Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Double-buffered, heterogeneous CPU + GPU integral digestion algorithm for single-excitation calculations involving a large number of excited states.

The most widely used quantum-chemical models for excited states are single-excitation theories, a category that includes configuration interaction with single substitutions, time-dependent density functional theory, and also a recently developed ab initio exciton model. When a large number of excited states are desired, these calculations incur a significant bottleneck in the "digestion" step in which two-electron integrals are contracted with density or density-like matrices. We present an implementation that moves this step onto graphical processing units (GPUs), and introduce a double-buffer scheme that minimizes latency by computing integrals on the central processing units (CPUs) concurrently with their digestion on the GPUs. An automatic code generation scheme simplifies the implementation of high-performance GPU kernels. For the exciton model, which requires separate excited-state calculations on each electronically coupled chromophore, the heterogeneous implementation described here results in speedups of 2-6× versus a CPU-only implementation. For traditional time-dependent density functional theory calculations, we obtain speedups of up to 5× when a large number of excited states is computed. © 2018 Wiley Periodicals, Inc.

Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems.

Single-excitation methods, namely, configuration interaction singles and time-dependent density functional theory (TDDFT), along with semiempirical versions thereof, represent the most computationally affordable electronic structure methods for describing electronically excited states, scaling as [Formula: see text] absent further approximations. This relatively low cost, combined with a treatment of electron correlation, has made TDDFT the most widely used excited-state quantum chemistry method over the past 20+ years. Nevertheless, certain inherent problems (beyond just the accuracy of this or that exchange-correlation functional) limit the utility of traditional TDDFT. For one, it affords potential energy surfaces whose topology is incorrect in the vicinity of any conical intersection (CI) that involves the ground state. Since CIs are the conduits for transitions between electronic states, the TDDFT description of photochemistry (internal conversion and intersystem crossing) is therefore suspect. Second, the [Formula: see text] cost can become prohibitive in large systems, especially those that involve multiple electronically coupled chromophores, for example, the antennae structures of light-harvesting complexes or the conjugated polymers used in organic photovoltaics. In such cases, the smallest realistic mimics might already be quite large from the standpoint of ab initio quantum chemistry. This Account describes several new computational methods that address these problems. Topology around a CI can be rigorously corrected using a "spin-flip" version of TDDFT, which involves an α → ß spin-flipping transition in addition to occupied → virtual excitation of one electron. Within this formalism, singlet states are generated via excitation from a high-spin triplet reference state, doublets from a quartet, etc. This provides a more balanced treatment of electron correlation between ground and excited states. Spin contamination is problematic away from the Franck-Condon region, but we describe a "spin-complete" version of the theory in which proper spin eigenstates are obtained by construction. For systems of coupled chromophores, we have developed an ab initio version of the Frenkel-Davydov exciton model in which collective excitations of the system are expanded in a basis of excited states computed for individual chromophores. The monomer calculations are trivially parallelizable, as is computation of the coupling matrix elements needed to construct the exciton Hamiltonian, and systems containing hundreds of chromophores can be tackled on commodity hardware. This enables calculations on organic semiconductors, where even small model systems exhibit a semicontinuum of excited states that renders traditional TDDFT computationally challenging. Despite including only single excitations on each monomer, the exciton model can describe entangled spins on two or more monomers, an effect that is responsible for excitation energy transfer between chromophores, for example, in singlet fission. Excitonic approximations can also be applied to the TDDFT equations themselves, and a particularly promising application is to describe the effects of environment on an excitation that is localized on a single chromophore. This "local excitation approximation" to TDDFT allows an essentially arbitrary number of solvent molecules to be included in the calculation in a highly parallelizable way such that the time-to-solution increases only very slowly as additional solvent molecules are added. It is therefore possible to converge the calculation with respect to describing an ever-larger portion of the environment at a quantum-mechanical level.

Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene.

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

Stress-induced changes in sleep in rodents: models and mechanisms.

