Hartree-Fock-Bogoliubov theory for number-parity-violating fermionic Hamiltonians.

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan-Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree-Fock-Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. We also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.

Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions.

Numerical difficulties associated with computing matrix elements of operators between Hartree-Fock-Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by zero in the standard formulation of the nonorthogonal Wick's theorem in the limit of vanishing HFB overlap. In this Communication, we present a robust formulation of Wick's theorem that stays well-behaved regardless of whether the HFB states are orthogonal or not. This new formulation ensures cancellation between the zeros of the overlap and the poles of the Pfaffian, which appears naturally in fermionic systems. Our formula explicitly eliminates self-interaction, which otherwise causes additional numerical challenges. A computationally efficient version of our formalism enables robust symmetry-projected HFB calculations with the same computational cost as mean-field theories. Moreover, we avoid potentially diverging normalization factors by introducing a robust normalization procedure. The resulting formalism treats even and odd number of particles on equal footing and reduces to Hartree-Fock as a natural limit. As proof of concept, we present a numerically stable and accurate solution to a Jordan-Wigner-transformed Hamiltonian, whose singularities motivated the present work. Our robust formulation of Wick's theorem is a most promising development for methods using quasiparticle vacuum states.

Strong-weak duality via Jordan-Wigner transformation: Using fermionic methods for strongly correlated su(2) spin systems.

The Jordan-Wigner transformation establishes a duality between su(2) and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicates that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams and provides a better starting point for addressing challenging spin problems.

Construction of linearly independent non-orthogonal AGP states.

We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

Exploring non-linear correlators on AGP.

Single-reference methods such as Hartree-Fock-based coupled cluster theory are well known for their accuracy and efficiency for weakly correlated systems. For strongly correlated systems, more sophisticated methods are needed. Recent studies have revealed the potential of the antisymmetrized geminal power (AGP) as an excellent initial reference for the strong correlation problem. While these studies improved on AGP by linear correlators, we explore some non-linear exponential Ansätze in this paper. We investigate two approaches in particular. Similar to Wahlen-Strothman et al. [Phys. Rev. B 91, 041114(R) (2015)], we show that the similarity transformed Hamiltonian with a Hilbert-space Jastrow operator is summable to all orders and can be solved over AGP by projecting the Schrödinger equation. The second approach is based on approximating the unitary pair-hopper Ansatz recently proposed for application on a quantum computer. We report benchmark numerical calculations against the ground state of the pairing Hamiltonian for both of these approaches.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Synthesis, Structure, and Magnetism of Tris(amide) [Ln{N(SiMe3 )2 }3 ]1- Complexes of the Non-traditional +2 Lanthanide Ions.

A new series of Ln2+ complexes has been synthesized that overturns two previous generalizations in rare-earth metal reduction chemistry: that amide ligands do not form isolable complexes of the highly reducing non-traditional Ln2+ ions, and that yttrium is a good model for the late lanthanides in these reductive reactions. Reduction of Ln(NR2 )3 (R=SiMe3 ) complexes in THF under Ar with M=K or Rb in the presence of 2.2.2-cryptand (crypt) forms crystallographically characterizable [M(crypt)][Ln(NR2 )3 ] complexes not only for the traditional Tm2+ ion and the configurational crossover ions, Nd2+ and Dy2+ , but also for the non-traditional Gd2+ , Tb2+ , Ho2+ , and Er2+ ions. Crystallographic data as well as UV/Vis, magnetic susceptibility, and density functional theory studies are consistent with the accessibility of 4fn 5d1 configurations for Ln2+ ions in this tris(silylamide) ligand environment. The Dy2+ complex, [K(crypt)][Dy(NR2 )3 ], has a higher magnetic moment than previously observed for any monometallic complex: 11.67 µB .

Random-Phase Approximation Methods.

Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.

Using Diamagnetic Yttrium and Lanthanum Complexes to Explore Ligand Reduction and C-H Bond Activation in a Tris(aryloxide)mesitylene Ligand System.

