threshold ζ. Another parameter λ is used to control the size of subsystems (Here λ is the total number of fragments within any primitive subsystem). 35,37,41 Then a series of derivative subsystems and their coefficients are determined to eliminate the overcounting of some kfragment (k < λ) terms due to the overlapping of primitive subsystems. 35,37,41 In the final step, if the distance between a pair of fragments is less than 2ζ or the distance between any pair of fragments among three fragments is less than 1.5ζ, the additional two- or threefragment primitive subsystem (if they are not generated in the preceding steps) will be


Page 7 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


generated. All the subsystems will be embedded in the field of natural charges on all atoms outside this subsystem to take the long-range electrostatic interaction and polarization effects into account. For an acetone-(H2 O)5 cluster in Figure 1 (a), we have shown all subsystems and their coefficients in Figure 1 (b). Here each molecule is defined as a fragment, in which the acetone molecule is an active fragment. For each subsystem in Figure 1 (b), background point charges are represented by wireframe model. Those subsystems containing the acetone molecule (subsys. 1, 2, 4, 5, and 7) are active ones. As decribed above, the active and inactive subsystems will be treated with excitedand ground-state methods, respectively. The natural charges of those atoms within the active and inactive fragments are extracted from the excited-state calculations on the active primitive subsystem and the ground-state calculations on the inactive primitive subsystems, respectively. Then the excited-state energy of the entire system could be obtained using Eq. 2 from excited-state or ground-state calculations on a series of embedded subsystems. The GEBF approach for excited states has been implemented for energy calculations at the levels of TDDFT and CC2 levels in the LSQC program. 57 It could also be extended to other excitedstate methods, including SAC-CI, EOM-CCSD, CC3, and etc. In the GEBF calculations for molecules in solutions, each solute or solvent molecule is defined as a fragment, ζ is set as 3.0 Å, λ is chosen as 4, and three- and two-fragment subsystems are also generated.

Computational Details In this work, the excitation energies for the n → π ∗ transitions of a conjugated aldehyde, C16 H17 CHO with various basis sets are investigated at the TDDFT level with ωB97XD functional. Here the geometry of C16 H17 CHO is optimized at the ωB97XD/6-31G(d) level in the ground state. Then, the excitation energies and solvatochromic shifts for the n → π ∗ transitions of acetone in two protic solvents (water and methanol), one polar solvent (acetonitrile), and one nonpolar solvent (carbon tetrachloride), and the π → π ∗ transitions of pyridine and uracil in aqueous solutions were studied based on the configurations from 7 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

QM/MM MD simulations. In our simulations, one acetone was solvated in 760 water, 491 methanol, 282 acetonitrile, and 214 carbon tetrachloride molecules, respectively, and one pyridine (or uracil) was solvated in 1200 water molecules. All the solutions were performed by QM/MM (or MM) MD simulations in the NPT ensemble at 1.0 bar and 298 K with the PBCs. In each QM/MM MD simulation, the solute molecule was treated with semi-empirical PM6 method with dispersion and hydrogen bond correction (PM6 for short), 58 whereas the solvent molecules were treated with general amber force field (GAFF) or TIP5P 59 for water molecules. The cutoff of non-bonded interactions was set to be 8 Å and the Coulombic interactions were treated with the Ewald summation. 60 The cutoff for the point charges to be included in the QM Hamiltonian was also set as 8 Å. The particle mesh Ewald (PME) approach 61 was used for the long range QM-MM electrostatic energies and forces and the long range QM-QM forces. The long range QM-QM energies are calculated using a regular Ewald approach. 60 The temperature was scaled by Langevin dynamics with the collision frequency γ being 1.0. 62 The Berendsen bath coupling method 63 was selected as a thermostat algorithm to control the pressure. The equations of the motion were integrated by the velocity Verlet algorithm 64 with bonds involving hydrogen constrained. 65 The time step was set as 1 fs and the trajectories were collected for every 100 fs. For acetone in solutions, the QM/MM (or MM) trajectories of 3 ns (in aqueous solution) or 1 ns (in methanol, acetonitrile, or carbon tetrachloride solutions) were used for analysis after 10 ns for equilibrium. For pyridine and uracil in aqueous solutions, the QM/MM trajectories of 1 ns were used for analysis after 2 ns for MM equilibrium followed by 0.4 ns for QM/MM equilibrium. In addition, the isolated acetone, pyridine, and uracil molecules were simulated by PM6 based semi-empirical MD simulation in the NPT ensemble at 1.0 bar and 298 K. With the classical MM and PM6 based QM/MM trajectories of acetone, pyridine, and uracil in solutions, the radial distribution functions (RDFs) of O (acetone)−O (water), O (acetone)−O (methanol), O (acetone)−N (acetonitrile), and O (acetone)− C (carbon tetrachloride) for acetone in solutions, the RDFs of N (pyridine)−O (water) for pyridine in aqueous


Page 8 of 50

Page 9 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


solution, and the RDFs of N1 (uracil)−O (water) for uracil in aqueous solution, are plotted in Figures S1 and S2, respectively. Here, N1 in uracil is the nitrogen atom neighboring to the C−H group. One can see that for acetone in aqueous and methanol solutions, and pyridine and uracil in aqueous solution, the heights of the first peak (or minima) from classical and QM/MM MD simulations are different for 0.1−0.3 due to the polarity of solvents. Thus, the clusters (or configurations) from QM/MM simulations were employed for the excited-state calculations. An acetone-water cluster (with 64 waters) and a pyridine-water cluster (with 43 waters) taken out from QM/MM MD simulations of acetone and pyridine in aqueous solution, respectively, are shown in Figure 2. From the QM/MM MD snapshots, 100 or 300 clusters were taken out with the equal time interval of 10 ps by using solute-solvent distance thresholds. The clusters including the water molecules with the nearest distance between water and acetone (or pyridine or uracil) less than r Å are called as r-Å acetone-water (or pyridine-water or uracil-water) clusters. The acetone-solvent clusters including the solvent molecules with the O(water)−O(acetone), O(methanol)−O(acetone), N(acetonitrile)−O(acetone), or C(carbon tetrachloride)−O(acetone) distance less than r Å are denoted as rO -Å acetone-solvent clusters. In addition, 100 or 300 isolated acetone, pyridine, or uracil molecules were taken out from the gas-phase PM6 MD snapshots. In this work, the excited-state energies of the aldehyde, clusters (or gas-phase molecules) were calculated by GEBF-TDDFT at the ωB97XD level or GEBF-CC2. In some cases, GEBF-TDDFT with CAM-B3LYP, 66 PBE0, 67 and B3LYP 68,69 functionals were also performed for comparison. The excited-state energies of the configurations in solutions were also computed by QM/MM [or QM(0)/MM], in which the TD-ωB97XD and GAFF (TIP5P for water) are employed for the QM (only the solute) and MM regions, respectively. For the configurations of pyridine and uracil in aqueous solutions, the QM/MM calculations with solute and η neighboring water molecules in the QM region are performed, which are denoted as QM(η)/MM. In addition, for the pyridine-water and uracil-water clusters, the electrostically-embeded cluster model (EECM) are carried out with only solute or solute