Psychological stressors have a prominent effect on sleep in general, and rapid eye movement (REM) sleep in particular. Disruptions in sleep are a prominent feature, and potentially even the hallmark, of posttraumatic stress disorder (PTSD) (Ross, R.J., Ball, W.A., Sullivan, K., Caroff, S., 1989. Sleep disturbance as the hallmark of posttraumatic stress disorder. American Journal of Psychiatry 146, 697-707). Animal models are critical in understanding both the causes and potential treatments of psychiatric disorders. The current review describes a number of studies that have focused on the impact of stress on sleep in rodent models. The studies are also in Table 1, summarizing the effects of stress in 4-h blocks in both the light and dark phases. Although mild stress procedures have sometimes produced increases in REM sleep, more intense stressors appear to model the human condition by leading to disruptions in sleep, particularly REM sleep. We also discuss work conducted by our group and others looking at conditioning as a factor in the temporal extension of stress-related sleep disruptions. Finally, we attempt to describe the probable neural mechanisms of the sleep disruptions. A complete understanding of the neural correlates of stress-induced sleep alterations may lead to novel treatments for a variety of debilitating sleep disorders.

Long-term effect of cued fear conditioning on REM sleep microarchitecture in rats.

STUDY OBJECTIVES: To study long-term effects of conditioned fear on REM sleep (REMS) parameters in albino rats. DESIGN: We have investigated disturbances in sleep architecture, including muscle twitch density as REMS phasic activity, and freezing behavior in wakefulness, upon reexposure to a conditioned stimulus (CS) on Day 1 and Day 14 postconditioning. SUBJECTS: Male Sprague-Dawley rats prepared for polysomnographic recordings. INTERVENTIONS: After baseline sleep recording, the animals in the experimental group received five pairings of a 5-sec tone, co-terminating with a 1-sec, 1 mAfootshock. The control rats received similar numbers of tones and shocks, but explicitly unpaired. On postconditioning days, after reexposure to tones alone, sleep and freezing behavior were recorded. MEASUREMENTS AND RESULTS: Conditioned fear significantly altered REMS microarchitecture (characterized as sequential-REMS [seq-REMS: < or =3 min episode separation] and single-REMS [sin-REMS: >3 min episode separation]) on Day 14. The total amount and number of seq-REMS episodes decreased, while the total amount and number of sin-REMS episodes increased. Further, the CS induced significant increases in freezing and REMS myoclonic twitch density in the experimental group. Reexposure to the CS produced no alterations in controls. CONCLUSIONS: The results suggest that conditioned fear causes REMS alterations, including difficulty in initiating a REMS episode as indicated by the diminution in the number of seq-REMS episodes. Another finding, the increase in phasic activity, agrees with the inference from clinical investigations that retrieval of fearful memories can be associated with the long-term REMS disturbances characteristic of posttraumatic stress disorder.

Hypoglycemia activates arousal-related neurons and increases wake time in adult rats.

Hypoglycemia resulting from excess of exogenous or endogenous insulin elicits central nervous system activation that contributes to counterregulatory hormone secretion. In adult humans without diabetes, hypoglycemia occurring during sleep usually produces cortical activation with awakening. However, in adult humans with type 1 diabetes, hypoglycemic arousal appears blunted or absent. We hypothesized that insulin injection sufficient to produce hypoglycemia would induce awakening in adult male rats. Polysomnographic studies were carried out to characterize the effect of insulin injection on measures of sleep and waking during a circadian time of increased sleep. Compared to a baseline day, insulin treatment more than doubled the time spent awake, from 18.4+/-2.6% after saline injection to 48.0+/-5.5% after insulin. Insulin injection also reduced rapid eye movement sleep (REMS) from 27.3+/-1.8% to 5.6+/-1.3%. The percent of time in non-REM sleep (NREMS) sleep was not different between saline and insulin days, however, NREMS after insulin was fragmented, with increased number and decreased duration of episodes. These electrophysiological data indicate that insulin-induced hypoglycemia is an arousing stimulus in rats, as in nondiabetic adult humans. We also studied the effect of insulin on activation of selected arousal-related neurons using immunohistochemical detection of Fos. Fos-immunoreactivity increased in orexin (OX) neurons after insulin, from 8.7+/-4.9% after saline injection to 37+/-9% after insulin. Basal forebrain cholinergic nuclei also showed increased Fos-immunoreactivity after insulin. These correlated behavioral and histological data provide targets for future studies of the neural pathways underlying hypoglycemic arousal.

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 ab initio 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. Ab initio 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.

Modulation of the ultradian human nasal cycle by sleep stage and body position.