[Y(N(SiMe3)2)3] reacts with (Ad,MeArOH)3mes to form the Y3+ complex [((Ad,MeArO)3mes)Y], 1-Y. This complex reacts with potassium metal in the presence of 2.2.2-cryptand to give a cocrystallized mixture of [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Y], 2-Y, and [K(2.2.2-cryptand)][((Ad,MeArO)3mes)YH], 3-Y. The electron paramagnetic resonance spectrum of this crystalline mixture exhibits an isotropic signal at 77 K ( giso = 2.000, Wiso = 1.8 mT), suggesting that 2-Y is best described as a Y3+ complex of the tris(aryloxide)mesitylene radical ((Ad,MeArO)3mes)4-. Evidence of the hydride ligand in 3-Y was obtained by 89Y-1H heteronuclear multiple quantum coherence NMR spectroscopy, and a coupling constant of JYH = 93 Hz was observed. A single crystal of 3-Y was also obtained in pure form and structurally characterized for comparison with the crystal data on the mixed component 2-Ln/3-Ln crystals. The origin of the hydride in 3-Ln is unknown, but further studies of the reduction of 1-La, previously found to form 2-La, revealed a possible source. Ligand-based C-H bond activation and loss of hydrogen can occur under reducing conditions to form a tetraanionic ligand derived from ((Ad,MeArO)3mes)3-, as observed in [K(2.2.2-cryptand)][((Ad,MeArO)3(C6Me3(CH2)2CH)La], 4-La.

Metal versus Ligand Reduction in Ln3+ Complexes of a Mesitylene-Anchored Tris(Aryloxide) Ligand.

The synthesis of 4f n Ln3+ complexes of the tris(aryloxide) mesitylene ligand, ((Ad,MeArO)3mes)3-, with Ln = La, Ce, Pr, Sm, and Yb, and their reduction with potassium have revealed that this ligand system can be redox active with some metals. Protonolysis of [Ln(N(SiMe3)2)3] (Ln = La, Ce, Pr, Sm, Yb) with the tris(phenol) (Ad,MeArOH)3mes yielded the Ln3+ complexes [((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 1-Ln. Single electron reduction of each 4f n complex, 1-Ln, using potassium yielded the reduced products, [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 2-Ln. The Sm and Yb complexes have properties consistent with the presence of Ln2+ ions with traditional 4f n+1 electron configurations. However, the La, Ce, and Pr complexes appear to formally contain Ln3+ ions and ((Ad,MeArO)3mes)4- ligands. Structural comparisons of the [((Ad,MeArO)3mes)Ln] and [((Ad,MeOAr)3mes)Ln]1- complexes along with UV-vis absorption and EPR spectroscopy as well as density functional theory calculations support these ground state assignments.

Fitting a round peg into a round hole: Asymptotically correcting the generalized gradient approximation for correlation.

We consider the implications of the Lieb-Simon limit for correlation in density functional theory. In this limit, exemplified by the scaling of neutral atoms to large atomic number, local density approximation (LDA) becomes relatively exact, and the leading correction to this limit for correlation has recently been determined for neutral atoms. We use the leading correction to the LDA and the properties of the real-space cutoff of the exchange-correlation hole to design, based upon Perdew-Burke-Ernzerhof (PBE) correlation, an asymptotically corrected generalized gradient approximation (acGGA) correlation which becomes more accurate per electron for atoms with increasing atomic number. When paired with a similar correction for exchange, this acGGA satisfies more exact conditions than PBE. Combined with the known rs -dependence of the gradient expansion for correlation, this correction accurately reproduces correlation energies of closed-shell atoms down to Be. We test this acGGA for atoms and molecules, finding consistent improvement over PBE but also showing that optimal global hybrids of acGGA do not improve upon PBE0 and are similar to meta-GGA values. We discuss the relevance of these results to Jacob's ladder of non-empirical density functional construction.

