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PubMed2002

Significance of orbital fatty tissue for exophthalmos in thyroid-associated ophthalmopathy.

PURPOSE: To correlate exophthalmos with the volume of extraocular muscle and orbital fatty tissue in thyroid-associated ophthalmopathy (TAO), using MRI that enables the orbital soft tissues to be well defined. METHODS: Thirty-three orbits, 20 from 10 patients with TAO and 13 from 13 controls, were employed. T1-weighted orbital MR slices 2 or 3 mm thick were obtained in axial, coronal and sagittal planes. Tracing the outlines of each structure, we measured the total sectional areas. Volumes of the extraocular muscle, of the fatty tissue and of the bony orbital cavity were calculated by multiplying the slice thickness. Exophthalmos was also measured using axial MRI. RESULTS: In TAO the volume increment of orbital fatty tissue (6.19 cm(3)) was much greater than that of extraocular muscle (1.16 cm(3)). Increase of exophthalmos by 1 mm needed a total orbital volume increment of 0.92 cm(3). The total orbital fatty tissue volume (correlation coefficient 0.70, P=0.06%) and the anterior orbital fatty tissue volume (0.64, P=0.23%) were more closely correlated with the degree of exophthalmos than was extraocular muscle volume (0.58, P=0.8%). Moreover, the volume increment of extraocular muscle and orbital fatty tissue was not always proportional. CONCLUSION: The results show that the orbital fatty tissue involvement is closely related to the degree of exophthalmos. For studying exophthalmos in TAO, the volumetric change, not only in ocular muscles, but also in orbital fatty tissue, should be taken into consideration.

Adipose Tissue↗

PubMed1999

An evaluation of the support provided by common internal orbital reconstruction materials.

PURPOSE: The objectives of this investigation were to assess the weight of the combined internal orbital contents, to evaluate the ability of common internal orbital reconstruction materials to resist loads, and to determine whether these materials provide enough load resistance to support the orbital contents. MATERIALS AND METHODS: The combined exonerated internal orbital contents (globe, fat, extraocular musculature, neurovascular structures, lacrimal apparatus, and musculocutaneous lids) from 16 human orbits were weighed. Five each of 13 different internal orbital reconstruction materials (titanium mesh, bioresorbables, Marlex [CR Bard, Cranston, RI], Medpore [Porex Medical, College Park, GA], Silastic [Dow Coming, Midland, MI], dried calvarium) were evaluated for their ability to resist loads applied by Instron 85.11 mechanical testing device (Canton, MA) when used to reconstruct uniform orbital floor defects in synthetic skulls (Sawbones, Vashon Island, WA). Yield load, yield displacement, maximum load, and displacement at maximum load were measured. A comparison was then made between orbital content weight and the load-resisting capabilities of the various materials. RESULTS: The weight of the combined internal orbital contents was 42.97+/-4.05 g (range, 37.80 to 51.03 g). All of the materials tested except Marlex mesh met or exceeded the requirements for support of the combined internal orbital contents. CONCLUSION: Except in the instance of complete loss of the orbital floor, all of the materials tested should provide adequate orbital support.

Absorbable Implants↗

PubMed1998

Growth of the fetal orbit and lens in normal pregnancies.

