Excited-State Deactivation Pathways in Uracil versus Hydrated Uracil: Solvatochromatic Shift in the ¹<i>n</i>π* State is the Key

Excited-state deactivation mechanisms of uracil are investigated using spin-flip time-dependent density functional theory. Two important minimum-energy crossing points are located, for both gas-phase and hydrated uracil, and optimized relaxation pathways connecting the most important critical points on the ¹<i>n</i>π* and ¹ππ* potential energy surfaces are determined. An ultrafast decay time constant, measured via femtosecond spectroscopy, is assigned to direct ¹ππ* → <i>S</i>₀ deactivation, while a slower decay component is assigned to indirect ¹ππ* → ¹<i>n</i>π* → <i>S</i>₀ deactivation. The shorter lifetime of the dark ¹<i>n</i>π* state in aqueous solution is attributed to a decrease in the energy barrier along the pathway connecting the ¹<i>n</i>π* minimum to a ¹ππ*/<i>S</i>₀ conical intersection. This barrier arises due to hydrogen bonding between uracil and water, leading to a blue-shift in the <i>S</i>₀ → ¹<i>n</i>π* excitation energy and considerable modification of energy barriers on the ¹<i>n</i>π* potential surface. These results illustrate how hydrogen bonding to the chromophore can significantly impact excited-state dynamics and also highlight that relaxation pathways can be elucidated using low-cost methods based on density functional theory

Local Excitation Approximations to Time-Dependent Density Functional Theory for Excitation Energies in Solution

We derive, implement, and test three different local excitation approximations (LEAs) to time-dependent density functional theory (TDDFT) that are designed to be extremely efficient for computing excitations that are localized on a single chromophore surrounded by explicit solvent molecules. One of these approximations is equivalent to the “TDDFT for molecular interactions” [TDDFT­(MI)] method that we have introduced previously, which exploits non-orthogonal, absolutely-localized molecular orbitals to approximate full TDDFT for systems consisting of multiple, weakly-coupled chromophores. Further approximations are possible when the excitation is localized on only a single subsystem and are introduced here to reduce the cost of LEA-TDDFT­(MI) with respect even to TDDFT­(MI). We apply these methods to compute solvatochromatic shifts for the <i>n</i> → π* excitations in aqueous acetone and pyridine. The LEA-TDDFT­(MI) method accurately reproduces the solvent-induced blue shifts in these systems, at a significant reduction in cost as compared to conventional TDDFT

Origins of Offset-Stacking in Porous Frameworks

Parallel-displaced π-stacking in the benzene dimer and larger polycyclic aromatic hydrocarbons is driven by competition between dispersion and exchange-repulsion interactions. The present work examines whether the same is true in porous frameworks that exhibit stacking interactions, including the [18]annulene dimer, porphyrin dimer, and several models of the covalent organic framework known as COF-1. Interaction energies and their components are computed using extended symmetry-adapted perturbation theory along two-dimensional scans representing slip-stacking. As in the polycyclic aromatic hydrocarbons studied previously, we find that the van der Waals interaction potential (defined as the sum of dispersion and Pauli repulsion) drives the system into a slip-stacked geometry. Electrostatics is a relatively small component of the total interaction energy. In the case of COF-1, the van der Waals potential drives the conformational preference whether or not a solvent molecule intercalates into the framework, although the presence of the guest (mesitylene) molecule substantially limits the low-energy slip-stacking configurations that are available. Even when the COF-1 pore is empty, a modest lateral offset of ≲1.5 Å is preferred, which is small compared to the pore size

Origins of Offset-Stacking in Porous Frameworks

Parallel-displaced π-stacking in the benzene dimer and larger polycyclic aromatic hydrocarbons is driven by competition between dispersion and exchange-repulsion interactions. The present work examines whether the same is true in porous frameworks that exhibit stacking interactions, including the [18]annulene dimer, porphyrin dimer, and several models of the covalent organic framework known as COF-1. Interaction energies and their components are computed using extended symmetry-adapted perturbation theory along two-dimensional scans representing slip-stacking. As in the polycyclic aromatic hydrocarbons studied previously, we find that the van der Waals interaction potential (defined as the sum of dispersion and Pauli repulsion) drives the system into a slip-stacked geometry. Electrostatics is a relatively small component of the total interaction energy. In the case of COF-1, the van der Waals potential drives the conformational preference whether or not a solvent molecule intercalates into the framework, although the presence of the guest (mesitylene) molecule substantially limits the low-energy slip-stacking configurations that are available. Even when the COF-1 pore is empty, a modest lateral offset of ≲1.5 Å is preferred, which is small compared to the pore size

Atomic Orbital Implementation of Extended Symmetry-Adapted Perturbation Theory (XSAPT) and Benchmark Calculations for Large Supramolecular Complexes

We report an implementation of extended symmetry-adapted perturbation theory (XSAPT) in the atomic orbital basis, extending this method to systems where the monomers are large. In our “XSAPT­(KS)” approach, monomers are described using range-separated Kohn–Sham (KS) density functional theory (DFT), with correct asymptotic behavior set by tuning the range-separation parameter ω in a monomer-specific way. This is accomplished either by conventional ionization potential (IP)-based tuning, in which ω is adjusted to satisfy the condition ε_HOMO(ω) = −IP­(ω), or else using a “global density-dependent” (GDD) condition, in which ω is fixed based on the size of the exchange hole. The latter procedure affords better results for both total interaction energies and energy components, when used in conjunction with our third-generation pairwise atom–atom dispersion potential (+<i>ai</i>D3). Three-body (triatomic) dispersion terms are found to be important when the monomers are large, and we incorporate these by means of an Axilrod–Teller–Muto term, <i>E</i>_disp,3B^ATM, which reduces errors in supramolecular interaction energies by about a factor of 2. The XSAPT­(KS) + <i>ai</i>D3 + <i>E</i>_disp,3B^ATM(ω_GDD) approach affords mean absolute errors as low as 1.2 and 4.2 kcal/mol, respectively, for the L7 and S12L benchmark test sets of large dimers. Such errors are comparable to those afforded by far more expensive methods, such as DFT-SAPT, and the closely related second-order perturbation theory with coupled dispersion (MP2C). We also survey the performance of various other quantum-chemical methods for these data sets and identify several semiempirical and DFT-based approaches whose accuracy approaches that of MP2C, at dramatically reduced cost

