Prediction of pseudoprogression in post-treatment glioblastoma using dynamic susceptibility contrast-derived oxygenation and microvascular transit time heterogeneity measures.

OBJECTIVES: To evaluate the added value of MR dynamic susceptibility contrast (DSC)-perfusion-weighted imaging (PWI)-derived tumour microvascular and oxygenation information with cerebral blood volume (CBV) to distinguish pseudoprogression from true progression (TP) in post-treatment glioblastoma. METHODS: This retrospective single-institution study included patients with isocitrate dehydrogenase (IDH) wild-type glioblastoma and a newly developed or enlarging measurable contrast-enhancing mass within 12 weeks after concurrent chemoradiotherapy. CBV, capillary transit time heterogeneity (CTH), oxygen extraction fraction (OEF), and cerebral metabolic rate of oxygen (CMRO2) were obtained from DSC-PWI. Predictors were selected using univariable logistic regression, and performance was measured with adjusted diagnostic odds with tumour volume and area under the curve (AUC) of receiver operating characteristics analysis. RESULTS: A total of 103 patients were included (mean age, 59.6 years; 59 women), with 67 cases of TP and 36 cases of pseudoprogression. Pseudoprogression exhibited higher CTH (4.0 vs. 3.4, p = .019) and higher OEF (12.7 vs. 10.7, p = .014) than TP, but a similar CBV (1.48 vs. 1.53, p = .13) and CMRO2 (7.7 vs. 7.3s, p = .598). Independent of tumour volume, both high CTH (adjusted odds ratio [OR] 1.52; 95% confidence interval [CI]: 1.11-2.09, p = .009) and high OEF (adjusted OR 1.17; 95% CI:1.03-1.33, p = .016) were predictors of pseudoprogression. The combination of CTH, OEF, and CBV yielded higher diagnostic performance (AUC 0.71) than CBV alone (AUC 0.65). CONCLUSION: High intratumoural capillary transit heterogeneity and high oxygen extraction fraction derived from DSC-PWI have enhanced the diagnostic value of CBV in pseudoprogression of post-treatment IDH-wild type glioblastoma. CLINICAL RELEVANCE STATEMENT: In the early post-treatment stage of glioblastoma, pseudoprogression exhibited both high oxygen extraction fraction and high capillary transit heterogeneity and these dynamic susceptibility contrast-perfusion weighted imaging derived parameters have added value in cerebral blood volume-based noninvasive differentiation of pseudoprogression from true progression. KEY POINTS: • Capillary transit time heterogeneity and oxygen extraction fraction can be measured noninvasively through processing of dynamic susceptibility contrast imaging. • Pseudoprogression exhibited higher capillary transit time heterogeneity and higher oxygen extraction fraction than true progression. • A combination of cerebral blood volume, capillary transit time heterogeneity, and oxygen extraction fraction yielded the highest diagnostic performance (area under the curve 0.71).

Hematopoietic stem-cell gene therapy is associated with restored white matter microvascular function in cerebral adrenoleukodystrophy.

Blood-brain barrier disruption marks the onset of cerebral adrenoleukodystrophy (CALD), a devastating cerebral demyelinating disease caused by loss of ABCD1 gene function. The underlying mechanism are not well understood, but evidence suggests that microvascular dysfunction is involved. We analyzed cerebral perfusion imaging in boys with CALD treated with autologous hematopoietic stem-cells transduced with the Lenti-D lentiviral vector that contains ABCD1 cDNA as part of a single group, open-label phase 2-3 safety and efficacy study (NCT01896102) and patients treated with allogeneic hematopoietic stem cell transplantation. We found widespread and sustained normalization of white matter permeability and microvascular flow. We demonstrate that ABCD1 functional bone marrow-derived cells can engraft in the cerebral vascular and perivascular space. Inverse correlation between gene dosage and lesion growth suggests that corrected cells contribute long-term to remodeling of brain microvascular function. Further studies are needed to explore the longevity of these effects.