Synthesis, Structure, and Reactivity of the Sterically Crowded Th3+ Complex (C5Me5)3Th Including Formation of the Thorium Carbonyl, [(C5Me5)3Th(CO)][BPh4].

The Th3+ complex, (C5Me5)3Th, has been isolated despite the fact that tris(pentamethylcyclopentadienyl) complexes are highly reactive due to steric crowding and few crystallographically characterizable Th3+ complexes are known due to their highly reducing nature. Reaction of (C5Me5)2ThMe2 with [Et3NH][BPh4] produces the cationic thorium complex [(C5Me5)2ThMe][BPh4] that can be treated with KC5Me5 to generate (C5Me5)3ThMe, 1. The methyl group on (C5Me5)3ThMe can be removed with [Et3NH][BPh4] to form [(C5Me5)3Th][BPh4], 2, the first cationic tris(pentamethylcyclopentadienyl) metal complex, which can be reduced with KC8 to yield (C5Me5)3Th, 3. Complexes 1-3 have metrical parameters consistent with the extreme steric crowding that previously has given unusual (C5Me5)- reactivity to (C5Me5)3M complexes in reactions that form less crowded (C5Me5)2M-containing products. However, neither sterically induced reduction nor (η1-C5Me5)- reactivity is observed for these complexes. (C5Me5)3Th, which has a characteristic EPR spectrum consistent with a d1 ground state, has the capacity for two-electron reduction via Th3+ and sterically induced reduction. However, it reacts with MeI to make two sterically more crowded complexes, (C5Me5)3ThI, 4, and (C5Me5)3ThMe, 1, rather than (C5Me5)2Th(Me)I. Complex 3 also forms more crowded complexes in reactions with I2, PhCl, and Al2Me6, which generate (C5Me5)3ThI, (C5Me5)3ThCl, and (C5Me5)3ThMe, 1, respectively. The reaction of (C5Me5)3Th, 3, with H2 forms the known (C5Me5)3ThH as the sole thorium-containing product. Surprisingly, (C5Me5)3ThH is also observed when (C5Me5)3Th is combined with 1,3,5,7-cyclooctatetraene. [(C5Me5)3Th][BPh4] reacts with tetrahydrofuran (THF) to make [(C5Me5)3Th(THF)][BPh4], 2-THF, which is the first (C5Me5)3M of any kind that does not have a trigonal planar arrangement of the (C5Me5)- rings. It is also the first (C5Me5)3M complex that does not ring-open THF. [(C5Me5)3Th][BPh4], 2, reacts with CO to generate a product characterized as [(C5Me5)3Th(CO)][BPh4], 5, the first example of a molecular thorium carbonyl isolable at room temperature. These results have been analyzed using density functional theory calculations.

End-On Bridging Dinitrogen Complex of Scandium.

The first (N═N)2- complex of a rare-earth metal with an end-on dinitrogen bridge, {K(crypt)}2{[(R2N)3Sc]2[µ-η1:η1-N2]} (crypt = 2.2.2-cryptand, R = SiMe3), has been isolated from the reduction of Sc(NR2)3 under dinitrogen at -35 °C and characterized by X-ray crystallography. The structure differs from the characteristic side-on structures previously observed for over 40 crystallographically characterized rare-earth metal (N═N)2- complexes of formula [A2Ln(THF)x]2[µ-η2:η2-N2] (Ln = Sc, Y, and lanthanides; x = 0, 1; A = anionic ligand such as amide, cyclopentadienide, and aryloxide). The 1.221(3) Å N-N distance and the 1644 cm-1 Raman stretch are consistent with the presence of an (N═N)2- bridge. The observed paramagnetism of the complex by Evans method measurements is consistent with DFT calculations that suggest a triplet (3A2) ground state in D3 symmetry involving two degenerate Sc-N2-Sc bonding orbitals. Upon brief exposure of the orange Sc3+ bridging dinitrogen complex to UV-light, photolysis to form the monomeric Sc2+ complex, [K(crypt)][Sc(NR2)3], was observed. Conversion of the Sc2+ complex to the Sc3+ dinitrogen complex was not observed with this crypt system, but it did occur with the 18-crown-6 (crown) analog which formed {K(crown)}2{[(R2N)3Sc]2[µ-η1:η1-N2]}. This suggests the importance of the alkali metal chelating agent in the reversibility of dinitrogen binding in this scandium system.