Breakdown of the Single-Exchange Approximation in Third-Order Symmetry-Adapted Perturbation Theory

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange–induction correction (<i>E</i>_exch–ind⁽³⁰⁾) fails to quench the attractive nature of the third-order induction (<i>E</i>_ind⁽³⁰⁾), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for <i>E</i>_exch–ind⁽³⁰⁾, based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a “hybrid” SAPT approach, in which a dimer Hartree–Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange–induction formulas that go beyond the SEA

Many-Body Expansion with Overlapping Fragments: Analysis of Two Approaches

The traditional many-body expansionin which a system’s energy is expressed in terms of the energies of its constituent monomers, dimers, trimers, etc.has recently been generalized to the case where the “monomers” (subsystems, or “fragments”) overlap. Two such generalizations have been proposed, and here, we compare the two, both formally and numerically. We conclude that the two approaches are distinct, although in many cases they yield comparable and accurate results when truncated at the level of dimers. However, tests on fluoride–water clusters suggest that the approach that we have previously called the “generalized many-body expansion” (GMBE) [<i>J. Chem. Phys.</i> <b>137</b>, 064113 (2012)] is more robust, with respect to the choice of fragments, as compared to an alternative “many overlapping body expansion” [<i>J. Chem. Theory Comput.</i> <b>8</b>, 2669 (2012)]. A more detailed justification for the GMBE is also provided here

Atomic Orbital Implementation of Extended Symmetry-Adapted Perturbation Theory (XSAPT) and Benchmark Calculations for Large Supramolecular Complexes

We report an implementation of extended symmetry-adapted perturbation theory (XSAPT) in the atomic orbital basis, extending this method to systems where the monomers are large. In our “XSAPT­(KS)” approach, monomers are described using range-separated Kohn–Sham (KS) density functional theory (DFT), with correct asymptotic behavior set by tuning the range-separation parameter ω in a monomer-specific way. This is accomplished either by conventional ionization potential (IP)-based tuning, in which ω is adjusted to satisfy the condition ε_HOMO(ω) = −IP­(ω), or else using a “global density-dependent” (GDD) condition, in which ω is fixed based on the size of the exchange hole. The latter procedure affords better results for both total interaction energies and energy components, when used in conjunction with our third-generation pairwise atom–atom dispersion potential (+<i>ai</i>D3). Three-body (triatomic) dispersion terms are found to be important when the monomers are large, and we incorporate these by means of an Axilrod–Teller–Muto term, <i>E</i>_disp,3B^ATM, which reduces errors in supramolecular interaction energies by about a factor of 2. The XSAPT­(KS) + <i>ai</i>D3 + <i>E</i>_disp,3B^ATM(ω_GDD) approach affords mean absolute errors as low as 1.2 and 4.2 kcal/mol, respectively, for the L7 and S12L benchmark test sets of large dimers. Such errors are comparable to those afforded by far more expensive methods, such as DFT-SAPT, and the closely related second-order perturbation theory with coupled dispersion (MP2C). We also survey the performance of various other quantum-chemical methods for these data sets and identify several semiempirical and DFT-based approaches whose accuracy approaches that of MP2C, at dramatically reduced cost

Low-Scaling Quantum Chemistry Approach to Excited-State Properties via an ab Initio Exciton Model: Application to Excitation Energy Transfer in a Self-Assembled Nanotube

We introduce a charge-embedding scheme for an excited-state quantum chemistry method aimed at weakly interacting molecular aggregates. The Hamiltonian matrix for the aggregate is constructed in a basis of direct products of configuration-state functions for the monomers, and diagonalization of this matrix affords excitation energies within ∼0.2 eV of the corresponding supersystem calculation. Both the basis states and the coupling matrix elements can be computed in a distributed way, resulting in an algorithm whose time-to-solution is independent of the number of chromophores, and we report calculations on systems with almost 55 000 basis functions using fewer than 450 processors. In a semiconducting organic nanotube, we find evidence of ultrafast, coherent dynamics followed by energy localization driven by static disorder. Truncation of the model system has a qualitative effect on the energy-transfer dynamics, demonstrating the importance of simulating an extended portion of the nanotube, which is not feasible using traditional quantum chemistry

Evidence for Singlet Fission Driven by Vibronic Coherence in Crystalline Tetracene

Singlet fission proceeds rapidly and with high quantum efficiency in both crystalline tetracene and pentacene, which poses a conundrum given that the process in tetracene is disfavored by the electronic energetics. Here, we use an <i>ab initio</i> exciton model to compute nonadiabatic couplings in the unit cell of tetracene in order to identify the modes that promote this process. Four intramolecular modes in the range of 1400–1600 cm^–1, which are nearly resonant with the single-exciton/multiexciton energy gap, appear to play a key role. <i>Ab initio</i> calculations of the electron/phonon coupling constants for these modes reveal that they are almost entirely of “Holstein” type, modulating the site energies rather than the intersite couplings. The constants are used to parametrize a vibronic Hamiltonian, simulations with which suggest a vibronically coherent singlet fission mechanism that proceeds spontaneously despite unfavorable electronic energetics. In the absence of vibronic coupling, there is no significant fission according to our model