Hemodynamic impairments within individual watershed areas in asymptomatic carotid artery stenosis by multimodal MRI.

Improved understanding of complex hemodynamic impairments in asymptomatic internal carotid artery stenosis (ICAS) is crucial to better assess stroke risks. Multimodal MRI is ideal for measuring brain hemodynamics and has the potential to improve diagnostics and treatment selections. We applied MRI-based perfusion and oxygenation-sensitive imaging in ICAS with the hypothesis that the sensitivity to hemodynamic impairments will improve within individual watershed areas (iWSA). We studied cerebral blood flow (CBF), cerebrovascular reactivity (CVR), relative cerebral blood volume (rCBV), relative oxygen extraction fraction (rOEF), oxygen extraction capacity (OEC) and capillary transit-time heterogeneity (CTH) in 29 patients with asymptomatic, unilateral ICAS (age 70.3 ± 7.0 y) and 30 age-matched healthy controls. In ICAS, we found significant impairments of CBF, CVR, rCBV, OEC, and CTH (strongest lateralization ΔCVR = -24%), but not of rOEF. Although the spatial overlap of compromised hemodynamic parameters within each patient varied in a complex manner, most pronounced changes of CBF, CVR and rCBV were detected within iWSAs (strongest effect ΔCVR = +117%). At the same time, CTH impairments were iWSA independent, indicating widespread dysfunction of capillary-level oxygen diffusivity. In summary, complementary MRI-based perfusion and oxygenation parameters offer deeper perspectives on complex microvascular impairments in individual patients. Furthermore, knowledge about iWSAs improves the sensitivity to hemodynamic impairments.

Noninvasive Characterization of Tumor Angiogenesis and Oxygenation in Bevacizumab-treated Recurrent Glioblastoma by Using Dynamic Susceptibility MRI: Secondary Analysis of the European Organization for Research and Treatment of Cancer 26101 Trial.

Background Relevance of antiangiogenic treatment with bevacizumab in patients with glioblastoma is controversial because progression-free survival benefit did not translate into an overall survival (OS) benefit in randomized phase III trials. Purpose To perform longitudinal characterization of intratumoral angiogenesis and oxygenation by using dynamic susceptibility contrast agent-enhanced (DSC) MRI and evaluate its potential for predicting outcome from administration of bevacizumab. Materials and Methods In this secondary analysis of the prospective randomized phase II/III European Organization for Research and Treatment of Cancer 26101 trial conducted between October 2011 and December 2015 in 596 patients with first recurrence of glioblastoma, the subset of patients with availability of anatomic MRI and DSC MRI at baseline and first follow-up was analyzed. Patients were allocated into those administered bevacizumab (hereafter, the BEV group; either bevacizumab monotherapy or bevacizumab with lomustine) and those not administered bevacizumab (hereafter, the non-BEV group with lomustine monotherapy). Contrast-enhanced tumor volume, noncontrast-enhanced T2 fluid-attenuated inversion recovery (FLAIR) signal abnormality volume, Gaussian-normalized relative cerebral blood volume (nrCBV), Gaussian-normalized relative blood flow (nrCBF), and tumor metabolic rate of oxygen (nTMRO2) was quantified. The predictive ability of these imaging parameters was assessed with multivariable Cox regression and formal interaction testing. Results A total of 254 of 596 patients were evaluated (mean age, 57 years ± 11; 155 men; 161 in the BEV group and 93 in non-BEV group). Progression-free survival was longer in the BEV group (3.7 months; 95% confidence interval [CI]: 3.0, 4.2) compared with the non-BEV group (2.5 months; 95% CI: 1.5, 2.9; P = .01), whereas OS was not different (P = .15). The nrCBV decreased for the BEV group (-16.3%; interquartile range [IQR], -39.5% to 12.0%; P = .01), but not for the non-BEV group (1.2%; IQR, -17.9% to 23.3%; P = .19) between baseline and first follow-up. An identical pattern was observed for both nrCBF and nTMRO2 values. Contrast-enhanced tumor and noncontrast-enhanced T2 FLAIR signal abnormality volumes decreased for the BEV group (-66% [IQR, -83% to -35%] and -33% [IQR, -71% to -5%], respectively; P < .001 for both), whereas they increased for the non-BEV group (30% [IQR, -17% to 98%], P = .001; and 10% [IQR, -13% to 82%], P = .02, respectively) between baseline and first follow-up. None of the assessed MRI parameters were predictive for OS in the BEV group. Conclusion Bevacizumab treatment decreased tumor volumes, angiogenesis, and oxygenation, thereby reflecting its effectiveness for extending progression-free survival; however, these parameters were not predictive of overall survival (OS), which highlighted the challenges of identifying patients that derive an OS benefit from bevacizumab. © RSNA, 2020 Online supplemental material is available for this article. See also the editorial by Dillon in this issue.

