Automated Insulin Delivery in Women with Pregnancy Complicated by Type 1 Diabetes.

BACKGROUND: Hybrid closed-loop insulin therapy has shown promise for management of type 1 diabetes during pregnancy; however, its efficacy is unclear. METHODS: In this multicenter, controlled trial, we randomly assigned pregnant women with type 1 diabetes and a glycated hemoglobin level of at least 6.5% at nine sites in the United Kingdom to receive standard insulin therapy or hybrid closed-loop therapy, with both groups using continuous glucose monitoring. The primary outcome was the percentage of time in the pregnancy-specific target glucose range (63 to 140 mg per deciliter [3.5 to 7.8 mmol per liter]) as measured by continuous glucose monitoring from 16 weeks' gestation until delivery. Analyses were performed according to the intention-to-treat principle. Key secondary outcomes were the percentage of time spent in a hyperglycemic state (glucose level >140 mg per deciliter), overnight time in the target range, the glycated hemoglobin level, and safety events. RESULTS: A total of 124 participants with a mean (±SD) age of 31.1±5.3 years and a mean baseline glycated hemoglobin level of 7.7±1.2% underwent randomization. The mean percentage of time that the maternal glucose level was in the target range was 68.2±10.5% in the closed-loop group and 55.6±12.5% in the standard-care group (mean adjusted difference, 10.5 percentage points; 95% confidence interval [CI], 7.0 to 14.0; P<0.001). Results for the secondary outcomes were consistent with those of the primary outcome; participants in the closed-loop group spent less time in a hyperglycemic state than those in the standard-care group (difference, -10.2 percentage points; 95% CI, -13.8 to -6.6); had more overnight time in the target range (difference, 12.3 percentage points; 95% CI, 8.3 to 16.2), and had lower glycated hemoglobin levels (difference, -0.31 percentage points; 95% CI, -0.50 to -0.12). Little time was spent in a hypoglycemic state. No unanticipated safety problems associated with the use of closed-loop therapy during pregnancy occurred (6 instances of severe hypoglycemia, vs. 5 in the standard-care group; 1 instance of diabetic ketoacidosis in each group; and 12 device-related adverse events in the closed-loop group, 7 related to closed-loop therapy). CONCLUSIONS: Hybrid closed-loop therapy significantly improved maternal glycemic control during pregnancy complicated by type 1 diabetes. (Funded by the Efficacy and Mechanism Evaluation Program; AiDAPT ISRCTN Registry number, ISRCTN56898625.).

Clinical utility of point-of-care glucose testing in the assessment of gestational diabetes: Prospective cohort study.

OBJECTIVE: To assess the clinical utility of point-of-care (POC) capillary blood glucose (CBG) testing in the assessment of gestational diabetes mellitus (GDM) during oral glucose tolerance test (OGTT). DESIGN: Prospective cohort study. SETTING: Antenatal clinics at King's College Hospital. POPULATION: Women screened for GDM between March and June 2020. METHODS: The CBG was measured using the POC StatStrip® test and the venous plasma glucose (VPG) was measured by Roche analyser (Cobas 8000 c702). GDM was diagnosed based on the 2015 National Institute for Health and Clinical Excellence (NICE) Clinical Guideline criteria. The two methods were compared statistically using Analyse-It 5.40.2. MAIN OUTCOME MEASURES: Diagnostic sensitivity, specificity, positive and negative predictive values (PPV and NPV) for the POC StatStrip® test, compared with VPG measured by reference laboratory method. RESULTS: A total of 230 women were included. The number and percentage of women with glucose concentrations above the GDM threshold using the POC StatStrip® test versus laboratory VPG measurement was 15 (6.5%) versus eight (3.4%) at fasting and 105 (45.6%) versus 72 (31.1%) at 2 h, respectively. The sensitivity and specificity values (and 95% CIs) for the POC StatStrip® test were 88% (52%-99%) and 97% (93%-98%) at fasting and 97% (91%-99%) and 79% (71%-84%) at 2 h, respectively. However, the specificity and the NPV for the POC StatStrip® test for concentrations of ≤5.0 mmol/L at fasting or <7.5 mmol/L at 2 h were 100%, and the sensitivity and the PPV for concentrations of >9.5 mmol/L at 2 h were 100%. CONCLUSIONS: In our cohort the POC measurement of CBG cannot entirely replace the laboratory method for the OGTT; however, it can be used to rule out/rule in GDM for glucose concentrations of ≤5.0 mmol/L at fasting or <7.5/>9.5 mmol/L at 2 h.

