Density-Based Multilevel Hartree-Fock Model

We introduce a density-based multilevel Hartree-Fock (HF) method where the electronic density is optimized in a given region of the molecule (the active region). Active molecular orbitals (MOs) are generated by a decomposition of a starting guess atomic orbital (AO) density, whereas the inactive MOs (which constitute the remainder of the density) are never generated or referenced. The MO formulation allows for a significant dimension reduction by transforming from the AO basis to the active MO basis. All interactions between the inactive and active regions of the molecule are retained, and an exponential parametrization of orbital rotations ensures that the active and inactive density matrices separately, and in sum, satisfy the symmetry, trace, and idempotency requirements. Thus, the orbital spaces stay orthogonal, and furthermore, the total density matrix represents a single Slater determinant. In each iteration, the (level-shifted) Newton equations in the active MO basis are solved to obtain the orbital transformation matrix. The approach is equivalent to variationally optimizing only a subset of the MOs of the total system. In this orbital space partitioning, no bonds are broken and no a priori orbital assignments are carried out. In the limit of including all orbitals in the active space, we obtain an MO density-based formulation of full HF

Oligoclonal band status in Scandinavian multiple sclerosis patients is associated with specific genetic risk alleles.

The presence of oligoclonal bands (OCB) in cerebrospinal fluid (CSF) is a typical finding in multiple sclerosis (MS). We applied data from Norwegian, Swedish and Danish (i.e. Scandinavian) MS patients from a genome-wide association study (GWAS) to search for genetic differences in MS relating to OCB status. GWAS data was compared in 1367 OCB positive and 161 OCB negative Scandinavian MS patients, and nine of the most associated SNPs were genotyped for replication in 3403 Scandinavian MS patients. HLA-DRB1 genotypes were analyzed in a subset of the OCB positive (n\u200a=\u200a2781) and OCB negative (n\u200a=\u200a292) MS patients and compared to 890 healthy controls. Results from the genome-wide analyses showed that single nucleotide polymorphisms (SNPs) from the HLA complex and six other loci were associated to OCB status. In SNPs selected for replication, combined analyses showed genome-wide significant association for two SNPs in the HLA complex; rs3129871 (p\u200a=\u200a5.7 710(-15)) and rs3817963 (p\u200a=\u200a5.7 710(-10)) correlating with the HLA-DRB1*15 and the HLA-DRB1*04 alleles, respectively. We also found suggestive association to one SNP in the Calsyntenin-2 gene (p\u200a=\u200a8.83 710(-7)). In HLA-DRB1 analyses HLA-DRB1*15 3601 was a stronger risk factor for OCB positive than OCB negative MS, whereas HLA-DRB1*04 3604 was associated with increased risk of OCB negative MS and reduced risk of OCB positive MS. Protective effects of HLA-DRB1*01 3601 and HLA-DRB1*07 3601 were detected in both groups. The groups were different with regard to age at onset (AAO), MS outcome measures and gender. This study confirms both shared and distinct genetic risk for MS subtypes in the Scandinavian population defined by OCB status and indicates different clinical characteristics between the groups. This suggests differences in disease mechanisms between OCB negative and OCB positive MS with implications for patient management, which need to be further studied