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

with its η neighboring water molecules treated by TDDFT, which are denoted as EECM(0) and EECM(η), respectively. In all the QM calculations, the 6-311++G(d,p) basis set is employed unless otherwise specified. All the MD simulations were performed by the AmberTools15 package. 70 The GEBF calculations were executed by the LSQC program. 42,57 The CC2 and TDDFT calculations for all subsystems in GEBF calculations or for the whole system were carried out with the PSI4 71 and GAUSSIAN09 72 programs, respectively. All calculations were carried out on workstations equipped with Intel Xeon CPUs with two octa-core E5-2670 2.60 GHz and two dodeca-core E5-2692 v2 2.20 GHz (or E5-2680 v3) 2.50 GHz.

Results and discussion The n → π ∗ transitions of aldehyde and acetone in solutions First, the lowest n → π ∗ excitation of conjugated aldehyde, C16 H17 CHO, molecule was studied by conventional and GEBF-TDDFT approaches with ωB97XD functional. In the GEBF approach, the molecule was divided into eight fragments (see Figure 3), in which the right fragment with aldehyde group is active one. The maximum numbers of fragments in the primitive subsystems, λ, are set as 3, 4, and 5, respectively. The 6-31G(d), 6-311G(d,p), 6-311++G(d,p), and cc-pVTZ basis sets were employed to invesitgate the basis-set dependence. The calculated n → π ∗ excitation was listed in Table 1. One can see that for all the four basis sets, the GEBF approach with λ = 4, 5 can reproduce the corresponding conventional TD-ωB97XD excitation energies. The excitation energy differences between the conventional and GEBF-TD-ωB97XD are less than 0.06, 0.04, and 0.02 eV, respectively. By comparing the results with different basis sets, we could find that two largest basis sets, 6-311++G(d,p) and cc-pVTZ, give the same excitation energies, 3.54 and 3.56 eV, respectively, for both conventional and GEBF(λ = 5) calculations. The triple-zeta basis set with polarization functions, 6-311G(d,p), could give reasonable results, while the 6-31G(d) ba10 ACS Paragon Plus Environment

Page 10 of 50

Page 11 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


sis set could not give the converged excitation energies. In addition, one can also see that the numbers of basis functions of the entired and maximum GEBF(λ = 4, 5) subsystems are 792, 440, and 528, respectively. The corresponding CPU times for the conventional and GEBF(λ = 4, 5) calculations are 538, 140, and 211 minutes, respectively, in a single node of supercomputer equipped with Intel Xeon E5-2692 v2 (2.20 GHz) processors on two dodeca-core. By comparing the divide-and-conquer TDDFT (DC-TDDFT) results by Nakai and co-workers, 33 we can find that the computational costs of GEBF(λ = 5)-TDDFT are similar as the DC-TDDFT with four units, 33 in which the size of largest subsystem is the same as the GEBF(λ = 5) one. And with the cc-pVTZ basis set, the difference between the conventional and GEBF-TDDFT excitation energies is 0.02 eV, which is slightly small than that (0.04 eV) between the conventional and DC-TDDFT ones. 33 The lowest n → π ∗ excitation of acetone in solutions have been studied by both the experiments 73 and calculations. 14–16,25,74–78 The solvatochromic shifts of acetone in various solutions, usually in aqueous solution, could be reasonably predicted by combining the MD simulations and the QM/MM methods or LMO-based approaches. 14–16,25,74,75,77 In Table S1, the excitation energies of the first singlet excited state of an isolated acetone molecule and rO -Å (rO =4-12) acetone-(H2 O)n (n up to 234) clusters from one MD snapshot are compared at the TDHF, TD-B3LYP, TD-CAM-B3LYP, TD-PBE0, TD-LC-ωPBE, and TD-ωB97XD levels with the 6-31G basis set. One can find that TDHF, TD-LC-ωPBE, and TD-ωB97XD can provide converged excitation energies, 4.93, 4.30, and 4.34 eV, respectively, at about rO =10. Thus, the ωB97XD functional is an appropriate choice for describing excitation energies for molecules in solutions, as in references. 77 To valid the accuracy of GEBF-TDDFT excitation energy, we have compared the conventional TDDFT and GEBF-TDDFT (with the ωB97XD functional) n → π ∗ excitation energies for eight acetone-(H2 O)8 clusters (see Figure S3) in Table S2. The results show that the deviations between the conventional and GEBF excitation energies for all the eight clusters are less than 0.01 eV. Thus, the GEBF-TDDFT approach could be used to predict



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the excitation energies of molecules in solutions. In Table 2, we have compared the statistically averaged TD-ωB97XD and GEBF-TDωB97XD n → π ∗ excitation energies of different numbers (20−300) of acetone molecules and 10O -Å acetone−water clusters, respectively. One can find that the average n → π ∗ excitation energies of acetone molecules and acetone−water clusters and the corresponding solvatochromic shifts converged to 4.40, 4.56, and 0.16 eV, respectively, for 100 configurations. As a result, the statistically averaged GEBF-TD-ωB97XD n → π ∗ excitation energies and the solvatochromic shifts of 100 10O -Å acetone-solvent clusters for four solvents (water, methanol, acetonitrile, and carbon tetrachloride) are compared with the corresponding experimental values in Table 3. The corresponding QM/MM values (also from 100 configurations), in which the TD-ωB97XD and the GAFF (or TIP5P for water) force field are employed for acetone and solvent molecules, respectively, are also listed. From Table 3, we can find that both QM/MM and GEBF-TDDFT methods can give reasonably good results on the experimental shifts, 0.22, 0.12, 0.06, and −0.03 eV for acetone in aqueous, methanol, acetonitrile, and carbon tetrachloride solutions, respectively. For two protic solvents (water and methanol), the calculated blue shifts are somewhat underestimated, but the GEBF shifts, 0.16 and 0.08 eV, are still slightly better than the corresponding QM/MM values, 0.14 and 0.07 eV, respectively. For the nonpolar carbon tetrachloride solvent, a small red shift (−0.02 eV) is predicted by the GEBF-TDDFT approach, but no shift is predicted from QM/MM calculations. Thus, the GEBF approach could be used to describe the n → π ∗ solvatochromic shifts of acetone in various solutions. The distributions of the n → π ∗ solvatochromic shifts of 100 acetone-solvent configurations calculated by GEBF-TDDFT are shown in Figure 4 (a-d). It can be seen that for all solvents, the shifts are distributed in a wide range, e.g. from −0.3 eV to 0.6 eV for water. For acetone in aqueous solutions, most of configurations are located in the section of (0.1, 0.2) eV. However, for acetone in carbon tetrachloride solutions, the total number of the configurations in the sections of (−0.2, −0.1) eV and (−0.1, 0.0) eV are larger than that in