Nonadiabatic transition probabilities for quantum systems in electromagnetic fields: Dephasing and population relaxation due to contact with a bath.

We contrast Dirac's theory of transition probabilities and the theory of nonadiabatic transition probabilities, applied to a perturbed system that is coupled to a bath. In Dirac's analysis, the presence of an excited state |k0⟩ in the time-dependent wave function constitutes a transition. In the nonadiabatic theory, a transition occurs when the wave function develops a term that is not adiabatically connected to the initial state. Landau and Lifshitz separated Dirac's excited-state coefficients into a term that follows the adiabatic theorem of Born and Fock and a nonadiabatic term that represents excitation across an energy gap. If the system remains coherent, the two approaches are equivalent. However, differences between the two approaches arise when coupling to a bath causes dephasing, a situation that was not treated by Dirac. For two-level model systems in static electric fields, we add relaxation terms to the Liouville equation for the time derivative of the density matrix. We contrast the results obtained from the two theories. In the analysis based on Dirac's transition probabilities, the steady state of the system is not an equilibrium state; also, the steady-state population ρkk,s increases with increasing strength of the perturbation and its value depends on the dephasing time T2. In the nonadiabatic theory, the system evolves to the thermal equilibrium with the bath. The difference is not simply due to the choice of basis because the difference remains when the results are transformed to a common basis.

Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states.

Using IBM's publicly accessible quantum computers, we have analyzed the entropies of Schrödinger's cat states, which have the form Ψ = (1/2)1/2 [|0 0 0⋯0〉 + |1 1 1⋯1〉]. We have obtained the average Shannon entropy SSo of the distribution over measurement outcomes from 75 runs of 8192 shots, for each of the numbers of entangled qubits, on each of the quantum computers tested. For the distribution over N fault-free measurements on pure cat states, SSo would approach one as N → ∞, independent of the number of qubits; but we have found that SSo varies nearly linearly with the number of qubits n. The slope of SSoversus the number of qubits differs among computers with the same quantum volumes. We have developed a two-parameter model that reproduces the near-linear dependence of the entropy on the number of qubits, based on the probabilities of observing the output 0 when a qubit is set to |0〉 and 1 when it is set to |1〉. The slope increases as the error rate increases. The slope provides a sensitive measure of the accuracy of a quantum computer, so it serves as a quickly determinable index of performance. We have used tomographic methods with error mitigation as described in the qiskit documentation to find the density matrix ρ and evaluate the von Neumann entropies of the cat states. From the reduced density matrices for individual qubits, we have calculated the entanglement entropies. The reduced density matrices represent mixed states with approximately 50/50 probabilities for states |0〉 and |1〉. The entanglement entropies are very close to one.

AiDAPT: automated insulin delivery amongst pregnant women with type 1 diabetes: a multicentre randomized controlled trial - study protocol.