Identification of the Formal +2 Oxidation State of Plutonium: Synthesis and Characterization of {PuII[C5H3(SiMe3)2]3}.

Over 70 years of chemical investigations have shown that plutonium exhibits some of the most complicated chemistry in the periodic table. Six Pu oxidation states have been unambiguously confirmed (0 and +3 to +7), and four different oxidation states can exist simultaneously in solution. We report a new formal oxidation state for plutonium, namely Pu2+ in [K(2.2.2-cryptand)][PuIICp″3], Cp″ = C5H3(SiMe3)2. The synthetic precursor PuIIICp″3 is also reported, comprising the first structural characterization of a Pu-C bond. Absorption spectroscopy and DFT calculations indicate that the Pu2+ ion has predominantly a 5f6 electron configuration with some 6d mixing.

Solution Synthesis, Structure, and CO2 Reduction Reactivity of a Scandium(II) Complex, {Sc[N(SiMe3 )2 ]3 }.

The first crystallographically characterizable complex of Sc2+ , [Sc(NR2 )3 ]- (R=SiMe3 ), has been obtained by LnA3 /M reactions (Ln=rare earth metal; A=anionic ligand; M=alkali metal) involving reduction of Sc(NR2 )3 with K in the presence of 2.2.2-cryptand (crypt) and 18-crown-6 (18-c-6) and with Cs in the presence of crypt. Dark maroon [K(crypt)]+ , [K(18-c-6)]+ , and [Cs(crypt)]+ salts of the [Sc(NR2 )3 ]- anion are formed, respectively. The formation of this oxidation state of Sc is also indicated by the eight-line EPR spectra arising from the I=7/2 45 Sc nucleus. The Sc(NR2 )3 reduction differs from Ln(NR2 )3 reactions (Ln=Y and lanthanides) in that it occurs under N2 without formation of isolable reduced dinitrogen species. [K(18-c-6)][Sc(NR2 )3 ] reacts with CO2 to produce an oxalate complex, {K2 (18-c-6)3 }{[(R2 N)3 Sc]2 (µ-C2 O4 -κ1 O:κ1 O'')}, and a CO2- radical anion complex, [(R2 N)3 Sc(µ-OCO-κ1 O:κ1 O')K(18-c-6)]n .

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules.

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order MoÌ·ller-Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFAs), and post-Kohn-Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5 and 10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 0.1% per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed, which uses monomers at full coupling, whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation-dissipation theorem, we obtain a nonperturbative "screened second-order" expression for the dispersion energy in terms of monomer quantities, which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. While the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series for MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete "electrodynamic" screening of the Coulomb interaction due to induced particle-hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust nonperturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies.

It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. Our analysis is facilitated by efficient and robust algorithms based on the resolution-of-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium- and large-size molecules with size-independent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition-metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measure α̅ of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a critical α̅ value of approximately 0.5, the RPA errors increase rapidly and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small α̅ values.

Bonding trends across the series of tricarbonato-actinyl anions [(AnO2)(CO3)3]4- (An = U-Cm): the plutonium turn.