Page 12 of 50

Page 13 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the section of (0.0, 0.1) eV, which leads to the red shift for acetone in carbon tetrachloride solution. In addition, the differences between QM/MM and GEBF n → π ∗ solvatochromic shifts of 100 acetone-water configurations are shown in Figure S4 for comparison. We can see that for a little more than half of the configurations, the QM/MM blue shifts are slightly less than the GEBF blue shifts. Especially, we have found significant differences between QM/MM and GEBF shifts for six 10O -Å configurations (whose 4O -Å counterparts are displayed in Figure S5). The corresponding results are listed in Table S3. One can see that QM/MM underestimates blue shifts for 0.12−0.16 eV in some configurations, each of which contains two hydrogen bonds between acetone and its neighboring water molecules (see Figure S5). The results indicate that the inclusion of spatially close water molecules into the QM region is essential for more accurate calculations. Thus, the GEBF approach may provide more reasonable results than QM/MM (with only the solute molecule in the QM region) for predicting the n → π ∗ solvatochromic shifts of acetone in protic solvents, such as water. Furthermore, we have employed the GEBF-CC2 method for the n → π ∗ excitation energies and solvatochromic shifts of acetone in aqueous solution. Here a smaller basis set, 6-311G(d,p), and 100 5-Å acetone-(H2 O)n (n = 35 − 47) clusters, are chosen for reducing the computational cost. The purpose of this study is to compare the performance of GEBF-CC2 with GEBF-TDDFT (with ωB97XD, CAM-B3LYP, and PBE0 functionals), with the results listed in Table 4. It can be seen that the statistically averaged n → π ∗ solvatochromic shifts calculated by GEBF-CC2, GEBF-TD-ωB97XD, and GEBF-TD-CAM-B3LYP are 0.12, 0.15, and 0.15 eV, respectively. The underestimate of the blue shifts may result from the relatively small basis set. GEBF-TD-PBE0 is found to give unreliable results (red shift). To make a detailed comparison between GEBF-CC2 and GEBF-TDDFT results, we have displayed the excitation energies and solvatochromic shifts calculated for eight clusters in Figure 5 and Table S4. One can see that for all the eight configurations, GEBF-TD-ωB97XD and GEBF-TD-CAM-B3LYP provide roughly the similar shifts to GEBF-CC2 ones, whereas



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

GEBF-TD-PBE0 results are very different from GEBF-CC2 results. For example, GEBFCC2 predicts the red shifts for Conf. 1 and 2 (shown in Figure S6), and blue shifts for the remaining six configurations, however, TD-PBE0 predicts the red shifts for Conf. 3 and 6. With larger basis sets and larger acetone-water clusters, GEBF-CC2 should provide more accurate descriptions on the n → π ∗ transition of molecules in solutions.

The lowest π → π ∗ transition of pyridine and uracil in aqueous solutions The lowest π → π ∗ transition of pyridine and uracil in solutions have also been studied both experimentally 79,80 and theoretically. 14,15 However, the solvatochromic shift (red shift) of pyridine and uracil in aqueous solutions calculated by QM/MM was significantly underestimated, compared with the experimental value. 14 Here the GEBF-TDDFT method (with the ωB97XD functional) is applied to investigate the lowest π → π ∗ transition of pyridine and uracil in aqueous solutions. In Table 5, we first compare the results obtained with GEBF-TDDFT, QM/MM, and the conventional TDDFT method for eight 5-Å pyridine-water clusters displayed in Figure S7. It should be mentioned that the GEBF oscillator strength of each configuration is approximately taken as the corresponding value of the subsystem with the pyridine molecule as its central fragment. From Table 5, one can see that for all the eight configurations, GEBF-TDDFT can reproduce the corresponding TDDFT excitation energies, solvatochromic shifts, and oscillator strengths with the maximum deviations being only 0.02 eV, 0.01 eV, and 0.005, respectively. However, the QM/MM method gives very different results to the corresponding TDDFT ones. For example, the conventional TDDFT, GEBF-TDDFT, and QM/MM shifts of the 8th configuration are −0.22, −0.23, and −0.05 eV, respectively. The occupied π-like MO and unoccupied π ∗ -like MO in this pyridine-water cluster are illustrated in Figure 6 (a) and (b), respectively, together with the corresponding π-like and π ∗ -like MOs in a GEBF subsystem with pyridine in the center and three neighboring water molecules, in Figure 6 (c) 14 ACS Paragon Plus Environment

Page 14 of 50

Page 15 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and (d), repectively. The lowest π → π ∗ excitation of pyridine in aqueous solution mainly originate from the transition from the π-like MO to the π ∗ -like MO. From Figure 6 (a), one can see that the π-like MO in the whole cluster is located in both the pyridine molecule and one neighboring water molecule. The same situation occurs in the GEBF subsystem shown in Figure 6 (c). Obviously, the π MO obtained by QM/MM is only located at the pyridine molecule. One may wonder whether QM/MM or EECM with a few neighboring water molecules in the QM region can give better predictions. Indeed, this is the case. The GEBF subsystem with three water molecules surrounding the pyridine in the center is just a EECM(3) cluster. The EECM(3) shift of this cluster is −0.16 eV, which is much better than the QM/MM result (−0.05 eV) with only the solute in the QM region. Nevertheless, this result differs by 0.06 eV from the conventional TDDFT value of the entire system. This result indicates that combination of all GEBF subsystems is important for achieving more accurate results. Thus for the π → π ∗ transitions of pyridine-water clusters, GEBF-TDDFT is able to reproduce the corresponding conventional TDDFT shifts, whereas QM/MM with a small QM region can not give reasonable results. An alternative way to improve the accuracy of QM/MM is to incorperate a number of water molecules in the QM region. However, such QM/MM calculations with large (or still small) QM region may require much more computational costs (or may not improve the accuracy remarkably). The statistically averaged values of the GEBF, EECM(η) (η=0,3), and QM(η)/MM (η=0,3,6) excitation energies with TD-ωB97XD functional and the solvatochromic shifts obtained from calculations on 100 pyridine (or uracil) molecules and 5-Å pyridine-water (or uracil-water) clusters are listed in Table 6, together with the corresponding experimental values. One can see that the absolute π → π ∗ excitation energies of both pyridine (or uracil) molecule and pyridine (or uracil) in aqueous solution are overestimated by QM/MM, EECM, and GEBF-TDDFT, consistent with a previous QM/MM study. 14 The experimental solvatochromic shifts of pyridine and uracil are −0.17 eV and −0.31 eV, respectively (red shift). For pyridine, the GEBF can provide a quite good shift, −0.16 eV, whereas EECM(0) and