BACKGROUND: Pregnant women with type 1 diabetes strive for tight glucose targets (3.5-7.8 mmol/L) to minimise the risks of obstetric and neonatal complications. Despite using diabetes technologies including continuous glucose monitoring (CGM), insulin pumps and contemporary insulin analogues, most women struggle to achieve and maintain the recommended pregnancy glucose targets. This study aims to evaluate whether the use of automated closed-loop insulin delivery improves antenatal glucose levels in pregnant women with type 1 diabetes. METHODS/DESIGN: A multicentre, open label, randomized, controlled trial of pregnant women with type 1 diabetes and a HbA1c of ≥48 mmol/mol (6.5%) at pregnancy confirmation and ≤ 86 mmol/mol (10%) at randomization. Participants who provide written informed consent before 13 weeks 6 days gestation will be entered into a run-in phase to collect 96 h (24 h overnight) of CGM glucose values. Eligible participants will be randomized on a 1:1 basis to CGM (Dexcom G6) with usual insulin delivery (control) or closed-loop (intervention). The closed-loop system includes a model predictive control algorithm (CamAPS FX application), hosted on an android smartphone that communicates wirelessly with the insulin pump (Dana Diabecare RS) and CGM transmitter. Research visits and device training will be provided virtually or face-to-face in conjunction with 4-weekly antenatal clinic visits where possible. Randomization will stratify for clinic site. One hundred twenty-four participants will be recruited. This takes into account 10% attrition and 10% who experience miscarriage or pregnancy loss. Analyses will be performed according to intention to treat. The primary analysis will evaluate the change in the time spent in the target glucose range (3.5-7.8 mmol/l) between the intervention and control group from 16 weeks gestation until delivery. Secondary outcomes include overnight time in target, time above target (> 7.8 mmol/l), standard CGM metrics, HbA1c and psychosocial functioning and health economic measures. Safety outcomes include the number and severity of ketoacidosis, severe hypoglycaemia and adverse device events. DISCUSSION: This will be the largest randomized controlled trial to evaluate the impact of closed-loop insulin delivery during type 1 diabetes pregnancy. TRIAL REGISTRATION: ISRCTN 56898625 Registration Date: 10 April, 2018.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities.

For a quantum system in a time-dependent perturbation, we prove that the variance in the energy depends entirely on the nonadiabatic transition probability amplitudes bk(t). Landau and Lifshitz introduced the nonadiabatic coefficients for the excited states of a perturbed quantum system by integrating by parts in Dirac's expressions for the coefficients ck (1)(t) of the excited states to first order in the perturbation. This separates ck (1)(t) for each state into an adiabatic term ak (1)(t) and a nonadiabatic term bk (1)(t). The adiabatic term follows the adiabatic theorem of Born and Fock; it reflects the adjustment of the initial state to the perturbation without transitions. If the response to a time-dependent perturbation is entirely adiabatic, the variance in the energy is zero. The nonadiabatic term bk (1)(t) represents actual excitations away from the initial state. As a key result of the current work, we derive the variance in the energy of the quantum system and all of the higher moments of the energy distribution using the values of |bk(t)|2 for each of the excited states along with the energy differences between the excited states and the ground state. We prove that the same variance (through second order) is obtained in terms of Dirac's excited-state coefficients ck(t). We show that the results from a standard statistical analysis of the variance are consistent with the quantum results if the probability of excitation Pk is set equal to |bk(t)|2, but not if the probability of excitation is set equal to |ck(t)|2. We illustrate the differences between the variances calculated with the two different forms of Pk for vibration-rotation transitions of HCl in the gas phase.

The interaction-induced dipole of H2-H: New ab initio results and spherical tensor analysis.

We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the exponential operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.

Adenosine-assisted neurovascular surgery: initial case series and review of literature.