OBJECTIVE: To construct nomograms of the size of the fetal orbit and lens during gestation. SUBJECTS: The study group included 349 normal pregnant women at 14-36 weeks' gestation. METHODS: Routine biometric measurements were obtained in all the participants; these included biparietal diameter, head and abdominal circumferences, measurements of the long bones and the diameters of the fetal orbit and lens. The orbital and lens circumference measurements were also related to gestational ages. RESULTS: A linear growth function was observed between gestational age (GA) and orbital diameter (r = 0.94; p < 0.00001; y = -0.66 + 0.5 x GA), orbital circumference (r = 0.94; p < 0.00001; y = -2.1 + 1.5 x GA) and orbital area (r = 0.94; p < 0.00001; y = -98.1 + 8.3 x GA). Significant correlation was also found between femoral length (FL) and orbital diameter (r = 0.95; p < 0.00001; y = 3.3 + 1.9 x FL), orbital circumference (r = 0.95; p < 0.00001; y = 10.3 + 5.9 x FL) and orbital area (r = 0.93; p < 0.00001; y = -28.2 + 32.2 x FL). A linear growth function was observed between orbital circumference and biparietal diameter (r = 0.94; p < 0.00001) and head circumference (r = 0.95; p < 0.00001). A linear growth function was also observed between gestational age and the diameter of the lens (r = 0.89; p < 0.00001; y = 0.88 + 1.4 x GA) the circumference of the lens (r = 0.89; p < 0.00001; y = 2.78 + 0.4 x GA) and the area of the lens (r = 0.89; p < 0.00001; y = -7.95 + 1.0 x GA). The correlation was found between the ratios of the diameters, circumferences and areas of the lens and the orbit. CONCLUSIONS: These results provide normative data of the growth of the fetal orbit and lens and may aid future studies relating to fetal eye anomalies.

Adult↗

PubMed2001

Endoscopically assisted repair of orbital floor fractures.

Traditionally, orbital floor fractures are repaired with standard transcutaneous or transconjunctival approaches. Complications such as external scarring, eyelid edema, ectropion, entropion, and granuloma formation have been associated with these open lid techniques. The endoscope has been used to assist in orbital floor exploration, to reduce entrapped orbital tissue, and to identify the posterior shelf for implant placement. However, an open lid incision is inevitable when implant placement is necessary. We present our experiences in repairing orbital floor fractures using transantral endoscopy without open lid incision.A 0-degree, 4-mm endoscope was placed through a 2 x 1.5-cm2 maxillary antrostomy to dissect the sinus roof. The endoscope was used to assist in the reduction of the floor fractures and prolapsed orbital tissue into the orbital cavity, if present. The orbital floor defect was reconstructed with titanium mesh or Medpor through the antrostomy under endoscopic control. This technique was applied to nine patients who had orbital floor fractures. Two of the patients had zygomatico-orbital fractures, whereas the rest had isolated orbital floor fractures. Three patients received Medpor reconstruction and the remaining six underwent titanium mesh reconstruction. The patients were followed up for 10 months on average. The enophthalmos was corrected in all patients but one, who suffered from mild enophthalmos because of uncorrected orbital medial wall fractures. Diplopia occurred in three patients preoperatively, which was resolved in two of them and improved in the other postoperatively. There have been no complications apart from transient anesthesia in the dermatome of the infraorbital nerve. The technique successfully reconstructed the orbital floor defects, minimized ocular globe manipulation, and eliminated a lower eyelid incision.

Adult↗

PubMed2004

Orbital involvement in juvenile nasopharyngeal angiofibroma: prevalence and treatment.

PURPOSE: To assess the prevalence of orbital invasion by juvenile nasoangiofibroma and to discuss its surgical treatment. METHODS: A retrospective review of the medical records and tomographic scans of a case series of 19 patients with juvenile nasoangiofibroma was performed. All scans were reviewed by a radiologist and an orbital surgeon. The presence of the tumor was assessed in the pterygopalatine fossa, nasal cavity, nasopharynx, paranasal sinuses, inferior orbital fissure, orbit, and middle cranial fossa. RESULTS: The most common structures invaded were pterygopalatine fossa (100%), nasal cavity (94.7%), sphenoid sinus (84.2%), and nasopharynx (73.7%). The orbit was invaded in 6 (31.6%) patients. In 5 of these patients, the tumor extended in the orbit through the inferior orbital fissure. Four patients with orbital invasion were successfully operated with the Le Fort I approach. CONCLUSIONS: Orbital involvement is relatively common in the setting of juvenile nasoangiofibroma extension. The main route of orbital invasion is the inferior orbital fissure. The Le Fort I osteotomy is an adequate approach for managing juvenile nasoangiofibroma when it invades the orbit.