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

QM(0)/MM only give −0.08 and −0.09 eV, respectively. For uracil, the GEBF gives a shift as −0.19 eV, which is still much better than the corresponding EECM(0) and QM(0)/MM results, −0.09 and −0.10 eV, respectively. With three or six water molecules included in the QM region, the EECM(3), QM(3)/MM, or QM(6)/MM only slightly improve the results by 0.01−0.03 eV than the corresponding EECM(0) and QM(0)/MM ones. It should be mentioned that the largest GEBF subsystems contain only solute and three water molecules. Thus, GEBF-TDDFT can give good or reasonable descriptions on the π → π ∗ solvatochromic shifts of pyridine and uracil in aqueous solutions if appropriate functionals and basis sets are used. The EECM and QM/MM with small QM regions (similar to or even large than the largest GEBF subsystems) are still not enough to describe the π → π ∗ excitations. The long-range electrostical interactions only contribute partially for the π → π ∗ solvatochromic shifts and the long-range noncovalent interactions of some distant solvent molecules are required to the taken into account explicitly. While for the n → π ∗ excitation, the long-range electrostical interactions contribute mainly for the corresponding solvatochromic shifts. The distributions of the π → π ∗ solvatochromic shifts of 100 pyridine-water and 100 uracil-water configurations are displayed in Figure 7 (a) and Figure 7 (b), respectively. It can be seen that for both pyridine and uracil, the shifts are distributed widely from −0.6 to 0.2 eV. Most of the configurations are predicted to have the red shifts in the range (−0.2, −0.1) eV and (−0.3, −0.2) eV, respectively, and only a small fraction of configurations leads to the blue shift in the interval (0.0, 0.1) eV.

Conclusions In this work, we have implemented the GEBF approach for localized excited states of large systems. The basic idea of this approach is that for localized excited states of a large system, its excited-state energy could be obtained with the combination of the excited-state energies of a series of “active subsystems” and the ground-state energies of the remaining


Page 16 of 50

Page 17 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


“inactive subsystems”. Here, each “active subsystem” contains the chromophore center, which is defined as an “active fragment” of the target system. All the subsystems are embedded in the field of point charges generated by distant atoms of the whole system to take the long-range interactions into account. Within the framework of the GEBF approach, we have implemented the CC2 and TDDFT methods for localized excited-state calculations of large systems. With the GEBF-TDDFT or GEBF-CC2 method, we have investigated the n → π ∗ transitions of an isolated conjugated aldehyde and acetone in aqueous, methanol, acetonitrile, and carbon tetrachloride solutions, and the lowest π → π ∗ transition of pyridine and uracil in aqueous solutions. Our benchmark calculations show that GEBF-TDDFT is able to reproduce the conventional TDDFT excitation energies for all studied systems and the solvatochromic shifts for large acetone-water, pyridine-water, and uracil-water clusters. GEBFCC2 could be used to validate GEBF-TDDFT results (with different functionals). For the n → π ∗ transitions of acetone in various solutions, GEBF-TDDFT shifts are slightly better than the corresponding TDDFT/MM results (if no solvent molecules are included in the QM region). For the lowest π → π ∗ transitions of pyridine and uracil in aqueous solutions, GEBF-TDDFT could provide much better solvatochromic shifts than those from TDDFT based QM/MM calculations (with only the solute or even including a few solvent molecules in the QM region). Our results suggest that GEBF-TDDFT and GEBF-CC2 methods are potentially applicable to molecules in the condensed phase or large systems with chromophore centers. In the future, we will implement the GEBF gradients for localized excited-states to allow geometry optimization of these excited states computationally feasible. In additional, we will implmented GEBF at more quantum chemistry levels, including SAC-CI, EOM-CCSD, and local-EOM-CCSD. Then we could further investigate the emission spectra for molecules in solutions, fluorescence proteins, and other complex systems.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos. 21333004, 21473087, 21361140376, and 21673110) and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase). We are grateful to the IBM Blade cluster system provided by the High Performance Computing Center at Nanjing University for some calculations.

Supporting Information Available Acetone-water or pyridine-water clusters taken out from QM/MM MD simulated snapshots, comparisons of the GEBF (or QM/MM or conventional) excitation energies or solvatochromic shifts of acetone-water (or pyridine-water) clusters at different levels or with different sizes, and the RDFs for acetone in solutions, and pyridine and uracil in aqueous solutions. The following files are available free of charge. • jp-2016-11193p_SI.pdf: supplemental tables and figures This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Nakatsuji, H. Cluster Expansion of the Wavefunction. Calculation of Electron Correlations in Ground and Excited States by SAC and SAC CI Theories. Chem. Phys. Lett. 1979, 67, 334–342. (2) Stanton, J. F.; Bartlett, R. J. The Equation of Motion Coupled-cluster Method. A Systematic Biorthogonal Approach to Molecular Excitation Energies, Transition Probabilities, and Excited State Properties. J. Chem. Phys. 1993, 98, 7029–7039.


Page 18 of 50

Page 19 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3) Koch, H.; Kobayashi, R.; Sanchez de Merás, A.; Jørgensen, P. Calculation of SizeIntensive Transition Moments from the Coupled Cluster Singles and Doubles Linear Response Function. J. Chem. Phys. 1994, 100, 4393–4400. (4) Christiansen, O.; Koch, H.; Jørgensen, P. The Second-Order Approximate Coupled Cluster Singles and Doubles Model CC2. Chem. Phys. Lett. 1995, 243, 409–418. (5) Andersson, K.; Malmqvist, P.-Å.; Roos, B. O. Second-Order Perturbation Theory with a Complete Active Space Self-consistent Field Reference Function. J. Chem. Phys. 1992, 96, 1218–1226. (6) Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Toward a Systematic Molecular Orbital Theory for Excited States. J. Phys. Chem. 1992, 96, 135–149. (7) Heinrichs, J. New Derivation of Time-Dependent Hartree-Fock Theory. Chem. Phys. Lett. 1968, 2, 315–318. (8) Runge, E.; Gross, E. K. U. Density-Functional Theory for Time-Dependent Systems. Phys. Rev. Lett. 1984, 52, 997–1000. (9) Gross, E.; Kohn, W. In Density Functional Theory of Many-Fermion Systems; Löwdin, P.-O., Ed.; Advances in Quantum Chemistry; Academic Press, 1990; Vol. 21; pp 255–291. (10) Miertuš, S.; Scrocco, E.; Tomasi, J. Electrostatic Interaction of a Solute with a Continuum. A Direct Utilizaion of AB Initio Molecular Potentials for the Prevision of Solvent Effects. Chem. Phys. 1981, 55, 117–129. (11) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999–3094.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(12) Warshel, A.; Levitt, M. Theoretical Studies of Enzymic Reactions: Dielectric, Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme. J. Mol. Biol. 1976, 103, 227–249. (13) Sneskov, K.; Schwabe, T.; Kongsted, J.; Christiansen, O. The Polarizable Embedding Coupled Cluster Method. J. Chem. Phys. 2011, 134, 104108. (14) Olsen, J. M.; Aidas, K.; Kongsted, J. Excited States in Solution through Polarizable Embedding. J. Chem. Theory Comput. 2010, 6, 3721–3734. (15) Steindal, A. H.; Ruud, K.; Frediani, L.; Aidas, K.; Kongsted, J. Excitation Energies in Solution: The Fully Polarizable QM/MM/PCM Method. J. Phys. Chem. B 2011, 115, 3027–3037. (16) Schwabe, T.; Sneskov, K.; Olsen, J. M. H.; Kongsted, J.; Christiansen, O.; Hättig, C. PERI-CC2: A Polarizable Embedded RI-CC2 Method. J. Chem. Theory Comput. 2012, 8, 3274–3283. (17) Zeng, Q.; Liang, W. Analytic Energy Gradient of Excited Electronic State within TDDFT/MMpol Framework: Benchmark Tests and Parallel Implementation. J. Chem. Phys. 2015, 143, 134104. (18) Zhao, G.-J.; Han, K.-L. Hydrogen Bonding in the Electronic Excited State. Acc. Chem. Res. 2012, 45, 404–413. (19) Crawford, T.; King, R. A. Locally Correlated Equation-of-Motion Coupled Cluster Theory for the Excited States of Large Molecules. Chem. Phys. Lett. 2002, 366, 611 – 622. (20) Korona, T.; Werner, H.-J. Local Treatment of Electron Excitations in the EOM-CCSD Method. J. Chem. Phys. 2003, 118, 3006–3019.