Cerebral aneurysms in complex anatomical locations and intraoperative rupture of aneurysms are challenging for neurosurgeons and anaesthetists alike. Mechanical and non-mechanical methods to reduce blood flow into aneurysms are well-recognised techniques to facilitate aneurysm exclusion from the circulation. Mechanical methods like temporary clipping of parent arteries, carotid artery ligation and endovascular balloon occlusion are commonly used in clinical practice. However, non-mechanical techniques such as rapid ventricular pacing and adenosine-induced cardiac standstill with hypotension are still emerging strategies. The aim of this study is to report our units' experience in the use of adenosine in aneurysm clipping and arteriovenous malformation (AVM) resection and review the literature. The records of all patients who had adenosine-assisted clipping of intracranial aneurysms and AVM resections in our institute between November 2015 and December 2016 were extracted from prospectively maintained database. The following data were collected: patient demographics, comorbidities, size and location of the aneurysms or AVM, number of boluses and total dose of adenosine administered, duration of cardiac standstill and hypotension (systolic blood pressure < 60 mmHg), intraoperative and postoperative complications and outcome scores at discharge. Literature search on Embase and PubMed for the terms "adenosine and clipping", "adenosine and aneurysm" and "adenosine and AVM" was performed. Eight aneurysms and two AVMs were identified. While both AVMs were elective procedures, half of the aneurysm clippings were on urgent basis. We used adenosine safely with spontaneous return of rhythm in all cases. Temporary clips to the parent artery were applied for brief periods in 2 patients who had pre-adenosine intraoperative rupture. We did not observe any immediate or late adverse events related to administration of adenosine. From our literature review, a total of ten case series and four case reports were identified. There were no reports on the use of adenosine in AVM resection. Transient adenosine-induced asystole is a safe and effective technique in facilitating surgical treatment of complex aneurysms and AVMs. In addition, adenosine use reduces the need, duration, and associated complications of temporary clip applications to parent arteries.

The impact of hypoglycaemia awareness status on regional brain responses to acute hypoglycaemia in men with type 1 diabetes.

AIMS/HYPOTHESIS: Impaired awareness of hypoglycaemia (IAH) in type 1 diabetes increases the risk of severe hypoglycaemia sixfold and can be resistant to intervention. We explored the impact of IAH on central responses to hypoglycaemia to investigate the mechanisms underlying barriers to therapeutic intervention. METHODS: We conducted [15O]water positron emission tomography studies of regional brain perfusion during euglycaemia (target 5 mmol/l), hypoglycaemia (achieved level, 2.4 mmol/l) and recovery (target 5 mmol/l) in 17 men with type 1 diabetes: eight with IAH, and nine with intact hypoglycaemia awareness (HA). RESULTS: Hypoglycaemia with HA was associated with increased activation in brain regions including the thalamus, insula, globus pallidus (GP), anterior cingulate cortex (ACC), orbital cortex, dorsolateral frontal (DLF) cortex, angular gyrus and amygdala; deactivation occurred in the temporal and parahippocampal regions. IAH was associated with reduced catecholamine and symptom responses to hypoglycaemia vs HA (incremental AUC: autonomic scores, 26.2 ± 35.5 vs 422.7 ± 237.1; neuroglycopenic scores, 34.8 ± 88.8 vs 478.9 ± 311.1; both p < 0.002). There were subtle differences (p < 0.005, k ≥ 50 voxels) in brain activation at hypoglycaemia, including early differences in the right central operculum, bilateral medial orbital (MO) cortex, and left posterior DLF cortex, with additional differences in the ACC, right GP and post- and pre-central gyri in established hypoglycaemia, and lack of deactivation in temporal regions in established hypoglycaemia. CONCLUSIONS/INTERPRETATION: Differences in activation in the post- and pre-central gyri may be expected in people with reduced subjective responses to hypoglycaemia. Alterations in the activity of regions involved in the drive to eat (operculum), emotional salience (MO cortex), aversion (GP) and recall (temporal) suggest differences in the perceived importance and urgency of responses to hypoglycaemia in IAH compared with HA, which may be key to the persistence of the condition.

Continuous glucose monitoring in pregnant women with type 1 diabetes (CONCEPTT): a multicentre international randomised controlled trial.