Adolescent↗

PubMed2002

Computer-assisted secondary reconstruction of unilateral posttraumatic orbital deformity.

Until now, computer-assisted surgery has not been practiced as part of the surgical routine of posttraumatic orbital reconstruction. The purpose of this study was to investigate the use of a navigation system for computer-assisted preoperative planning with virtual reconstruction to obtain symmetry of the orbits and intraoperative control of virtual contours in comparison with the clinically achieved surgical results. A further objective of the computer-assisted orbital analysis was to use an ideal measurement for the two-dimensional and three-dimensional changes following orbital reconstruction and to check the equality of the postoperative values for the affected orbits in comparison with those of the unaffected sides. Patients with unilateral posttraumatic orbital defects (n = 18) underwent computer-assisted surgery and preoperative planning using a spiral computed tomography database. Surgical procedures were preplanned with virtual correction by mirroring an individually defined three-dimensional segment from the unaffected side onto the deformed side, creating an ideal unilateral reconstruction. These computer-models were intraoperatively used as virtual templates to navigate the preplanned contours and the globe projection using the Stryker-Leibinger navigation system. Individual noninvasive registration with an overall inaccuracy of approximately 1 mm was achieved by using a maxillary occlusal splint with four markers. The mirroring of the unaffected side allowed an ideal virtual reconstruction. A mean decrease in enlarged orbital volume of 4.0 (SD +/- 1.9) cm was achieved, as was a mean increase in the sagittal globe projection of 5.88 (SD +/- 2.98) mm. With a paired Student test, the decrease between the preoperative and postoperative differences of the affected and unaffected sides was proved significant for orbital volume, globe projection, and computed tomography-based Hertel scale changes (p < 0.01). In 15 of 18 cases, simultaneous malar bone advancement resulted primarily in an additional increase in orbital volume before intraorbital augmentation with calvarial split-bone grafts could be performed. Intraorbital bony augmentation included one (n = 1), two (n = 7), three (n = 8), and all four (n = 2) orbital walls. Computer-assisted preoperative planning enables the surgeon to predict reconstructive surgical steps before the operation. Highly vulnerable structures such as the optic nerve can be detected and avoided intraoperatively, and virtually preplanned bone graft positions and/or orbital frame contours can be checked. Computer-assisted preoperative planning and surgery thus advance the difficult surgical field of orbital reconstruction, particularly through a greater exploitation of radiologic information without additional radiation to the patient.

Adolescent↗

PubMed2000

Reversal of dysthyroid optic neuropathy following orbital fat decompression.

AIMS: To document the successful treatment of five patients with dysthyroid optic neuropathy by orbital fat decompression instead of orbital bone decompression after failed medical therapy. METHODS: Eight orbits of five patients with dysthyroid optic neuropathy were selected for orbital fat decompression as an alternative to bone removal decompression. Treatment with systemic corticosteroids and/or orbital radiotherapy was either unsuccessful or contraindicated in each case. All patients satisfied clinical indications for orbital bone decompression to reverse the optic neuropathy. High resolution computerised tomographic (CT) scans were performed in all cases and in each case showed signs of enlargement of the orbital fat compartment. As an alternative to bone decompression, orbital fat decompression was performed on all eight orbits. RESULTS: Orbital fat decompression was performed on five patients (eight orbits) with optic neuropathy. Optic neuropathy was reversed in all cases. There were no cases of postoperative diplopia, enophthalmos, globe ptosis, or anaesthesia. All patients were followed for a minimum of 1 year. CONCLUSIONS: In a subset of patients with an enlarged orbital fat compartment and in whom extraocular muscle enlargement is not the solitary cause of optic neuropathy, fat decompression is a surgical alternative to bony decompression.

Adipose Tissue↗

PubMed1997

Intracranial neurological injuries associated with orbital fracture.