Theophylline as an Add-On to Thrombolytic Therapy in Acute Ischemic Stroke: A Randomized Placebo-Controlled Trial.

BACKGROUND AND PURPOSE: Delayed recanalization increases the risk of infarct growth and poor clinical outcome in acute ischemic stroke. The vasoactive agent theophylline has shown neuroprotective effects in animal stroke models but inconclusive results in case series and randomized clinical trials. The primary objective of this study was to evaluate whether theophylline, as an add-on to thrombolytic therapy, is safe and effective in acute ischemic stroke patients. METHODS: The TEA-Stroke trial (The Theophylline in Acute Ischemic Stroke) was an investigator-initiated 2-center, proof-of-concept, phase II clinical study with a randomized, double-blinded, placebo-controlled design. The main inclusion criteria were magnetic resonance imaging-verified acute ischemic stroke, moderate to severe neurological deficit (National Institutes of Health Stroke Scale score of ≥4), and treatment with thrombolysis within 4.5 hours of onset. Participants were randomly assigned in the ratio 1:1 to either 220 mg of intravenous theophylline or placebo. The co-primary outcomes were early clinical improvement on the National Institutes of Health Stroke Scale score and infarct growth on magnetic resonance imaging at 24-hour follow-up. RESULTS: Theophylline as an add-on to thrombolytic therapy improved the National Institutes of Health Stroke Scale score at 24 hours by mean 4.7 points (SD, 5.6) compared with an improvement of 1.3 points (SD, 7.5) in the control group (P=0.044). Mean infarct growth was 141.6% (SD, 126.5) and 104.1% (SD, 62.5) in the theophylline and control groups, respectively (P=0.146). Functional independence at 90 days was 61% in the theophylline group and 58% in the control group (P=0.802). CONCLUSIONS: This proof-of-concept trial investigated theophylline administration as an add-on to thrombolytic therapy in acute ischemic stroke. The co-primary end points early clinical improvement and infarct growth at 24-hour follow-up were not significantly different after post hoc correction for multiplicity (Bonferroni technique). The small study size precludes a conclusion as to whether theophylline has a neuroprotective effect but provides a promising clinical signal that may support a future clinical trial. Registration: URL: https://www.clinicaltrials.gov. Unique identifier: EudraCT number 2013-001989-42.

Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization.

We derive equations for describing the time evolution of variational wave functions in linear and exponential parameterization with a second-quantization (SQ) formulation. The SQ formalism covers time-dependent Hartree (TDH), while exact states and approximate vibrational configuration interaction wave functions are described using state-transfer operators. We present detailed expressions for efficient evaluation of TDH in linear (L-TDH) and exponential (X-TDH) parametrization and an efficient implementation supporting linear scaling with respect to the number of degrees of freedom M when the Hamiltonian operator contains a constant number of terms per mode independently of the size of the system. The computational cost of the X-TDH method is reduced significantly compared to the L-TDH method for systems with many operator terms per mode such as is typical for accurate molecular potential-energy surfaces. Numerical results for L-TDH and X-TDH are presented which confirm the theoretical reduction of the M scaling compared to standard first-quantization formulations. Calculations on Henon-Heiles potentials with more than 105 dimensions and polycyclic aromatic hydrocarbons with up to 264 modes have been performed. Thus, the SQ formulation and the X-TDH method pave the way for studying the time-resolved quantum dynamics of large molecules.