BACKGROUND: Pregnant women with type 1 diabetes are a high-risk population who are recommended to strive for optimal glucose control, but neonatal outcomes attributed to maternal hyperglycaemia remain suboptimal. Our aim was to examine the effectiveness of continuous glucose monitoring (CGM) on maternal glucose control and obstetric and neonatal health outcomes. METHODS: In this multicentre, open-label, randomised controlled trial, we recruited women aged 18-40 years with type 1 diabetes for a minimum of 12 months who were receiving intensive insulin therapy. Participants were pregnant (≤13 weeks and 6 days' gestation) or planning pregnancy from 31 hospitals in Canada, England, Scotland, Spain, Italy, Ireland, and the USA. We ran two trials in parallel for pregnant participants and for participants planning pregnancy. In both trials, participants were randomly assigned to either CGM in addition to capillary glucose monitoring or capillary glucose monitoring alone. Randomisation was stratified by insulin delivery (pump or injections) and baseline glycated haemoglobin (HbA1c). The primary outcome was change in HbA1c from randomisation to 34 weeks' gestation in pregnant women and to 24 weeks or conception in women planning pregnancy, and was assessed in all randomised participants with baseline assessments. Secondary outcomes included obstetric and neonatal health outcomes, assessed with all available data without imputation. This trial is registered with ClinicalTrials.gov, number NCT01788527. FINDINGS: Between March 25, 2013, and March 22, 2016, we randomly assigned 325 women (215 pregnant, 110 planning pregnancy) to capillary glucose monitoring with CGM (108 pregnant and 53 planning pregnancy) or without (107 pregnant and 57 planning pregnancy). We found a small difference in HbA1c in pregnant women using CGM (mean difference -0·19%; 95% CI -0·34 to -0·03; p=0·0207). Pregnant CGM users spent more time in target (68% vs 61%; p=0·0034) and less time hyperglycaemic (27% vs 32%; p=0·0279) than did pregnant control participants, with comparable severe hypoglycaemia episodes (18 CGM and 21 control) and time spent hypoglycaemic (3% vs 4%; p=0·10). Neonatal health outcomes were significantly improved, with lower incidence of large for gestational age (odds ratio 0·51, 95% CI 0·28 to 0·90; p=0·0210), fewer neonatal intensive care admissions lasting more than 24 h (0·48; 0·26 to 0·86; p=0·0157), fewer incidences of neonatal hypoglycaemia (0·45; 0·22 to 0·89; p=0·0250), and 1-day shorter length of hospital stay (p=0·0091). We found no apparent benefit of CGM in women planning pregnancy. Adverse events occurred in 51 (48%) of CGM participants and 43 (40%) of control participants in the pregnancy trial, and in 12 (27%) of CGM participants and 21 (37%) of control participants in the planning pregnancy trial. Serious adverse events occurred in 13 (6%) participants in the pregnancy trial (eight [7%] CGM, five [5%] control) and in three (3%) participants in the planning pregnancy trial (two [4%] CGM and one [2%] control). The most common adverse events were skin reactions occurring in 49 (48%) of 103 CGM participants and eight (8%) of 104 control participants during pregnancy and in 23 (44%) of 52 CGM participants and five (9%) of 57 control participants in the planning pregnancy trial. The most common serious adverse events were gastrointestinal (nausea and vomiting in four participants during pregnancy and three participants planning pregnancy). INTERPRETATION: Use of CGM during pregnancy in patients with type 1 diabetes is associated with improved neonatal outcomes, which are likely to be attributed to reduced exposure to maternal hyperglycaemia. CGM should be offered to all pregnant women with type 1 diabetes using intensive insulin therapy. This study is the first to indicate potential for improvements in non-glycaemic health outcomes from CGM use. FUNDING: Juvenile Diabetes Research Foundation, Canadian Clinical Trials Network, and National Institute for Health Research.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state.

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r0 in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H2 in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, αxx and αzz show the expected functional forms, to leading order in r-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

Nonadiabatic transition probabilities in a time-dependent Gaussian pulse or plateau pulse: Toward experimental tests of the differences from Dirac's transition probabilities.