We attempted to define the central nervous system (CNS) concomitants of various types of orbital fractures in children by reviewing the records of 95 inpatients with admission diagnoses including orbital fracture who presented to the Children's National Medical Center from 1987 through 1994. Patients were divided into three age groups: group I: 0-5 years; group II: 6-12 years; group III: older than 12 years. Orbital fractures were classified by location: roof alone (A); orbital roof plus another orbital wall (B), and orbital fractures sparing the roof (C). Mechanisms of injury included falls (F), motor vehicle accidents (M), and blunt injuries (S). Admission Glasgow Coma Scale (GCS), neurosurgical intervention, nature of associated intracranial injury, and presence of residual neurologic deficit were recorded. Group I included 38 patients, while groups II and III included 28 and 29, respectively. There were 61 boys and 34 girls. Most fractures confined to the roof occurred in group I patients (12 of 16 fractures; 75%). Twenty-four of the 38 group I patients (63%) sustained orbital fractures involving the roof compared to 12 (43%) and 6 (21%) in groups II and III, respectively. Children with orbital fractures involving the roof and another orbital wall, regardless of age, had lower admission GCS. Over half of type B fracture patients (19/26) were involved in motor vehicle accidents. Intracranial injuries were identified in 26 of the 73 patients (36%) whose CT included the brain. Fifteen of 26 patients (58%) with intracranial injuries sustained fractures involving the orbital roof, but only 3 of these had a type A fracture. Seven of the patients with intracranial injury required emergent neurosurgical procedures. Younger children with maxillofacial injury sparing the orbital roof appear more likely to have coexisting intracranial injury, as reflected by CT findings and GCS on admission, than their older cohorts with similar injuries. Fracture of more than one orbital wall greatly increases risk of concurrent intracranial injury in all age groups.

Accidental Falls↗

PubMed2006

Elasticity, viscosity, and deformation of orbital fat.

PURPOSE: For development of a finite element analysis model of orbital mechanics, it was necessary to determine the material properties of orbital fat and its degree of deformation in eye rotation. METHODS: Elasticity and viscosity of orbital fat of eight orbits of four calves and two orbits of one rhesus monkey were measured with a parallel-plate rheometer. The degree of deformation of orbital fat was studied in two human subjects by magnetic resonance imaging (MRI) through the optic nerve in seven (first subject) or fourteen positions of gaze from left to right. Bifurcations of veins in the fat were used as markers for displacement of the fat. RESULTS: The elastic shear modulus (G') of calf orbital fat was between 250 Pa and 500 Pa, and of monkey orbital fat it was between 500 Pa and 900 Pa. The viscous shear modulus (G'') of calf orbital fat was between 80 Pa and 150 Pa, and for monkey orbital fat it was between 300 Pa and 500 Pa. In the MRI scans, it was found that markers in the fat, 1 to 5 mm posterior to the sclera, rotated with the eye for 36% to 53% of eye rotation; the remainder was accounted for by sliding of the eye within the Tenon capsule and within the orbital fat. CONCLUSIONS: Elastic and viscous shear moduli of orbital fat are low. Little energy is dissipated in the fat. The required deformation of the fat during eye rotation is limited because the eye slides, to some extent, within the Tenon capsule.

Adipose Tissue↗

PubMed2003

The morphology and morphometry of the so-called "meningo-orbital foramen" in humans.

The so-called meningo-orbital foramen creates an additional link between the orbit and the cranial cavity. This bony canal, not always present in the human skull, contains a branch from the middle meningeal artery, providing an accessory blood supply to the orbit. This vessel, like the foramen, is characterised by great variability. Although older textbooks of basic anatomy suggested that it was a rare occurrence, some current data indicate a more frequent incidence of this foramen. These discrepancies were verified in our research. 92 orbits were studied on 46 macerated human skulls (25 male and 21 female). Although the incidence of the meningo-orbital foramen in the material as a whole was 28%, the foramen in female skulls was observed to be 40.5%, compared to 18% in male skulls. This difference was statistically significant. A double foramen was encountered in three orbits, and in one orbit there was a triple foramen. This means that in the material as a whole multiple foramina were observed in 4% of cases. Two measurements were taken to determine the localisation of the meningo- orbital foramen. The minimal distance between the supraorbital notch (or foramen) and the meningo-orbital foramen was 35.0 (28-44) mm. The minimal distance from the cross-point of the entrance to the orbit and the fronto-zygomatic suture was (21.3-35.5) mm. This indicates that the meningo-orbital foramen can lie near an operating field in some surgical interventions through the lateral orbital wall.