Prediction of Tissue Outcome and Assessment of Treatment Effect in Acute Ischemic Stroke Using Deep Learning.

BACKGROUND AND PURPOSE: Treatment options for patients with acute ischemic stroke depend on the volume of salvageable tissue. This volume assessment is currently based on fixed thresholds and single imagine modalities, limiting accuracy. We wish to develop and validate a predictive model capable of automatically identifying and combining acute imaging features to accurately predict final lesion volume. METHODS: Using acute magnetic resonance imaging, we developed and trained a deep convolutional neural network (CNNdeep) to predict final imaging outcome. A total of 222 patients were included, of which 187 were treated with rtPA (recombinant tissue-type plasminogen activator). The performance of CNNdeep was compared with a shallow CNN based on the perfusion-weighted imaging biomarker Tmax (CNNTmax), a shallow CNN based on a combination of 9 different biomarkers (CNNshallow), a generalized linear model, and thresholding of the diffusion-weighted imaging biomarker apparent diffusion coefficient (ADC) at 600×10-6 mm2/s (ADCthres). To assess whether CNNdeep is capable of differentiating outcomes of ±intravenous rtPA, patients not receiving intravenous rtPA were included to train CNNdeep,-rtpa to access a treatment effect. The networks' performances were evaluated using visual inspection, area under the receiver operating characteristic curve (AUC), and contrast. RESULTS: CNNdeep yields significantly better performance in predicting final outcome (AUC=0.88±0.12) than generalized linear model (AUC=0.78±0.12; P=0.005), CNNTmax (AUC=0.72±0.14; P<0.003), and ADCthres (AUC=0.66±0.13; P<0.0001) and a substantially better performance than CNNshallow (AUC=0.85±0.11; P=0.063). Measured by contrast, CNNdeep improves the predictions significantly, showing superiority to all other methods (P≤0.003). CNNdeep also seems to be able to differentiate outcomes based on treatment strategy with the volume of final infarct being significantly different (P=0.048). CONCLUSIONS: The considerable prediction improvement accuracy over current state of the art increases the potential for automated decision support in providing recommendations for personalized treatment plans.

ABCD1 dysfunction alters white matter microvascular perfusion.

Cerebral X-linked adrenoleukodystrophy is a devastating neurodegenerative disorder caused by mutations in the ABCD1 gene, which lead to a rapidly progressive cerebral inflammatory demyelination in up to 60% of affected males. Selective brain endothelial dysfunction and increased permeability of the blood-brain barrier suggest that white matter microvascular dysfunction contributes to the conversion to cerebral disease. Applying a vascular model to conventional dynamic susceptibility contrast magnetic resonance perfusion imaging, we demonstrate that lack of ABCD1 function causes increased capillary flow heterogeneity in asymptomatic hemizygotes predominantly in the white matter regions and developmental stages with the highest probability for conversion to cerebral disease. In subjects with ongoing inflammatory demyelination we observed a sequence of increased capillary flow heterogeneity followed by blood-brain barrier permeability changes in the perilesional white matter, which predicts lesion progression. These white matter microvascular alterations normalize within 1 year after treatment with haematopoietic stem cell transplantation. For the first time in vivo, our studies unveil a model to assess how ABCD1 alters white matter microvascular function and explores its potential as an earlier biomarker for monitoring disease progression and response to treatment.

Increased cortical capillary transit time heterogeneity in Alzheimer's disease: a DSC-MRI perfusion study.