For a quantum system subject to a time-dependent perturbing field, Dirac's analysis gives the probability of transition to an excited state |k⟩ in terms of the norm square of the entire excited-state coefficient ck(t) in the wave function. By integrating by parts in Dirac's equation for ck(t) at first order, Landau and Lifshitz separated ck (1)(t) into an adiabatic term ak (1)(t) that characterizes the gradual adjustment of the ground state to the perturbation without transitions and a nonadiabatic term bk (1)(t) that depends explicitly on the time derivative of the perturbation at times t' ≤ t. Landau and Lifshitz stated that the probability of transition in a pulsed perturbation is given by |bk(t)|2, rather than by |ck(t)|2. We use the term "transition probability" to refer to the probability that a true excited-state component is present in the time-evolved wave function, as opposed to a smooth modification of the initial state. In recent work, we have examined the differences between |bk(t)|2 and |ck(t)|2 when a system is perturbed by a harmonic wave in a Gaussian envelope. We showed that significant differences exist when the frequency of the harmonic wave is off-resonance with the transition frequency. In this paper, we consider Gaussian perturbations and pulses that rise via a half Gaussian shoulder to a level plateau and later return to zero via a down-going half Gaussian. While the perturbation is constant, the transition probability |bk(t)|2 does not change. By contrast, |ck(t)|2 continues to oscillate while the perturbation is constant, and its time averaged value differs from |bk(t)|2. We suggest a general type of experiment to prove that the transition probability is given by |bk(t)|2, not |ck(t)|2. We propose a ratio test that does not require accurate knowledge of transition matrix elements or absolute field intensities.

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms.

For a perturbed quantum system initially in the ground state, the coefficient ck(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term ak(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H0 without transitions; ak(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term bk(t) describes excitation into another quantum state k; bk(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by bk(t) 2, as first stated by Landau and Lifshitz. In this work, we contrast bk(t) 2 and ck(t) 2. The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ωk0 is on resonance with the frequency ω of the cosine wave, bk(t) 2 and ck(t) 2 rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ωk0 ≠ ω), bk(t) 2 and ck(t) 2 differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when ak(t) ≡ 0. If ωk0 < ω, bk(t) 2 generally exceeds ck(t) 2, while the opposite is true when ωk0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)2]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

Experiences of gestational diabetes and gestational diabetes care: a focus group and interview study.

BACKGROUND: Gestational diabetes mellitus (GDM) is an increasingly common condition of pregnancy. It is associated with adverse fetal, infant and maternal outcomes, as well as an increased risk of GDM in future pregnancies and type 2 diabetes for both mother and offspring. Previous studies have shown that GDM can result in an emotionally distressing pregnancy, but there is little research on the patient experience of GDM care, especially of a demographically diverse UK population. The aim of this research was to explore the experiences of GDM and GDM care for a group of women attending a large diabetes pregnancy unit in southeast London, UK, in order to improve care. METHODS: Framework analysis was used to support an integrated analysis of data from six focus groups with 35 women and semi-structured interviews with 15 women, held in 2015. Participants were purposively sampled and were representative of the population being studied in terms of ethnicity, age, deprivation score and body mass index (BMI). RESULTS: We identified seven themes: the disrupted pregnancy, projected anxiety, reproductive asceticism, women as baby machines, perceived stigma, lack of shared understanding and postpartum abandonment. These themes highlight the often distressing experience of GDM. While most women were grateful for the intensive support they received during pregnancy, the costs to their personal autonomy were high. Women described feeling valued solely as a means to produce a healthy infant, and felt chastised if they failed to adhere to the behaviours required to achieve this. This sometimes had an enduring impact to the potential detriment of women's long-term psychological and physical health. CONCLUSIONS: This study reveals the experiences of a demographically diverse group of patients with GDM, reflecting findings from previous studies globally and extending analysis to the context of improving care. Healthcare delivery may need to be reoriented to improve the pregnancy experience and help ensure women are engaged and attentive to their own health, particularly after birth, without compromising clinical pregnancy outcomes. Areas for consideration in GDM healthcare include: improved management of emotional responses to GDM; a more motivational approach; rethinking the medicalisation of care; and improved postpartum care.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field.