Female↗

PubMed2006

[Clinical analysis of orbital metastasis from nasopharyngeal carcinoma].

OBJECTIVE: Metastasis of nasopharyngeal carcinoma (NPC) to the orbit has been rarely known. We report 11 patients with metastasis of NPC to the orbit and discuss their clinical characteristics and prognosis. METHODS: Eleven patients with orbital metastasis of NPC who were seen between January 1, 1991 and December 31, 2003 in Zhongshan Ophthalmic Center, Sun Yat-sen University, were retrospectively reviewed. RESULTS: Among 11 patients, there were nine males and two females. The mean age at diagnosis was 45.5 years. The left eye was involved in ten cases, and right eye in one. There were seven patients with a known history of NPC and four with no NPC history at the time of presentation. The seven patients with NPC history developed orbital metastasis at a mean time of 12.7 months (range 2.0 - 60.0 months) after the diagnosis of NPC. The mean duration of eye lesions at presentation was 10.3 months (range 0.7 - 36.0 months). Nine patients developed single metastatic focus and two patients had two foci in the affected orbit. The main component of the tumor was located in the nasal part of the orbit in eight cases, in the temporal part in two, and in the orbital apex in one. The anterior part of the orbit was affected in eight cases. The neoplasm was resected completely or partly through surgery. The diagnosis was histopathologically confirmed as NPC. Among them, four cases were squamous cell carcinomas, two cases lymphoepitheliomas, and five cases unclassified carcinomas. At the last following up examination, five patients had died as a result of disseminated metastasis, one patient had died of unknown cause and three were still alive with no active metastasis. Two patients had lost follow-up. The mean survival time after orbital diagnosis was 21 months. CONCLUSIONS: NPC with orbital metastasis is rare. However, it is the most common primary cancer metastasizing to the orbit in our Center. Most of them were located in the anterior nasal part of the orbit. The prognosis of these metastasis cases is very poor.

Adult↗

PubMed1993

Bone-graft reconstruction of the monkey orbital floor with iliac grafts and titanium mesh plates: a histometric study.

Bone-graft reconstruction of large orbital defects has been difficult because of a lack of marginal support of the grafts and unpredictable resorption. A titanium mesh orbital plate has been developed to provide this marginal support for bone grafts. However, the problem of unpredictable bone-graft resorption remains. To determine if this plate has any effect on graft resorption, this study was designed to quantitate the dimensions and composition of bone autografts (1) with and without titanium plate support and (2) in the anterior and posterior orbit. Bilateral full-thickness large orbital floor defects were surgically created in five monkeys, and a titanium orbital floor plate was fixed with screws into the right orbit. Two iliac crest grafts were measured and placed transversely and without fixation in each orbit, one anterior and the other posterior to the axis of the globe. The orbits were retrieved 28 weeks after surgery and were analyzed histologically and histometrically. Comparison of the supported and nonsupported grafts revealed no differences in their histologic appearance. There were three significant histometric findings: (1) resorption of bone was similar for those grafts which spanned an orbital floor defect and those which were supported by a titanium plate; (2) resorption of grafts in the posterior orbit did not differ from that of grafts in the anterior orbit; and (3) resorption of approximately one-third of bone-graft thickness and width had taken place during the 28-week study interval. We conclude that the benefits of bone-graft support by a titanium mesh orbital floor plate are not offset by any alteration in bone-graft resorption.

Animals↗

PubMed2006

Orbital overlap and chemical bonding.

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).

Journal Article↗

PubMed2006

Orbital signatures of methyl in L-alanine.