Alzheimer's disease (AD) is characterized by the accumulation of hyperphosphorylated tau and neurotoxic Aß in the brain parenchyma. Hypoxia caused by microvascular changes and disturbed capillary flows could stimulate this build-up of AD-specific proteins in the brain. In this study, we compared cerebral microcirculation in a cohort of AD and mild cognitive impairment (MCI) patients with that of age-matched controls, all without a history of diabetes or of hypertension for more than 2 years, using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Vascular flow disturbances were quantified using a parametric model and mapped to the mid-cortical surface for group-wise statistical analysis. We found widespread hypoperfusion in patients compared with controls and identified areas of increased relative capillary transit time heterogeneity (RTH), consistent with low tissue oxygen tension. Notably, RTH was positively correlated with white matter hyperintensities and positively correlated with symptom severity in the patient cohort. These correlations extended over large parts of the temporal, parietal, and frontal cortices. The results support the hypothesis of disturbed capillary flow patterns in AD and suggest that DSC-MRI may provide imaging biomarkers of impaired cerebral microcirculation in AD.

Reliable estimation of microvascular flow patterns in patients with disrupted blood-brain barrier using dynamic susceptibility contrast MRI.

PURPOSE: To present and quantify the performance of a method to compute tissue hemodynamic parameters from dynamic susceptibility contrast (DSC) MRI data in brain tissue with possible nonintact blood-brain barrier. THEORY AND MATERIALS AND METHODS: We propose a Bayesian scheme to obtain perfusion metrics, including capillary transit-time heterogeneity (CTH), from DSC-MRI data in the presence of contrast agent extravasation. Initial performance assessment is performed through simulations. Next, we assessed possible over- or under correction for tracer extravasation in two patients receiving contrast agent preloading and two patients not receiving preloading. Perfusion metrics for N = 60 patients diagnosed with either grade III (N = 14) or grade IV gliomas (N = 46) were analyzed across tissue types to evaluate the ability to distinguish regions with different hemodynamic patterns. Finally, N = 4 patient cases undergoing anti-angiogenic treatment are evaluated qualitatively for treatment effects. All patient data were acquired at 3.0 Tesla. RESULTS: The simulation studies showed good robustness against low signal-to-noise ratios, exemplified with Pearson correlations of R = 0.833 (mean transit time) and R = 0.738 (CTH) at signal-to-noise ratio = 20. Region-of-interest analysis of the N = 60 glioma patients showed that cerebral blood volume (CBV) significantly separated enhancing core from edema (grade IV: P < 10-8 , grade III: P < 0.05) and enhancing core from normal appearing ipsilateral white matter (NAWM) (grade IV: P < 10-8 , grade III: P < 0.05). The microvascular parameters were particularly good in separating edematous tissue from NAWM tissue in grade IV gliomas (P < 0.001). Finally, CTH separated grade III and grade IV core tissue (P < 0.05). CONCLUSION: We have demonstrated robustness of the proposed Bayesian algorithm against experimental noise and demonstrated complementary value in microvascular parameters to the CBV parameter in separating tissue types in gliomas. LEVEL OF EVIDENCE: 3 Technical Efficacy: Stage 2 J. MAGN. RESON. IMAGING 2017;46:537-549.

Capillary Transit Time Heterogeneity Is Associated with Modified Rankin Scale Score at Discharge in Patients with Bilateral High Grade Internal Carotid Artery Stenosis.