OBJECTIVE:: The nasal cycle, which is present in a significant number of people, is an ultradian side-to-side rhythm of nasal engorgement associated with cyclic autonomic activity. We studied the nasal cycle during REM/non-REM sleep stages and examined the potentially confounding influence of body position on lateralized nasal airflow. METHODS:: Left- and right-side nasal airflow was measured in six subjects during an eight-hour sleep period using nasal thermistors. Polysomnography was performed. Simultaneously, body positions were monitored using a video camera in conjunction with infrared lighting. RESULTS:: Significantly greater airflow occurred through the right nasal chamber (relative to the left) during periods of REM sleep than during periods of non-REM sleep (p<0.001). Both body position (p < 0.001) and sleep stage (p < 0.001) influenced nasal airflow lateralization. CONCLUSIONS:: This study demonstrates that the lateralization of nasal airflow and sleep stage are related. Some types of asymmetrical somatosensory stimulation can alter this relationship.

Social partnering alters sleep in fear-conditioned Wistar rats.

Social support, when provided following a traumatic experience, is associated with a lower incidence of stress-related psychiatric disorders. Our hypothesis was that providing a social interaction period with a naive conspecific would improve sleep architecture in response to cued fear conditioning in Wistar rats. Rats were randomly assigned to either the socially isolated or socially partnered groups. Rats assigned to the socially isolated group were individually housed following electrode implantation and fear conditioning. Rats assigned to the socially partnered group were initially paired-housed, and then one rat from each pair was randomly chosen for sleep electrode implantation and fear conditioning. Rats from both groups were habituated to a recording chamber, and baseline sleep was recorded over 22 hours. One day later (Training Day), they were fear-conditioned to 10 presentations of a tone (800 Hz, 90 dB, 5 sec) co-terminating with a mild electric foot shock (1.0 mA, 0.5 sec), at 30-sec intervals. While rats in the socially isolated group were left undisturbed in their home cage for 30-min, socially partnered rats interacted for 30 minutes with their non-stressed rat partner immediately after fear conditioning and while the auditory tones were presented on Days 1 and 14. The results indicated that social interaction increased sleep efficiency in partnered rats compared to isolated rats following the fear conditioning procedure. This was due to an increase in the amount of rapid eye movement sleep (REMS) during the light phase. Evaluation of REMS microarchitecture revealed that the increase in REMS was due to an increase in the number of single REMS episodes (siREMS), which represented a more consolidated REMS pattern. A surprising finding was that partnered rats had a greater number of sequential REMS episodes (seqREMS) at Baseline, on the Training Day and on Day 1 when compared to isolated rats. The greater number of seqREMS episodes in partnered rats may be due to the partnering procedure and not fear conditioning, as the effect was also seen at Baseline. Thus it appears that while the partnering procedure may have given rise to a fragmented REMS pattern, social partnering promoted a greater consolidation of REMS in response to the fear conditioning procedure.

Corticotropin-releasing factor microinjection into the central nucleus of the amygdala alters REM sleep.

Psychological stressors have a prominent effect on rapid eye movement sleep (REMS) in humans and animals. We hypothesized that the stress-related neurochemical corticotropin-releasing factor (CRF), acting in the amygdala, could initiate neural events that lead to REMS alterations. Therefore, we made bilateral microinjections of three different doses of CRF into the central nucleus of the amygdala (CeA) in five rats. Only the lowest dose of CRF (1 ng) induced a change in sleep, specifically REMS, during the 4-h post-injection period. Thus, REMS alterations following psychological stress may depend, in part, on CRF release in the CeA.

A rodent model of sleep disturbances in posttraumatic stress disorder: the role of context after fear conditioning.

BACKGROUND: A prominent sleep disturbance, likely including a disruption of rapid eye movement sleep (REMS) continuity, characterizes posttraumatic stress disorder (PTSD). We set out to develop a fear conditioning paradigm in rats that displays alterations in sleep architecture analogous to those in PTSD. METHODS: Baseline polysomnographic recordings of rats were performed in a neutral context to which the rats had been habituated for several days. Rats were then shock- or mock-trained in a distinctly different context, and their sleep was studied the following day in that context. A separate group of rats was shock-trained and studied in the neutral context on the following 2 days. RESULTS: Rats that slept in the neutral context exhibited a REMS-selective increase in sleep 24 hours after training and increases in REMS and non-REMS 48 hours after training. In contrast, rats that slept in the presence of situational reminders of the training context exhibited a REMS-selective decrease in sleep 24 hours later. Animals that were mock-trained showed no changes in sleep. CONCLUSIONS: Shock training induced days-long changes in sleep architecture that were disrupted when the animal was exposed to situational reminders of the training context.