Page 20 of 50

Page 21 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(21) Crawford, T. D. In Recent Progress in Coupled Cluster Methods: Theory and Applications; Cársky, P., Paldus, J., Pittner, J., Eds.; Springer Netherlands: Dordrecht, 2010; pp 37–55. (22) Li, Q.; Li, Q.; Shuai, Z. Local Configuration Interaction Single Excitation Approach: Application to Singlet and Triplet Excited States Structure for Conjugated Chains. Syn. Met. 2008, 158, 330–335. (23) Miura, M.; Aoki, Y. Ab Initio Theory for Treating Local Electron Excitations in Molecules and Its Performance for Computing Optical Properties. J. Comput. Chem. 2009, 30, 2213–2230. (24) Miura, M.; Aoki, Y. Linear-Scaled Excited State Calculations at Linear Response TimeDependent Hartree-Fock Theory. Mol. Phys. 2010, 108, 205–210. (25) Zhang, C.; Yuan, D.; Guo, Y.; Li, S. Efficient Implementation of Local Excitation Approximation for Treating Excited States of Molecules in Condensed Phase. J. Chem. Theory Comput. 2014, 10, 5308–5317. (26) Wu, F.; Liu, W.; Zhang, Y.; Li, Z. Linear-Scaling Time-Dependent Density Functional Theory Based on the Idea of "From Fragments to Molecule". J. Chem. Theory Comput. 2011, 7, 3643–3660. (27) Zhang, H.; Malrieu, J.-P.; Ma, H.; Ma, J. Implementation of Renormalized Excitonic Method at Ab Initio Level. J. Comput. Chem. 2012, 33, 34–43. (28) Ma, Y.; Ma, H. Calculating Excited States of Molecular Aggregates by the Renormalized Excitonic Method. J. Phys. Chem. A 2013, 117, 3655–3665. (29) Khait, Y. G.; Hoffmann, M. R. Embedding Theory for Excited States. J. Chem. Phys. 2010, 133, 044107.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(30) Severo Pereira Gomes, A.; Jacob, C. R. Quantum-Chemical Embedding Methods for Treating Local Electronic Excitations in Complex Chemical Systems. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2012, 108, 222–277. (31) Daday, C.; Knig, C.; Valsson, O.; Neugebauer, J.; Filippi, C. State-Specific Embedding Potentials for Excitation-Energy Calculations. J. Chem. Theory Comput. 2013, 9, 2355–2367. (32) Chiba, M.; Fedorov, D. G.; Kitaura, K. Time-Dependent Density Functional Theory Based upon the Fragment Molecular Orbital Method. J. Chem. Phys. 2007, 127, 104108. (33) Yoshikawa, T.; Kobayashi, M.; Fujii, A.; Nakai, H. Novel Approach to Excited-State Calculations of Large Molecules Based on Divide-and-Conquer Method: Application to Photoactive Yellow Protein. J. Phys. Chem. B 2013, 117, 5565–5573. (34) Li, S.; Li, W.; Fang, T. An Efficient Fragment-Based Approach for Predicting the Ground-State Energies and Structures of Large Molecules. J. Am. Chem. Soc. 2005, 127, 7215–7226. (35) Li, W.; Li, S.; Jiang, Y. Generalized Energy-Based Fragmentation Approach for Computing the Ground-State Energies and Properties of Large Molecules. J. Phys. Chem. A 2007, 111, 2193–2199. (36) Hua, W.; Fang, T.; Li, W.; Yu, J.-G.; Li, S. Geometry Optimizations and Vibrational Spectra of Large Molecules from a Generalized Energy-Based Fragmentation Approach. J. Phys. Chem. A 2008, 112, 10864–10872. (37) Hua, S.; Hua, W.; Li, S. An Efficient Implementation of the Generalized Energy-Based Fragmentation Approach for General Large Molecules. J. Phys. Chem. A 2010, 114, 8126–8134.


Page 22 of 50

Page 23 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(38) Li, W. Linear Scaling Explicitly Correlated MP2-F12 and ONIOM Methods for the Long-range Interactions of the Nanoscale Clusters in Methanol Aqueous Solutions. J. Chem. Phys. 2013, 138, 014106. (39) Hua, S.; Li, W.; Li, S. The Generalized Energy-Based Fragmentation Approach with an Improved Fragmentation Scheme: Benchmark Results and Illustrative Applications. ChemPhysChem 2013, 14, 108–115. (40) Wang, K.; Li, W.; Li, S. Generalized Energy Based Fragmentation CCSD(T)-F12 Method and Application to Water Clusters (H2 O)20 . J. Chem. Theory Comput. 2014, 10, 1546–1553. (41) Li, S.; Li, W.; Ma, J. Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates. Acc. Chem. Res. 2014, 47, 2712–2720. (42) Li, W.; Chen, C.; Zhao, D.; Li, S. LSQC: Low Scaling Quantum Chemistry Program. Int. J. Quantum Chem. 2015, 115, 641–646. (43) Li, S.; Li, W. Fragment Energy Approach to Hartree-Fock Calculations of Macromolecules. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2008, 104, 256–271. (44) Li, W.; Dong, H.; Li, S. In Frontiers in Quantum Systems in Chemistry and Physics; Wilson, S., Grout, P., Maruani, J., Delgado-Barrio, G., Piecuch, P., Eds.; Progress in Theoretical Chemistry and Physics; Springer Netherlands, 2008; Vol. 18; pp 289–299. (45) Li, H.; Li, W.; Li, S.; Ma, J. Fragmentation-Based QM/MM Simulations: Length Dependence of Chain Dynamics and Hydrogen Bonding of Polyethylene Oxide and Polyethylene in Aqueous Solutions. J. Phys. Chem. B 2008, 112, 7061–7070. (46) Jiang, N.; Tan, R. X.; Ma, J. Simulations of Solid-State Vibrational Circular Dichro-