BACKGROUND AND PURPOSE: Perfusion weighted imaging (PWI) is inherently unreliable in patients with severe perfusion abnormalities. We compared the diagnostic accuracy of a novel index of microvascular flow-patterns, so-called capillary transit time heterogeneity (CTH) to that of the commonly used delay parameter Tmax in patients with bilateral high grade internal carotid artery stenosis (ICAS). METHODS: Consecutive patients with bilateral ICAS ≥ 70%NASCET who underwent PWI were retrospectively examined. Maps of CTH and Tmax were analyzed with a volumetric approach using several thresholds. Predictors of favorable outcome (modified Rankin scale at discharge 0-2) were identified using univariate and receiver operating characteristic (ROC) curve analysis. RESULTS: Eighteen patients were included. CTH ≥ 30s differentiated best between patients with favorable and unfavorable outcome when both hemispheres were taken into account (sensitivity 83%, specificity 73%, area under the curve [AUC] 0.833 [confidence interval (CI) 0.635; 1.000]; p = 0.027). The best discrimination using Tmax was achieved with a threshold of ≥ 4s (sensitivity 83%, specificity 64%, AUC 0.803 [CI 0.585;1.000]; p = 0.044). The highest AUC was found for left sided volume with CTH ≥ 15s (sensitivity 83%, specificity 91%, AUC 0.924 [CI 0.791;1.000]; p = 0.005). CONCLUSION: The study suggests that CTH is superior to Tmax in discriminating ICAS patients with favorable from non-favorable outcome. This finding may reflect the simultaneous involvement of large vessels and microvessels in ICAS and underscore the need to diagnose and manage both aspects of the disease.

Capillary dysfunction: its detection and causative role in dementias and stroke.

In acute ischemic stroke, critical hypoperfusion is a frequent cause of hypoxic tissue injury: As cerebral blood flow (CBF) falls below the ischemic threshold of 20 mL/100 mL/min, neurological symptoms develop and hypoxic tissue injury evolves within minutes or hours unless the oxygen supply is restored. But is ischemia the only hemodynamic source of hypoxic tissue injury? Reanalyses of the equations we traditionally use to describe the relation between CBF and tissue oxygenation suggest that capillary flow patterns are crucial for the efficient extraction of oxygen: without close capillary flow control, "functional shunts" tend to form and some of the blood's oxygen content in effect becomes inaccessible to tissue. This phenomenon raises several questions: Are there in fact two hemodynamic causes of tissue hypoxia: Limited blood supply (ischemia) and limited oxygen extraction due to capillary dysfunction? If so, how do we distinguish the two, experimentally and in patients? Do flow-metabolism coupling mechanisms adjust CBF to optimize tissue oxygenation when capillary dysfunction impairs oxygen extraction downstream? Cardiovascular risk factors such as age, hypertension, diabetes, hypercholesterolemia, and smoking increase the risk of both stroke and dementia. The capillary dysfunction phenomenon therefore forces us to consider whether changes in capillary morphology or blood rheology may play a role in the etiology of some stroke subtypes and in Alzheimer's disease. Here, we discuss whether certain disease characteristics suggest capillary dysfunction rather than primary flow-limiting vascular pathology and how capillary dysfunction may be imaged and managed.

Reliable estimation of capillary transit time distributions using DSC-MRI.

The regional availability of oxygen in brain tissue is traditionally inferred from the magnitude of cerebral blood flow (CBF) and the concentration of oxygen in arterial blood. Measurements of CBF are therefore widely used in the localization of neuronal response to stimulation and in the evaluation of patients suspected of acute ischemic stroke or flow-limiting carotid stenosis. It was recently demonstrated that capillary transit time heterogeneity (CTH) limits maximum oxygen extraction fraction (OEF(max)) that can be achieved for a given CBF. Here we present a statistical approach for determining CTH, mean transit time (MTT), and CBF using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Using numerical simulations, we demonstrate that CTH, MTT, and OEF(max) can be estimated with low bias and variance across a wide range of microvascular flow patterns, even at modest signal-to-noise ratios. Mean transit time estimated by singular value decomposition (SVD) deconvolution, however, is confounded by CTH. The proposed technique readily identifies malperfused tissue in acute stroke patients and appears to highlight information not detected by the standard SVD technique. We speculate that this technique permits the non-invasive detection of tissue with impaired oxygen delivery in neurologic disorders such as acute ischemic stroke and Alzheimer's disease during routine diagnostic imaging.

The role of the cerebral capillaries in acute ischemic stroke: the extended penumbra model.