Molecular orbital signatures of the methyl substituent in L-alanine have been identified with respect to those of glycine from information obtained in coordinate and momentum space, using dual space analysis. Electronic structural information in coordinate space is obtained using ab initio (MP2/TZVP) and density functional theory (B3LYP/TZVP) methods, from which the Dyson orbitals are simulated based on the plane wave impulse approximation into momentum space. In comparison to glycine, relaxation in geometry and valence orbitals in L-alanine is found as a result of the attachment of the methyl group. Five orbitals rather than four orbitals are identified as methyl signatures. That is, orbital 6a in the core shell, orbitals 11a and 12a in the inner valence shell, and orbitals 19a and 20a in the outer valence shell. In the inner valence shell, the attachment of methyl to glycine causes a splitting of its orbital 10a' into orbitals 11a and 12a of L-alanine, whereas in the outer valence shell the methyl group results in an insertion of an additional orbital pair of 19a and 20a. The frontier molecular orbitals, 24a and 23a, are found without any significant role in the methylation of glycine.

Alanine↗

PubMed2004

An efficient method for calculating maxima of homogeneous functions of orthogonal matrices: applications to localized occupied orbitals.

We present here three new algorithms (one purely iterative and two DIIS-like [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function f(U)=Tr(AU) has exactly one local (and global) maximum for U special orthogonal [i.e., UU(T)=1 and det(U)=1]. This is proved in the Appendix. One application of these algorithms is the computation of localized orbitals, including, for example, Boys and Edmiston-Ruedenberg (ER) orbitals. The Boys orbitals are defined as the set of orthonormal orbitals which, for a given vector space of orbitals, maximize the sum of the distances between orbital centers. The ER orbitals maximize total self-interaction energy. The algorithm presented here computes Boys orbitals roughly as fast as the traditional method (Jacobi sweeps), while, for large systems, it finds ER orbitals potentially much more quickly than traditional Jacobi sweeps. In fact, the required time for convergence of our algorithm scales quadratically in the region of a few hundred basis functions (though cubicly asymptotically), while Jacobi sweeps for the ER orbitals traditionally scale as the number of occupied orbitals to the fifth power. As an example of the utility of the method, we provide below the ER orbitals of nitrated and nitrosated benzene, and we discuss the chemical implications.

Journal Article↗

PubMed2005

On the accuracy of one-component pseudopotential spin-orbit calculations.

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calculation, include valence spin-orbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spin-orbit configuration interaction (CI) with singles from the reference ground-state configuration gives rise to double counting of these spin-orbit effects. Two new methods that avoid such double counting have been investigated. The first, so-called "explicit" method, calculates explicitly, by means of a four-component spin-orbit CI, the double-counted spin-orbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spin-orbit effects as well as the so-called "pseudovariational collapse," this method is shown to be cumbersome. In the second "implicit" method the spin-orbit pseudopotential is extracted at the spin-orbit polarized and relaxed level by means of a single-excitation spin-orbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the double-counting problem.

Journal Article↗

PubMed2006

Bonding analysis using localized relativistic orbitals: water, the ultrarelativistic case and the heavy homologues H2X (X = Te, Po, eka-Po).

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).

Journal Article↗

PubMed2000

[Classification of the orbital margin fractures].

OBJECTIVE: To study the classification of the orbital margin fractures. METHODS: There are 65 cases of the orbital margin fractures classified by Reduction-Orbital-Classification from January 1995 to December 1999 in Macau Conde de Sao Juanuario Hospital. RESULTS: The 65 cases are classified into six type: I Stable orbital fracture, II Orbital floor (blow-out) fracture, III Orbital-zygomatic fracture, IV Orbital-naso-maxillary fracture, V Comminuted fracture of the inferior orbital rim, VI Complex orbital fractures. CONCLUSION: The Reduction-Orbital-Classification are a complete, precise, practical, simple way for the orbital fractures; It not only presents the exist of the orbital margin fractures but also means the Classification for convenience of the treatment and treatment guiding the classification.

English Abstract↗