Actinyl-tricarbonato anions [(AnO2)(CO3)3]4- (An = U-Cm) in various environments were investigated using theoretical approaches of quantum-mechanics, molecular-mechanics and cluster-models. Cations and solvent molecules in the 2nd coordination sphere affect the equatorial An←Oeq bonds more than the axial An[triple bond, length as m-dash]Oax bonds. Common actinide contraction is found for calculated and experimental axial bond lengths of 92U to 94Pu, though no longer for 94Pu to 96Cm. The tendency of U to Pu forming actinyl(vi) species dwindles away toward Cm, which already features the preferred AnIII/LnIII oxidation state of the later actinides and all lanthanides. The well known change from d-type to typical U-Pu-Cm type and then to f-type behavior is labeled as the plutonium turn, a phenomenon that is caused by f-orbital energy-decrease and f-orbital localization with increase of both nuclear charge and oxidation state, and a non-linear variation of effective f-electron population across the actinide series. Both orbital and configuration mixing and occupation of antibonding 5f type orbitals increase, weakening the AnOax bonds and reducing the highest possible oxidation states of the later actinides.

Efficacy and accuracy of a novel rapid prototyping drill template for cervical pedicle screw placement.

OBJECTIVE: To develop and validate the efficacy and accuracy of a novel drill template for cervical pedicle instrumentation. MATERIALS AND METHODS: A CT scan of the cervical vertebrae was performed, and a 3D model of the vertebrae was reconstructed using MIMICS 10.01 software. The 3D vertebral model was then exported in STL format, and opened in a workstation running UGS Imageware 12.0 software to determine the optimal pedicle screw size and orientation. A virtual navigational template was established according to the laminar anatomic trait, and physical navigational templates were manufactured using rapid prototyping. The navigational templates were used intraoperatively to assist in the placement of cervical pedicle screws. RESULTS: In all, 84 pedicle screws were placed, and the accuracy of screw placement was confirmed with postoperative X-rays and CT scans. Eighty-two screws were rated as Grade 0, 2 as Grade 1, and no screws as Grade 2 or 3. Hence, safer screw positioning was accomplished with the drill template technique. CONCLUSIONS: This study demonstrates a patient-specific template technique that is easy to use, can simplify the surgical act, and generates highly accurate cervical pedicle screw placement. The advantages of this technology over traditional techniques are that it enables planning of the screw trajectory to be completed prior to surgery, and that the screw can be sized to fit the patient's anatomy.

A novel computer-assisted drill guide template for lumbar pedicle screw placement: a cadaveric and clinical study.

BACKGROUND: The great accuracy of computer-assisted operative systems for pedicle screw insertion makes them highly desirable for spinal surgeries. However, computer-assisted pedicle screw placement is expensive, and the learning curve for these techniques is significant. We have developed a novel method of spinal pedicle stereotaxy by reverse engineering (RE) and rapid prototyping (RP) and have validated the method's accuracy by cadaveric and clinical study. METHODS: A volumetric CT scan was performed on each desired lumbar vertebra and a three-dimensional (3D) reconstruction model was generated with MIMICS 10.1, while the optimal screw size and orientation were determined using UG Imageware 12.1. A drill template was created using UG Imageware 12.1, with a surface that is the inverse of the vertebral surface. The drill template and its corresponding vertebra were manufactured using RP. The method was tested on six cadavers without any fluoroscopic control at surgery. Eventually, the technology was applied in six clinical cases. RESULTS: The accuracy of the drill template was confirmed by preoperatively drilling the screw trajectory into the vertebra biomodel. In the cadaveric experiment, 36 pedicle screws were inserted and no pedicle perforation was observed by postoperative CT scan. In the six clinical patients, the best fit for positioning the template was easily found manually during the operation. The required time between fixation of the template to the lamina and insertion of the pedicle screw into each segment (one or two vertebrae) was 1-2 min. In total, 22 screws were inserted into T12-L5, with two to four screws/patient. No misplacement occurred using the individual templates. Fluoroscopy was used only once after all the pedicle screws had been inserted. The method significantly reduces operation time and radiation exposure for the members of the surgical team. CONCLUSIONS: The authors have developed a novel computer-assisted drill template for lumbar pedicle screw placement. This method has shown its ability to customize the placement and size of each screw, based on the unique morphology of the lumbar vertebra. The potential use of drill templates to place lumbar pedicle screws is promising.