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ism Spectroscopy of (S)-Alternarlactam by Using Fragmentation Quantum Chemical Calculations. J. Phys. Chem. B 2011, 115, 2801–2813. (47) Li, W.; Hua, W.; Fang, T.; Li, S. In Computational Methods for Large Systems: Electronic Structure Approaches for Biotechnology and Nanotechnology; Reimers, J. R., Ed.; Wiley Blackwell, 2011; pp 227–258. (48) Fang, T.; Li, W.; Gu, F.; Li, S. Accurate Prediction of Lattice Energies and Structures of Molecular Crystals with Molecular Quantum Chemistry Methods. J. Chem. Theory Comput. 2015, 11, 91–98. (49) Fang, T.; Jia, J.; Li, S. Vibrational Spectra of Molecular Crystals with the Generalized Energy-Based Fragmentation Approach. J. Phys. Chem. A 2016, 120, 2700–2711. (50) Zhang, L.; Li, W.; Fang, T.; Li, S. Ab Initio Molecular Dynamics with Intramolecular Noncovalent Interactions for Unsolvated Polypeptides. Theor. Chem. Acc. 2016, 135, 34. (51) Koch, H.; Christiansen, O.; Jørgensen, P.; Sanchez de Merás, A. M.; Helgaker, T. The CC3 Model: An Iterative Coupled Cluster Approach Including Connected Triples. J. Chem. Phys. 1997, 106, 1808–1818. (52) Chai, J.-D.; Head-Gordon, M. Long-range Corrected Hybrid Density Functionals with Damped Atom-atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620. (53) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211–7218. (54) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735–746.


Page 24 of 50

Page 25 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(55) Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comput. Chem. 1984, 5, 129–145. (56) Besler, B. H.; Merz, K. M.; Kollman, P. A. Atomic Charges Derived from Semiempirical Methods. J. Comput. Chem. 1990, 11, 431–439. (57) Li, S.; Li, W.; Fang, T.; Ma, J.; Hua, W.; Hua, S.; Jiang, Y. LSQC Program, Version 2.2. Nanjing University, Nanjing, (31 August 2012), see http://itcc.nju.edu.cn/lsqc. (58) Korth, M. Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields. J. Chem. Theory Comput. 2010, 6, 3808–3816. (59) Mahoney, M. W.; Jorgensen, W. L. A Five-Site Model for Liquid Water and the Reproduction of the Density Anomaly by Rigid, Nonpolarizable Potential Functions. J. Chem. Phys. 2000, 112, 8910–8922. (60) Ewald, P. P. Die Berechnung Optischer und Elektrostatischer Gitterpotentiale. Ann. Phys. 1921, 369, 253–287. (61) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577–8593. (62) Uberuaga, B. P.; Anghel, M.; Voter, A. F. Synchronization of Trajectories in Canonical Molecular-Dynamics Simulations: Observation, Explanation, and Exploitation. J. Chem. Phys. 2004, 120, 6363–6374. (63) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684–3690. (64) Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Clusters of Molecules: Application to Small Water Clusters. J. Chem. Phys. 1982, 76, 637–649. (65) Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of N-Alkanes. J. Comput. Phys. 1977, 23, 327–341. (66) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. (67) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158–6170. (68) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648–5652. (69) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785–789. (70) Case, D.; Berryman, J.; Betz, R.; Cerutti, D.; Cheatham III, T.; Darden, T.; Duke, R.; Giese, T.; Gohlke, H.; Goetz, A. et al. AMBER 2015. University of California, San Francisco, 2015. (71) Turney, J. M.; Simmonett, A. C.; Parrish, R. M.; Hohenstein, E. G.; Evangelista, F. A.; Fermann, J. T.; Mintz, B. J.; Burns, L. A.; Wilke, J. J.; Abrams, M. L. et al. Psi4: An Open-Source Ab Initio Electronic Structure Program. WIREs Comput. Mol. Sci. 2012, 2, 556–565. (72) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09 Revision B.01. Gaussian Inc. Wallingford CT 2009. 26 ACS Paragon Plus Environment

Page 26 of 50

Page 27 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(73) Renge, I. Solvent Dependence of n → π* Absorption in Acetone. J. Phys. Chem. A 2009, 113, 10678–10686. (74) Gao, J. Monte Carlo Quantum Mechanical-Configuration Interaction and Molecular Mechanics Simulation of Solvent Effects on the n → π* Blue Shift of Acetone. J. Am. Chem. Soc. 1994, 116, 9324–9328. (75) Kaminski, J. W.; Gusarov, S.; Wesolowski, T. A.; Kovalenko, A. Modeling Solvatochromic Shifts Using the Orbital-Free Embedding Potential at Statistically Mechanically Averaged Solvent Density. J. Phys. Chem. A 2010, 114, 6082–6096. (76) Li, Y.-K.; Zhu, Q.; Li, X.-Y.; Fu, K.-X.; Wang, X.-J.; Cheng, X.-M. Spectral Shift of the n → π* Transition for Acetone and Formic Acid with an Explicit Solvent Model. J. Phys. Chem. A 2011, 115, 232–243. (77) Ma, H.; Ma, Y. Solvent Effect on Electronic Absorption, Fluorescence, and Phosphorescence of Acetone in Water: Revisited by Quantum Mechanics/Molecular Mechanics (QM/MM) Simulations. J. Chem. Phys. 2013, 138, 224505. (78) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Electronic Absorption Spectra and Solvatochromic Shifts by the Vertical Excitation Model: Solvated Clusters and Molecular Dynamics Sampling. J. Phys. Chem. B 2015, 119, 958–967. (79) Andon, R. J. L.; Cox, J. D.; Herington, E. F. G. The Ultra-Violet Absorption Spectra and Dissociation Constants of Certain Pyridine Bases in Aqueous Solution. Trans. Faraday Soc. 1954, 50, 918–927. (80) Clark, L. B.; Peschel, G. G.; Tinoco, I. Vapor Spectra and Heats of Vaporization of Some Purine and Pyrimidine Bases. J. Phys. Chem. 1965, 69, 3615–3618.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: Comparison of the Conventional and GEBF(λ=3,4,5)-TD-ωB97XD n → π ∗ Excitation Energies of C16 H17 CHO with Different Basis Sets.a basis set conventionalb GEBF(λ=3)c GEBF(λ=4)c GEBF(λ=5)c 6-31G(d) 3.60 (306) 3.66 (136) 3.64 (170) 3.62 (204) 6-311G(d,p) 3.55 (432) 3.61 (192) 3.59 (240) 3.57 (288) 6-311++G(d,p) 3.54 (522) 3.59 (232) 3.57 (290) 3.56 (348) cc-pVTZ 3.54 (792) 3.59 (352) 3.57 (440) 3.56 (528) a b All energies are in eV; Number of basis functions of the full system included in parentheses; c Number of basis functions of the largest GEBF subsystem included in parentheses.