Tetrodotoxin inactivation of pontine regions: influence on sleep-wake states.

Studies using various methodologies have implicated n. reticularis pontis oralis (RPO) and n. subcoeruleus (SubC) in the generation of rapid eye movement sleep (REM). In rats, electrolytic lesions in these regions may give rise to the phenomenon of REM without atonia (REM-A), in which the electrophysiological features of REM are normal except that atonia is absent and elaborate behaviors may be exhibited. However, electrolytic lesions damage both cell bodies and fibers of passage, and the neural reorganization and adaptation that can occur post-lesion can complicate interpretation. Tetrodotoxin (TTX) is a sodium channel blocker that temporarily inactivates both neurons and fibers of passage and thus may be functionally equivalent to an electrolytic lesion, but without allowing time for neural adaptation. In this study, we examined the influence of microinjections of TTX into RPO and SubC on sleep in freely behaving rats. Rats (90 day old male Sprague-Dawley) were implanted with electrodes for recording EEG and EMG. Guide cannulae were implanted aimed into RPO or SubC. Each animal received one unilateral microinjection (TTXUH: 5.0 ng/0.2 microl) and two bilateral microinjections (TTXBL: 2.5 ng/0.1 microl; TTXBH: 5.0 ng/0.2 microl) of TTX, and control microinjections of saline alone (SAL). The injections were made 2 h following lights on, and sleep was recorded for the subsequent 22 h. Sleep was scored from computerized records in 10 s epochs. Recordings from the 10-h light period and the 12-h dark period were examined separately. TTX inactivation of RPO could decrease REM and non-REM (NREM), whereas inactivation of SubC produced relatively more specific decreases in REM with smaller effects on NREM. The results complement studies that have implicated RPO and SubC in REM generation. REM-A was not observed, suggesting that REM-A is a complex phenomenon that requires time for reorganization of the nervous system after insult.

Sleep-related neurons in the central nucleus of the amygdala of rats and their modulation by the dorsal raphe nucleus.

The amygdala (AMY) plays an important role in initiating appropriate neurobehavioral responses to emotionally arousing events. Its major efferents from the central nucleus (Ace) to the basal forebrain, hypothalamus and brainstem permit it to influence sleep mechanisms. To characterize further the neuronal activity of AMY during sleep and wakefulness, we recorded single neuronal activity in Ace across behavioral states in freely moving, normally behaving rats. Of the 49 neurons recorded from Ace, 24 neurons had firing patterns related to sleep-wakefulness (S-W). Of these, 50% (n = 12) had a high firing frequency during wakefulness (W) or both W and REM sleep (REM), 12% (n = 3) were non-REM (NREM)-related, 17% (n = 4) had a high firing rate in REM (REM-ON), and 20% (n = 5) fired at a low rate during REM. Because serotonin introduced into AMY during REM induces short-latency changes of state, we also studied the effects of low frequency (1 Hz) electrical stimulation of the dorsal raphe nucleus (DRN) on Ace neurons. All REM-ON neurons recorded from Ace were inhibited by DRN stimulation, and other cell types were unaffected. Thus, we found that the majority of cells in Ace related to S-W fired slowly during NREM and increased their discharge during W and/or REM, and that the DRN has the potential for modulating the spontaneous activity of REM-ON cells in rats.

Differential effect of sleep-wake states on lingual and dorsal neck muscle activity in rats.

Postural tone is reduced during slow-wave sleep (SWS) and absent during rapid eye movement sleep (REMS). In obstructive sleep apnea subjects, upper airway dilating muscles, including those of the tongue, show a similar pattern; this contributes to sleep-related airway obstructions. However, in healthy subjects, state-dependent changes in the activity of pharyngeal muscles are variable. In seven chronically instrumented Sprague-Dawley rats, an animal model used to study sleep and sleep-disordered breathing, we quantified lingual and postural muscle activity across the sleep-wake states by measuring the root mean square levels of the electromyograms (EMG) in successive 10s intervals collected during 2h of recording at a constant circadian time (1-3p.m.). The nuchal EMG was low and steady during SWS and further reduced with occasional twitches during REMS. In contrast, the mean lingual EMG during SWS was only 5.9+/-1.6% (S.E.) of its mean in wakefulness, and during REMS, it increased to 46+/-15% (S.E.) (p<0.03) due to the appearance of phasic bursts, the intensity of which progressively increased. The lingual and nuchal activities also had different time courses during state transitions. In obstructive sleep apnea subjects, the sleep-wake changes in the activity of pharyngeal muscles may become similar to those in postural muscles as a result of pharyngeal tone adaptations to the disorder.