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term Hm and a field term Hf, and show that both Hm and Hf have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.

Non-adiabatic current densities, transitions, and power absorbed by a molecule in a time-dependent electromagnetic field.

The energy of a molecule subject to a time-dependent perturbation separates completely into adiabatic and non-adiabatic terms, where the adiabatic term reflects the adjustment of the ground state to the perturbation, while the non-adiabatic term accounts for the transition energy [A. Mandal and K. L. C. Hunt, J. Chem. Phys. 137, 164109 (2012)]. For a molecule perturbed by a time-dependent electromagnetic field, in this work, we show that the expectation value of the power absorbed by the molecule is equal to the time rate of change of the non-adiabatic term in the energy. The non-adiabatic term is given by the transition probability to an excited state k, multiplied by the transition energy from the ground state to k, and then summed over the excited states. The expectation value of the power absorbed by the molecule is derived from the integral over space of the scalar product of the applied electric field and the non-adiabatic current density induced in the molecule by the field. No net power is absorbed due to the action of the applied electric field on the adiabatic current density. The work done on the molecule by the applied field is the time integral of the power absorbed. The result established here shows that work done on the molecule by the applied field changes the populations of the molecular states.

Quantum mechanical calculation of the collision-induced absorption spectra of N2-N2 with anisotropic interactions.

We present quantum mechanical calculations of the collision-induced absorption spectra of nitrogen molecules, using ab initio dipole moment and potential energy surfaces. Collision-induced spectra are first calculated using the isotropic interaction approximation. Then, we improve upon these results by considering the full anisotropic interaction potential. We also develop the computationally less expensive coupled-states approximation for calculating collision-induced spectra and validate this approximation by comparing the results to numerically exact close-coupling calculations for low energies. Angular localization of the scattering wave functions due to anisotropic interactions affects the line strength at low energies by two orders of magnitude. The effect of anisotropy decreases at higher energy, which validates the isotropic interaction approximation as a high-temperature approximation for calculating collision-induced spectra. Agreement with experimental data is reasonable in the isotropic interaction approximation, and improves when the full anisotropic potential is considered. Calculated absorption coefficients are tabulated for application in atmospheric modeling.

Ground and excited states of vanadium hydroxide isomers and their cations, VOH(0,+) and HVO(0,+).

Employing correlation consistent basis sets of quadruple-zeta quality and applying both multireference configuration interaction and single-reference coupled cluster methodologies, we studied the electronic and geometrical structure of the [V,O,H](0,+) species. The electronic structure of HVO(0,+) is explained by considering a hydrogen atom approaching VO(0,+), while VOH(0,+) molecules are viewed in terms of the interaction of V(+,2+) with OH(-). The potential energy curves for H-VO(0,+) and V(0,+)-OH have been constructed as functions of the distance between the interacting subunits, and the potential energy curves have also been determined as functions of the H-V-O angle. For the stationary points that we have located, we report energies, geometries, harmonic frequencies, and dipole moments. We find that the most stable bent HVO(0,+) structure is lower in energy than any of the linear HVO(0,+) structures. Similarly, the most stable state of bent VOH is lower in energy than the linear structures, but linear VOH(+) is lower in energy than bent VOH(+). The global minimum on the potential energy surface for the neutral species is the X(3)A" state of bent HVO, although the X(5)A" state of bent VOH is less than 5 kcal/mol higher in energy. The global minimum on the potential surface for the cation is the X(4)Σ(-) state of linear VOH(+), with bent VOH(+) and bent HVO(+) both more than 10 kcal/mol higher in energy. For the neutral species, the bent geometries exhibit significantly higher dipole moments than the linear structures.