Page 28 of 50

Page 29 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2: The Statistically Averaged TD-ωB97XD and GEBF-TD-ωB97XD n → π ∗ Excitation Energies of Nconf. (Nconf. = 20−300) Configurations of Acetone Molecules and 10O -Å Acetone−Water Clusters, Respectively, and the Corresponding Solvatochromic Shifts with the 6-311++G(d,p) Basis Set.a Nconf. 20 40 60 80

vapor 4.41 4.40 4.42 4.41

water shift Nconf. vapor 4.59 0.19 100 4.40 4.57 0.17 150 4.39 4.56 0.14 200 4.39 4.56 0.15 300 4.40 a All energies are in eV.


water 4.56 4.56 4.56 4.56

shift 0.16 0.17 0.17 0.16


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 3: Comparison of the GEBF-TDDFT, QM/MM, and Experimental n → π ∗ Excitation Energies and Solvatochromic Shifts of Acetone in Solutions. The GEBF-TDDFT and QM/MM Results are Obtained from the Statistical Averaging of 100 10O -Å Acetone−Solvent Clusters.a solvent GEBF-TDDFTb QM/MMb,c Expl. vapor 4.40 4.40 4.46 water 4.56 (0.16) 4.54 (0.14) 4.68 (0.22) methanol 4.48 (0.08) 4.47 (0.07) 4.58 (0.12) acetonitrile 4.46 (0.06) 4.46 (0.06) 4.52 (0.06) carbon tetrachloride 4.38 (−0.02) 4.40 (0.00) 4.43 (−0.03) a All energies are in eV. The solvatochromic shift is included in parentheses; b TD-ωB97XD/6-311++G(d,p) is used in all QM calculations; c GAFF or TIP5P force field is employed in the MM calculations.


Page 30 of 50

Page 31 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4: Comparison of the Statistically Averaged GEBF-X, (X=CC2, TDωB97XD, TD-CAM-B3LYP, and TD-PBE0), and Experimental n → π ∗ Excitation Energies and Solvatochromic Shifts of 100 5-Å Acetone−Water Clusters with the 6-311G(d,p) Basis Set.a solvent CC2 TD-ωB97XD TD-CAM-B3LYP TD-PBE0 Expl. vapor 4.50 4.41 4.41 4.39 4.46 water 4.62 4.56 4.55 4.01 4.68 shift 0.12 0.15 0.14 −0.38 0.22 a All energies are in eV. The solvatochromic shift is included in parentheses.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 5: Comparison of the conventional TDDFT, GEBF-TDDFT, and QM/MM π → π ∗ Excitation Energies (ν), Solvatochromic Shifts (∆ν), and Oscillator Strengths (f ) of Eight 5-Å Pyridine−Water Configurations.a TDDFTb GEBFb QM/MMb,c conf. ν (∆ν)d f ν (∆ν)d f ν (∆ν)d f 1 5.46 (0.04) 0.033 5.46 (0.04) 0.028 5.46 (0.04) 0.033 2 5.41 (−0.01) 0.024 5.41 (−0.01) 0.022 5.53 (0.11) 0.031 3 5.41 (−0.01) 0.036 5.40 (−0.02) 0.032 5.45 (0.03) 0.033 4 5.08 (−0.34) 0.021 5.07 (−0.35) 0.022 5.19 (−0.23) 0.023 5 5.27 (−0.15) 0.017 5.26 (−0.16) 0.012 5.35 (−0.07) 0.014 6 5.29 (−0.13) 0.039 5.27 (−0.15) 0.041 5.32 (−0.10) 0.037 7 5.15 (−0.27) 0.071 5.14 (−0.28) 0.073 5.22 (−0.20) 0.073 8 5.20 (−0.22) 0.064 5.19 (−0.23) 0.065 5.37 (−0.05) 0.053 Ave. 5.28 (−0.14) 0.038 5.27 (−0.15) 0.037 5.36 (−0.06) 0.037 a b All energies are in eV; TD-ωB97XD/6-311++G(d,p) is used in all TDDFT calculations; c TIP5P force field is employed in the MM calculations; d The solvatochromic shift is included in parentheses.


Page 32 of 50

Page 33 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6: Comparison of the GEBF-TDDFT, EECM(η), QM(η)/MM, and Experimental π → π ∗ Excitation Energies and Solvatochromic Shifts of Pyridine and Uracil in Aqueous Solutions. The GEBF-TDDFT, EECM and QM/MM Results are Obtained from the Statistical Averaging of 100 5-Å Pyridine−Water and Uracil−Water Clusters.a EECM(η)b QM(η)/MMb,c solute GEBF η=0 η=3 η=0 η=3 η=6 Expl. pyridine 5.26 5.34 5.31 5.33 5.32 5.30 4.82 (−0.16) (−0.08) (−0.11) (−0.09) (−0.10) (−0.12) (−0.17) uracil 5.01 5.11 5.09 5.10 5.08 5.07 4.77 (−0.19) (−0.09) (−0.11) (−0.10) (−0.12) (−0.13) (−0.31) a All energies are in eV. η is number of water molecules included in QM region of EECM or QM/MM calculations. The TDDFT and experimental π → π ∗ excitation energies of vapor pyridine is 5.42 and 4.99 eV, respectively. The TDDFT and experimental π → π ∗ excitation energies of vapor uracil is 5.20 and 5.08 eV, respectively. The solvatochromic shift is included in parentheses; b TD-ωB97XD/6-311++G(d,p) is used in all QM calculations; c TIP5P force field is employed in the MM calculations. b



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure Captions • Figure 1. The illustration of GEBF subsystems for localized excited states of an acetone-(H2 O)5 cluster: (a) full system and (b) subsystems. In all the subsystems, subsys. 1, 2, 4, 5, and 7, are active ones. For each subsystem, the point charges are represented by wireframe model, and the coefficient is included in parentheses. • Figure 2.