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.

The central nucleus of the amygdala and the wake-promoting effects of modafinil.

Modafinil, a novel non-amphetamine stimulant recently approved for the treatment of narcolepsy, has been shown to increase waking in both animals and humans. However, its mechanism of action is currently unknown. Earlier research into the brain structures responsible for the wake-producing actions of modafinil implicated the central nucleus of the amygdala (ACe) as a possible site of action [Neuroscience 87 (1998) 905-911; Neurosci. Lett. 241 (1998) 95-98]. The present experiments were designed to test the hypothesis that the ACe is, at least in part, involved in the wake-producing actions of modafinil. In the first experiment, rats with lesions of the ACe were injected systemically with varying doses of modafinil and sleep was recorded. At the highest dose, modafinil significantly increased waking and decreased sleep. However, there was no interaction between the lesion and the effect of the drug. In the second experiment, varying doses of modafinil were injected directly into the ACe and sleep was recorded. Injection of modafinil into the ACe did not affect sleep architecture. Thus, ACe does not play a simple role in modafinil's wake-promoting action. We suggest that more complex testing will be required to elucidate its role.

A serotonergic (5-HT2) receptor mechanism in the laterodorsal tegmental nucleus participates in regulating the pattern of rapid-eye-movement sleep occurrence in the rat.

Serotonin [5-hydroxytryptamine (5-HT)] plays an inhibitory role in rapid-eye-movement (REM) sleep although the exact mechanism(s) and site(s) of action are not known. It is commonly assumed that 5-HT exerts its influence on REM sleep via input from the dorsal raphe nucleus (DRN) directly onto cholinergic neurons involved in the generation of REM sleep. 5-HT(2) receptor sites have been found on cholinergic neurons in the laterodorsal tegmental nucleus (LDT) and pedunculopontine tegmental nucleus (PPT). We locally microinjected the 5-HT(2) agonist DOI ((+/-)-1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane HCl) and the 5-HT(2) antagonist, ketanserin, in LDT in rats to determine whether these receptor sites are involved in the regulation of behavioral states. DOI and ketanserin primarily affected REM sleep, by significantly decreasing or increasing, respectively, the number, but not the duration, of REM sleep episodes. DOI specifically decreased the occurrence of clusters of REM sleep episodes appearing at intervals less than or equal to 3 min (sequential episodes) without affecting single episodes separated by more than 3 min. An opposite effect of ketanserin on REM sleep clusters, although not statistically significant, was observed.

Diagnosis of rapid eye movement sleep disorder with electroencephalography and treatment with tricyclic antidepressants in a dog.

A 9-month-old, female Labrador retriever mix was presented for two types of seizure-like episodes, one of which occurred only during sleep. The two types of episodes were morphologically distinct. An electroencephalogram (EEG) demonstrated that the sleep-associated episodes occurred during rapid eye movement (REM) sleep, supporting a diagnosis of a REM behavior disorder. Based on their morphology and response to antiseizure medications, the waking episodes were diagnosed as seizures. The animal was also diagnosed with an obsessive-compulsive and generalized anxiety disorder. The REM behavior disorder and anxiety-related behaviors improved with tricyclic antidepressant therapy.

Ab Initio Implementation of the Frenkel-Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates.

A fragment-based method for computing vertical excitation energies of molecular clusters is introduced based on an ab initio implementation of a Frenkel-Davydov exciton model consisting of singly excited monomer basis states. Our strategy is to construct and diagonalize the exact Hartree-Fock Hamiltonian in such a basis. Matrix elements between nonorthogonal determinants are computed via the corresponding orbital transformation and the resulting generalized eigenvalue problem is solved to determine collective excitation energies and wave functions. The basis may be expanded to include higher-lying fragment excited states in order to account for interfragment polarization effects. Absolute errors of ≲0.1 eV (relative to supersystem methods) are achievable for systems such as water clusters and crystalline arrays of organic chromophores such as pentacene and napthalenediimide. Preliminary tests for a nine-chromophore subunit of an organic nanotube suggest that it is possible to target the optically bright state, even when it is a high-lying excitation, by using carefully selected basis states. The highly parallel nature of this method provides a foundation for further developments to treat collective excitations in large molecular assemblies.