The pathophysiology of cerebral ischemia is traditionally understood in relation to reductions in cerebral blood flow (CBF). However, a recent reanalysis of the flow-diffusion equation shows that increased capillary transit time heterogeneity (CTTH) can reduce the oxygen extraction efficacy in brain tissue for a given CBF. Changes in capillary morphology are typical of conditions predisposing to stroke and of experimental ischemia. Changes in capillary flow patterns have been observed by direct microscopy in animal models of ischemia and by indirect methods in humans stroke, but their metabolic significance remain unclear. We modeled the effects of progressive increases in CTTH on the way in which brain tissue can secure sufficient oxygen to meet its metabolic needs. Our analysis predicts that as CTTH increases, CBF responses to functional activation and to vasodilators must be suppressed to maintain sufficient tissue oxygenation. Reductions in CBF, increases in CTTH, and combinations thereof can seemingly trigger a critical lack of oxygen in brain tissue, and the restoration of capillary perfusion patterns therefore appears to be crucial for the restoration of the tissue oxygenation after ischemic episodes. In this review, we discuss the possible implications of these findings for the prevention, diagnosis, and treatment of acute stroke.

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory.

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo̸ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.

Vibrational absorption spectra from vibrational coupled cluster damped linear response functions calculated using an asymmetric Lanczos algorithm.

We report the theory and implementation of vibrational coupled cluster (VCC) damped response functions. From the imaginary part of the damped VCC response function the absorption as function of frequency can be obtained, requiring formally the solution of the now complex VCC response equations. The absorption spectrum can in this formulation be seen as a matrix function of the characteristic VCC Jacobian response matrix. The asymmetric matrix version of the Lanczos method is used to generate a tridiagonal representation of the VCC response Jacobian. Solving the complex response equations in the relevant Lanczos space provides a method for calculating the VCC damped response functions and thereby subsequently the absorption spectra. The convergence behaviour of the algorithm is discussed theoretically and tested for different levels of completeness of the VCC expansion. Comparison is made with results from the recently reported [P. Seidler, M. B. Hansen, W. Györffy, D. Toffoli, and O. Christiansen, J. Chem. Phys. 132, 164105 (2010)] vibrational configuration interaction damped response function calculated using a symmetric Lanczos algorithm. Calculations of IR spectra of oxazole, cyclopropene, and uracil illustrate the usefulness of the new VCC based method.

Vibrational contributions to cubic response functions from vibrational configuration interaction response theory.

In continuation of our recent paper on vibrational quadratic response functions for vibrational configuration interaction wave functions, we present in this paper a derivation and implementation of the pure vibrational cubic response function for vibrational configuration interaction wave functions. In addition, we present combined electronic and vibrational cubic response functions derived from sum-over-states expressions in the Born-Oppenheimer framework and a discussion of complicating issues. The implementation enables analytic calculation of the pure vibrational cubic response function via response theory, which constitutes a part of the vibronic cubic response function.

A Lanczos-chain driven approach for calculating damped vibrational configuration interaction response functions.

We present an approach based on the Lanczos method for calculating the vibrational configuration interaction response functions necessary for evaluating the pure vibrational contributions to the polarizabilities and first hyperpolarizabilities of molecules. The method iteratively builds a tridiagonal representation of the central response matrix, which is subsequently used for solving the response equations. From the same chain, the response functions can be evaluated approximately for any frequency as well as using any complex damping factor. Applications to formaldehyde, cyclopropene, and uracil illustrate the concepts presented.

Vibrational absorption spectra calculated from vibrational configuration interaction response theory using the Lanczos method.

The Lanczos method is used to efficiently obtain the linear vibrational response function for all frequencies in an arbitrary interval. The complex part of the response function gives the absorption spectrum which can subsequently be analyzed. The method provides a way to obtain global information on the absorption spectrum without explicitly converging all vibrational eigenstates of the system. The tridiagonal Lanczos matrix used to obtain the response functions needs only be constructed once for each operator. Example calculations on cyclopropene and uracil are presented.

Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: quadratic response functions from vibrational configuration interaction wave functions.

Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H(2)O, CH(2)O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.