An acetone-water cluster and a pyridine-water cluster taken out from

QM/MM-MD simulated snapshots of acetone and pyridine in aqueous solution, respectively. • Figure 3. The fragmentation of the C16 H17 CHO molecule. The right fragment with aldehyde group is active fragment. • Figure 4. The distributions of the n → π ∗ excitation energy shift of acetone calculated at the GEBF-TD-ωB97XD/6-311++G(d,p) level in (a) aqueous, (b) methanol, (c) acetonitrile, and (d) carbon tetrachloride solutions. • Figure 5. Comparison of the GEBF-X (X=CC2, TD-ωB97XD, TD-CAM-B3LYP, and TD-PBE0) n → π ∗ excitation energies shifts of eight 5-Å acetone-water clusters with the 6-311G(d,p) basis set. • Figure 6. Schematic representation for the occupied π-like MO (a,c) and unoccupied π ∗ -like MO (b,d) in the whole system (a,b) and in the first GEBF subsystem (c,d) from the ωB97XD calculations of the 8th 5-Å pyridine-water configuration. The occupied and unoccupied MOs mainly contribute to the π → π ∗ excitation of pyridine in aqueous solution. • Figure 7. The distributions of the π → π ∗ excitation energy shift of pyridine calculated at the GEBF-TD-ωB97XD/6-311++G(d,p) level in aqueous solution.


Page 34 of 50

Page 35 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) full system

(b) subsystems

1 (1, active) 2 (1, active)

7 (-1, active)

8 (-1)

3 (1)

4 (1, active)

9 (1)

10 (1)

5 (-1, active)

11 (-2)

6 (-1)

12 (-1)

Figure 1: The illustration of GEBF subsystems for localized excited states of an acetone(H2 O)5 cluster: (a) full system and (b) subsystems. In all the subsystems, subsys. 1, 2, 4, 5, and 7, are active ones. For each subsystem, the point charges are represented by wireframe model, and the coefficient is included in parentheses.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: An acetone-water cluster and a pyridine-water cluster taken out from QM/MM-MD simulated snapshots of acetone and pyridine in aqueous solution, respectively.


Page 36 of 50

Page 37 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: The fragmentation of the C16 H17 CHO molecule. The right fragment with aldehyde group is active fragment.



40

40

(b) in methanol Number of configurations

Number of configurations

(a) in aqueous 30

20

10

0

30

20

10

0 −0.3

−0.2

−0.1 0.0 0.1 0.2 0.3 Excitation energy shift (eV)

0.4

0.5

−0.3

40

−0.2

−0.1 0.0 0.1 0.2 Excitation energy shift (eV)

0.3

40

(d) in carbon tetrachloride Number of configurations

(c) in acetonitrile Number of configurations

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 50

30

20

10

0

30

20

10

0 −0.3

−0.2


0.3

−0.5

−0.4

−0.3 −0.2 −0.1 0.0 0.1 Excitation energy shift (eV)

0.2

0.3

Figure 4: The distributions of the n → π ∗ excitation energy shift of acetone calculated at the GEBF-TD-ωB97XD/6-311++G(d,p) level in (a) aqueous, (b) methanol, (c) acetonitrile, and (d) carbon tetrachloride solutions.


Page 39 of 50

0.5

Excitation energy shift (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2

0.0

−0.2

CC2 TD−ωB97XD TD−CAM−B3LYP TD−PBE0

−0.5 1

2

3

4 5 Configuration

6

7

8

Figure 5: Comparison of the GEBF-X (X=CC2, TD-ωB97XD, TD-CAM-B3LYP, and TDPBE0) n → π ∗ excitation energies shifts of eight 5-Å acetone-water clusters with the 6311G(d,p) basis set.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: Schematic representation for the occupied π-like MO (a,c) and unoccupied π ∗ -like MO (b,d) in the whole system (a,b) and in the first GEBF subsystem (c,d) from the ωB97XD calculations of the 8th 5-Å pyridine-water configuration. The occupied and unoccupied MOs mainly contribute to the π → π ∗ excitation of pyridine in aqueous solution.


Page 40 of 50

Page 41 of 50

40

40

(b) uracil Number of configurations

(a) pyridine Number of configurations

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30

20

10

0

30

20

10

0 −0.6

−0.5

−0.4 −0.3 −0.2 −0.1 0.0 Excitation energy shift (eV)

0.1

−0.6

−0.5

−0.4 −0.3 −0.2 −0.1 0.0 Excitation energy shift (eV)

0.1

Figure 7: The distributions of the π → π ∗ excitation energy shift of pyridine calculated at the GEBF-TD-ωB97XD/6-311++G(d,p) level in aqueous solution.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry

Ge ne r al i z e dEne r gyBas e dFr agme nt at i onf orLoc al i z e dExc i t e dSt at e s


Page 42 of 50

Page 43 of 50


(a) full system 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 (1, active) 24 25 26 27 28 29 30 31 7 (-1, active) 32

(b) subsystems

2 (1, active)

3 (1)

4 (1, active)

5 (-1, active)

6 (-1)

ACS Paragon Plus Environment

8 (-1)

9 (1)

10 (1)

11 (-2)

12 (-1)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


Page 44 of 50

Page 45 of 50

1 2 3

The Journal of Physical Chemistry ACS Paragon Plus Environment

40

40


(b) in methanol The Journal of Physical Chemistry

30

Page 46 of 50

30

20

10

0 −0.3

−0.2

−0.1 0.0 0.1 0.2 0.3 Excitation energy shift (eV)

0.4

0.5

−0.3

−0.2


0.3

40

(c) in acetonitrile

(d) in carbon tetrachloride


1 2 3 20 4 5 6 10 7 8 9 0 10 11 1240 13 14 1530 16 17 18 20 19 20 21 2210 23 24 25 0 26



(a) in aqueous

30

20

10

ACS Paragon Plus Environment 0 −0.3

−0.2


0.3

−0.5

−0.4

−0.3 −0.2 −0.1 0.0 0.1 Excitation energy shift (eV)

0.2

0.3

0.5

Page 47 of 50


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


0.2

0.0

−0.2

CC2 TD−ωB97XD TD−CAM−B3LYP TD−PBE0

−0.5 1

2

ACS Paragon Plus 3 4 Environment 5

Configuration

6

7

8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Schematic representation for the occupied π-like MO and unoccupied π* -like MO in the whole system and in the first GEBF subsystem. 423x242mm (72 x 72 DPI)


Page 48 of 50

40

40

(b) uracil The Journal of Physical Chemistry Number of configurations


pyridine Page (a) 49 of 50 30

1 2 3 20 4 5 6 10 7 8 9 0 10 11

30

20

10

ACS Paragon Plus Environment 0 −0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0.0


0.1

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0.0


0.1

The Journal of Physical Chemistry Page 50 of 50

1 2 ACS Paragon Plus Environment 3 4 G i z e dEne r gyBas e dFr agme nt at i onf orLoc al i z e dExc i t e dSt at e s 5eneral

Generalized Energy-Based Fragmentation Approach for Localized

Recommend Documents