Vorinostat Plus Tacrolimus & Methotrexate to Prevent Graft vs Host Disease Following Unrelated Stem Cell Transplant

Inclusion Criteria: * A prospective patient for allogeneic HSCT for hematologic conditions, both malignant and non-malignant. Donor can be unrelated marrow or peripheral blood cells. A patient with history of CNS involvement is eligible if CNS disease is in remission at time of study consideration. * Age between 18-75 years * The donor and recipient must have an HLA-8/8 allelic match at the HLA-A, -B, -C, and -DRB1. * Diagnosis of following diseases (subject to additional complex screening criteria) * Acute Myelogenous Leukemia: * First remission (cytogenetic intermediate or high risk) * Second or subsequent remission * Chronic Myelogenous Leukemia: * First, subsequent chronic phases, or atypical * Accelerated Phase * Myelodysplastic syndromes * Chronic Lymphocytic Leukemia * Primary Myelofibrosis * Mature B Cell Malignancies (including Mantle Cell Lymphoma, Follicular Lymphoma. Diffuse Large B Cell Lymphoma, Non-Hodgkin Lymphoma not otherwise specified) * Karnofsky (Attempt to classify a cancer patients' activities of daily life that runs from 0 to 100 where 100 represents perfect health and 0 represents death) \>70% * Life expectancy of greater than 6 months. * Organ and marrow function as defined by the institutional BMT (Bone Marrow Transplant) program clinical practice guidelines * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. * Able to swallow capsules/tablets Exclusion Criteria: * Not a candidate for an unrelated donor allogeneic transplant conditioning regimen based on the current institutional BMT program clinical practice guidelines. Organ function criteria will be utilized per the current institutional BMT program clinical practice guidelines. There will be no restriction to study entry based on hematological parameters. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat * Undergoing a total body irradiation (TBI)-based conditioning regimen (TBI 1200 cGy) * Uncontrolled illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Patients still under therapy for presumed or proven infection are eligible provided there is clear evidence (radiographic findings and/or culture results) that the infection is well-controlled. Patients under treatment for infection will be enrolled only after clearance from the PI * Any medical or psychological comorbidities/conditions that would keep the patient from complying with the needs of the protocol and/or would markedly increase the risk of morbidity and mortality. * Pregnant women or nursing mothers. * Evidence of HIV seropositivity and/or positive PCR assay, HTLV1 / HTLV2 seropositivity. * Evidence of Hepatitis B or Hepatitis C PCR positivity. * Less than 18 years of age. * A history of prolonged QTc syndrome. * Taking or have had prior treatment with a drug like vorinostat within the last 30 days.